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As the kaleidoscope initially showed, the built-in algorithms of filmmakers mean that there are certain appearances that we can show our world with, while there are others that they cannot show. Their possibilities of appearance may seem endless and seductive, but we must keep in mind that the extension of reality that these motives offer us is at the same time obscuring the deficiencies of the machine. For example. when Beck's DVS amazes us with water-like beauty but can't draw a circle. Or when Whitney's Arabesque program can calculate 360 points in a split second, but is bound by geometric laws.

However, motifs alone cannot delineate a film machine, because as we saw in the analysis of the motifs, film machines can also imitate each other, and thus a sign is not necessarily exclusive to one practice. In contrast, the algorithm model lets us understand that we can consider not only the film machine as the sum of some motifs, but also as the union of motifs. Namely, in the algorithm, they are systematized by virtue of their causal inputs and parameters, and this leads to the algorithm not only producing images but also latently animating them as it dictates the kinetic behavior of an appearance, e.g. in the form of movement, transformation and variation possibilities.

== The algorithm in 5 film machines ==
One of the interesting results of using the concept of algorithm is that the identification of a filmmaker's algorithm builds an isomorphic relation with the other filmmakers. It is obvious to apply the I / O model to geometric equations such as Whitney's Arabesque, but also in less obvious contexts the difference between input, parameter and output contributes with new thought paths. Gasparcolor's three strips can be understood as inputs, and with this observation Rainbow Dance is similar to an algorithmic exploration of the technique. The optical printer has also provided inputs in the form of the strips that are copied, but here a problem with the parameter concept causes us to distinguish more sharply between the appearances (wipes, multi-exposure, split screen, slow-motion, etc.) from the actual parameters that are, so to speak, the "buttons" on the machine, ie matte, exposure, sequencer, etc.

The application of the model to the projector-and-strip machine in direct film requires a more abstract interpretation of the concept, since the parameters here may be the optical predicates that the animation fabric (e.g. paint) is applied to resemble. Here, the rapid pace of the projector contributes to us perceptually primarily perceiving the predicates and not their carrying objects, and it opened to an algorithmic interpretation of Lye's A Color Box, where he varies the basic technical motifs by crossing and merging their predicative association chains.

Finally, the model was also used on Beck's Direct Video Synthesizer, although this complex film machine is poorly represented through an overall I / O model, for example. does not take into account the possible patches or the more precise interaction between the modules. However, we can see how both VtP's propensity for symmetry and Beck's oscillator inputs have promoted motifs and movement patterns in the work. The mixer has promoted additive as well as parametric-programmed color mixing, which also contributes to new movement patterns, e.g. in the form of the yin-yang motif. And finally, the video feedback allowed the dots to transform with its cybernetic system.

== The 6 motifs ==
At the same time, the use of the algorithm model to compare and map the processed filmmakers has given some clarity on how filmmakers imitate each other and how to treat this genealogy. The most important points here are to distinguish between input and parameter, to distinguish between parameter and appearance, and between the appearance itself and its function in the work.

This genealogical approach to the filmmakers can be seen as a systematization of the observations brought about by the study of the six leads. Common to these motives is that everyone can be observed in two or more of the film machines treated here. We can even show that their presence in the specific works is a trace of the used film machines, either as a symbol, a conveyance or an algorithmic necessity. But at the same time, they present us with an art-historical problem, because they also occur across film machines and environments. So how can we determine whether they are motivated by the film machine used (similar to a material-technological approach) or by the film history (a hermeneutic-iconographic approach).

We found the dot in three movie environments. In all cases, it had a symbolic character feature, referring to the Arabesque digital pixel, the emulsion film's perforation in A Color Box, and the TV screen's grid lines in Illuminated Music. The similar phenomenon is thus charged with different meanings depending on the context of the environment. In A Color Box it is not the actual strip perforation we see, and the appearance is thus symbolic. In Arabesque, the dot, in contrast, is the pixel of the computer screen, which reflects that Whitney's algorithm calculates the screen in geometric points. Here is the dot computer's discrete minority that lets the circle pixelate and dissolve it into Arabesque's running points. Faced with this, Beck's dot appears as a unit that is both a building block, for example. in TV flicker, but which also in itself contains a flicker. That reality is not the digital discrete, but the analog divisibility of the video signal and the underlying vibrating alternating voltage.

We found the gap from symmetry at Beck, but it was previously made on optical printers, among other things. in Pat O'Neill's 7362. In DVS, the subject is carried by the center reference signal of the VtP module, which is fundamental to the imaging of this synthesizer. The motif is found in Illuminated Music, e.g. where it divides the screen into bilateral symmetry. Beck, however, chooses to let these occur along with false instances of the gulf, which seek to camouflage the distinction between natural and unnatural occurrences. In this, his use differs from O'Neill's use of symmetry as an abstraction strategy. O'Neill's use of the prominence for abstraction seems, in 7362, to be promoted by the optical printer because he uses the effect in interaction with other of the printer's abstracting features, notably multi-exposure and colorful solarization. Later, in the digital environment, the gap has also found a popular spread in the form of "mirror effect" in Apple's PhotoBooth program.

The wave is a central motif, both in Lye's A Color Box and at Beck. At Lye, the subject is a variation of the strip, which is an applied revitalization in direct film that confronts the viewer with the reality of the strip as it runs vertically through the projector. As Lye deflects the continuous line to make it wave, he revitalizes another aspect of the projector, namely that it engages the continuous film strip in successive frames. At the same time, the wave creates another appearance where the line appears to vibrate on the spot. As a result, the arrangement of paint on the strip is not only based on static optical predicates, but also creates new forms of motion. In comparison, the wave at Beck is almost opposite to Lye's frantic fragmentation. Beck's waves are calm and stable in the image, and they serve as demonstrations of the VtP module's ability to translate the oscillator signal from rolling, horizontal lines to graphical waves reminiscent of the oscilloscope's screen. Their propensity to wave only vertically is due to advances in the horizontal loading principle of the environment. Thus, a possible genealogy in the chemical-mechanical environment does not point to Lye's striping, but to weary scan photography, whose wave effects are horizontally oriented, due to the vertical loading principle of the camera shutter.

The color blending of the filmmakers is yet another motif that goes across multiple environments, although it is not a figure in the same sense as the dot, chasm and wave. Nevertheless, the use of color holds deep traces of the filmmakers' algorithm. In Rainbow Dance, Lye used Gasparcolor as a filmmaker, considering the system's strips as three separate algorithm inputs rather than as one unified rendering system. The algorithmic practice leads him to an unreal and synthetic use of color, where he exchanges color channels in color fantasy. But in addition, the process also allows him to release the color as an independent image element, for example. expresses kinetic energy as the three tennis players hit the ball, or contradict spatial dimensions, using Gasparcolor's color layer like the spatial stratification of the cell animation, but letting the front, middle and background collapse through color changes. Contrary to Lye's practice, color is embedded in the image structure of the DVS, where it necessarily comes by form and motion, with the color chord module of the film machine filling in the surfaces first drawn by the VtP module. On the video screen, these colors are created by the additive color blend (as opposed to the subtractive of the strip) of red, green and blue, and it causes its blends to escape the pure light as substance. But, crucially, the DVS is not bound in this color process because Beck, with the VtP module, can program how to express specific interactions between surfaces in color. In this way, the film machine introduces a break with both Gasparcolor and the color printer of the optical printer, which in many ways prejudges the programmability of the digital environment.

Closely related is the dynamic free scraping used by Lye in Rainbow Dance. The appearance is based on the optical printer's matte technique, e.g. promotes turning the silhouette of a figure into an abstract texture, with Lye using the figure as a hole in the background for a new space. Where this practice reflects the DVS's dynamic filling of shapes with texture, Lye's use includes an algorithmic conveyance of the optical printer. For where the free scraping of a character has not been associated with transitions in normal cinematic practice, Lye uses it as a transition, where e.g. the figure remains constant while the background changes, and vice versa. This practice is obvious if one considers it from the optical printer's algorithm: Here both collage and "wipe" appearances are made by using the matte parameter, and in the work with the optical printer this relationship can foster the fusion of the two appearances so that the scraping takes over the function of the flip-flop and becomes a stage transition. This use is particularly linked to the optical printer, and continues to be unlike many digital film machines, where the matte-based wipes and exposure-based dissolves and fades have all become intersectional parameters used in most editors' interfaces. .

In continuation of this problem is also the split screen appearance, which as a technique goes back in both optical printer, video synthesizer and digital TV graphics. However, in the genealogy of this motif between the environments, we see an increasing spatial dynamics of the picture-in-picture, reflecting a changing parametric embedding in their algorithms. In the optical printer, the appearance comes from the math parameter, and this elaborate process is dynamized into "raster scan" synthesizers like Scanimate, where the cut, position, size and skew become the new parameters that let the artist model and even animate each input signal. with immediate effect. The final limitation of the video synthesizer is that it can only modulate the image as a surface. By contrast, digital 3D programs allow graphics to be reshaped and adapt to curved surfaces and spaces - a trend that can still be seen in the augmented reality-like integration of graphics into TV's photographic space, e.g. in the TV newspaper on DR1.

The echo effect is seen in Lye's Rainbow Dance, where the bouncing silhouette exposes colored traces of the movement, and in Illuminated Music, where the dancing dots multiply toward the center of the image and merge to form a star. In Lye, the motif extends by Marey's photographs, where one stage of motion is exposed on the same photograph, so the result is a figure stretched in time and space. The appearance here comes from the optical printer, which exposes the subject several times on the same frame, but therefore it must also allow the movement to unfold in the surface so that it remains clear. Also in Beck, whose echoes are made by video feedback, the subject holds both space and time dimensions, with the repetition in space being a delay in time as the camera films the screen displaying its own image. But here, the video format reveals its essence in that it projects the echo into the depths of the image. The echo gradually merges and becomes a new figure, and its strident movements are direct traces of the feedback technique's cybernetic system, which is about to re-balance itself.

== The machine genealogy as a film-historiographical approach ==
As the six lead motif analyzes show, the question of the motive versus historical motivation of the motif is complex, and will probably rarely be answered as either / or. It is, on the other hand, a question that we can ask to examine the nuances of origin. Of course, we cannot isolate the artist from the influence of cinematic history - let alone the influence of reality, psychology and other arts - and although a motif is widely conveyed by a filmmaker, it also requires an artist who has a hand on the machine or who makes it a work. However, the analyzes show that we can, however, strengthen our sensitivity to what new features in the subject may indicate the film machine's agent.

The issue has been discussed in modern art history since Semper and Riegl's time, and it may not stand as such to solve. On the other hand, our analytical search for demonstrable traces in the specific film works opens up to rephrase the issue into a film archaeological issue. What history would account for instead changing the focus to investigate the filmmakers' own history and to map their imitations, transformations and fractures?

For this project, the algorithm acts as an obvious model that can form the basis for this study. First, it allows us to distinguish between a appearance and a parameter-based imitation of a subject, and secondly, the algorithm gives an expectation of what practice will be associated with a given film machine.

However, this requires a broader historical study that takes into account: (1) the economic and cultural motivations and conditions for new film machines to be invented and developed, (2) a mapping of the concrete imitations and exchanges that occur between film machines, and what improvements, refinements and streamlining they bring, and (3) how these film machines' changing algorithms manifest themselves historically in the film language, since the canonized film story's invisibility of the machines at significant points could be challenged by the film history (s) of the filmmakers.

== The digital filmmaker ==
However, the formulation of the film machine method's further possibility as a genealogical project is not purely a historical matter. It is as much a matter of understanding the mechanical dynamics that have become even more relevant with the spread of the digital environment.

Finally, I will grab the ball from Chapter 2 and ask how the filmmaker can explain (mis) the use of analog noise in the DR documentary Skeletons in Tax. Considered static, the series is problematic because it (1) mixes noise from separate environments and (2) consistently associates visible framelines with clips in the movie - two features that both indicate that the previous indexes are being detached from their machine context in the digital environment.

These errors also become evident if you consider them from the film machine's method. But on the contrary, they can now also be considered as traces of the digital editing program if one wants to look for a deeper root cause than the creators are just ignorant or playing postmodern.

The typical digital editor's interface is built on a timeline where clips are sequenced and cropped. These clips that come from outside are the program's inputs. In addition, I want to highlight two parameters: First, filters that you put over one (or more) clip, e.g. to make the clip black and white, slow motion, out of focus, etc. Second, transitions that you put between two clips to determine a transition - more or less like the transitions between slides in PowerPoint.

Having identified the program algorithm, it is now possible to demonstrate that the DR series use of noise is a practice promoted by the program algorithm. The first type of error may indicate that the emulsion film scratches and error exposure and the flicker and scanlines of the video are all appearances for the filter parameter. Ie those in the interface are presented as the same tool - e.g. as an effect that adds graphic depth or texture to the image. Similarly, we can assume that the second error with visible framelines is an appearance on the transition parameter, that is, along with the optical printer wipes, Scanimate's skewed "raster scan" transitions and digital 3D cubes - in which case the film machine even promotes it. consistent use of the effect of clips.
However, these problems must not lead to a general condemnation of the digital environment, because it is precisely a practice associated with specific film machines (programs) and not, for example. the computer as such.

In the history of filmmakers, we have seen that these imitations where some aspects are reduced while others are expanded are terms. However, these genealogies at the same time require that we become aware of these processes. In particular, the spread of digital film (and image) machines has a huge impact on creative practice. An example could be the Instagram photo app, which offers filters such as polaroid, pixelation, solarization, etc. These terms were originally associated with special apparatus and developing techniques that required money, time and technical talent to use. But with apps and software, there is a landslide where the appearances become economized, streamlined and automated so everyone can use them. Ie the appearances that were initially technical and experimental become democratized when acquired by users through their own creative practices.

The algorithmic model of the filmmaker method can then add that the appearances in Instagram are also being conventionalized. Because just like in the editor, the algorithmic scheme in filters has an impact on practice. But in addition to the mixing of machines and environments as the filter risks, there is also a significant parametric reduction. For instead of imitating e.g. the parameters of the dark chamber, such as the temperature, concentration and application times of the chemicals, are merely imitated the end products, ie appearances such as solarization, sepia, 8mm noise, etc.

However, when comparing Instagram with Adobe Photoshop, it becomes clear that digital cannot be generalized into one category. For in Photoshop, there is precisely a similarly wide range of parameters that can be used. Ift. the film machines here could point to Adobe AfterEffects, which is a key-frame-based editor. The program thus promotes a practice that is full of parameters and just as cumbersome as working with the optical printer. And many of its algorithmic capabilities are not just imitations and simulations of previous filmmakers' techniques - they even go so far into the digital environment that the user can program plug-ins for their effects themselves.

Here, the algorithm model can become a critical tool for accessing these interfaces, as the method contributes to a central distinction between input, parameter, output and appearance, as well as principles for how these conditions can be detected and influenced in works.

The film machine method is in opposition to both digital aesthetics and traditional film studies. Ift. aforementioned, because the subject field is fundamentally expanded to include all four environments. And according to the latter, because the method challenges the traditional concept of works, since works are now empirical to illuminate the film machine as an object. With these two crucial differences, it is possible with the history of the film machine not to read digital as a newcomer, but as a return to 19th-century optomechanical film machines, where (rich) children and adults also owned zoetropes, laterna magica, flip books and kaleidoscopes , and spent hours exploring and imprisoning them.

The use here was recreational and playful, and it was not intended to create works, but merely a diversion for the individual user. But the aesthetic exploration that lay in this process was not fruitless for this reason. For example. a large part of the apparatus was categorized as "philosophical toys" with reference to e.g. the thaumatrope and zoetrope made newly discovered perceptual phenomena such as the phi effect and the inertia of the eye experience for the user, in that you can turn the disc or drum yourself and watch the figures merge and come alive.

Thus, while the perceptual and the substantive are mediated by an artist or operator in traditional works, the digital interactivity promotes a possible return of the user, who himself acquires the perceptual and substantive behavior of the algorithm and seeks their association. The finished works can in this light be seen as a "frozen play", which the archaeological study of the film machine behind can "animate". With this, the theory of the filmmaker not only becomes a checklist for whether this or that motive is now also used in the work of a specific filmmaker, but also a question that the work can be brought back to life when we know its filmmaking origins and can enter into dialogue with the poetics that the artist has explored.

In addition, this aesthetically-creative supplement to the filmmaker method can illuminate how the acquisition of an algorithm allows us to experience the legalities contained in the individual technologies and environments. For man, not only interact with film machines, but also through them. They let us interact with algorithms that we acquire, whatever this algorithm derives from a geometric equation (Whitney), projector and strip synthesis (Lye), analog electronic systems (Beck), optics laws (Wilfred), simulations of our own reality (3D programs), alternate realities, or our perception (Zoetropen). And while these topics are as diverse as there are different filmmakers, they do share a principle: that the filmmaker lets algorithms become experienced cinematographically.

Cine-Machine as Method: Conclusion

2020-04-20T18:08:56Z

Kzxpr:

As the kaleidoscope initially showed, the built-in algorithms of filmmakers mean that there are certain appearances that we can show our world with, while there are others that they cannot show. Their possibilities of appearance may seem endless and seductive, but we must keep in mind that the extension of reality that these motives offer us is at the same time obscuring the deficiencies of the machine. For example. when Beck's DVS amazes us with water-like beauty but can't draw a circle. Or when Whitney's Arabesque program can calculate 360 points in a split second, but is bound by geometric laws.

However, motifs alone cannot delineate a film machine, because as we saw in the analysis of the motifs, film machines can also imitate each other, and thus a sign is not necessarily exclusive to one practice. In contrast, the algorithm model lets us understand that we can consider not only the film machine as the sum of some motifs, but also as the union of motifs. Namely, in the algorithm, they are systematized by virtue of their causal inputs and parameters, and this leads to the algorithm not only producing images but also latently animating them as it dictates the kinetic behavior of an appearance, e.g. in the form of movement, transformation and variation possibilities.

== The algorithm in 5 film machines ==
One of the interesting results of using the concept of algorithm is that the identification of a filmmaker's algorithm builds an isomorphic relation with the other filmmakers. It is obvious to apply the I / O model to geometric equations such as Whitney's Arabesque, but also in less obvious contexts the difference between input, parameter and output contributes with new thought paths. Gasparcolor's three strips can be understood as inputs, and with this observation Rainbow Dance is similar to an algorithmic exploration of the technique. The optical printer has also provided inputs in the form of the strips that are copied, but here a problem with the parameter concept causes us to distinguish more sharply between the appearances (wipes, multi-exposure, split screen, slow-motion, etc.) from the actual parameters that are, so to speak, the "buttons" on the machine, ie matte, exposure, sequencer, etc.

The application of the model to the projector-and-strip machine in direct film requires a more abstract interpretation of the concept, since the parameters here may be the optical predicates that the animation fabric (e.g. paint) is applied to resemble. Here, the rapid pace of the projector contributes to us perceptually primarily perceiving the predicates and not their carrying objects, and it opened to an algorithmic interpretation of Lye's A Color Box, where he varies the basic technical motifs by crossing and merging their predicative association chains.

Finally, the model was also used on Beck's Direct Video Synthesizer, although this complex film machine is poorly represented through an overall I / O model, for example. does not take into account the possible patches or the more precise interaction between the modules. However, we can see how both VtP's propensity for symmetry and Beck's oscillator inputs have promoted motifs and movement patterns in the work. The mixer has promoted additive as well as parametric-programmed color mixing, which also contributes to new movement patterns, e.g. in the form of the yin-yang motif. And finally, the video feedback allowed the dots to transform with its cybernetic system.

== The 6 motifs ==
At the same time, the use of the algorithm model to compare and map the processed filmmakers has given some clarity on how filmmakers imitate each other and how to treat this genealogy. The most important points here are to distinguish between input and parameter, to distinguish between parameter and appearance, and between the appearance itself and its function in the work.

This genealogical approach to the filmmakers can be seen as a systematization of the observations brought about by the study of the six leads. Common to these motives is that everyone can be observed in two or more of the film machines treated here. We can even show that their presence in the specific works is a trace of the used film machines, either as a symbol, a conveyance or an algorithmic necessity. But at the same time, they present us with an art-historical problem, because they also occur across film machines and environments. So how can we determine whether they are motivated by the film machine used (similar to a material-technological approach) or by the film history (a hermeneutic-iconographic approach).

We found the dot in three movie environments. In all cases, it had a symbolic character feature, referring to the Arabesque digital pixel, the emulsion film's perforation in A Color Box, and the TV screen's grid lines in Illuminated Music. The similar phenomenon is thus charged with different meanings depending on the context of the environment. In A Color Box it is not the actual strip perforation we see, and the appearance is thus symbolic. In Arabesque, the dot, in contrast, is the pixel of the computer screen, which reflects that Whitney's algorithm calculates the screen in geometric points. Here is the dot computer's discrete minority that lets the circle pixelate and dissolve it into Arabesque's running points. Faced with this, Beck's dot appears as a unit that is both a building block, for example. in TV flicker, but which also in itself contains a flicker. That reality is not the digital discrete, but the analog divisibility of the video signal and the underlying vibrating alternating voltage.

We found the gap from symmetry at Beck, but it was previously made on optical printers, among other things. in Pat O'Neill's 7362. In DVS, the subject is carried by the center reference signal of the VtP module, which is fundamental to the imaging of this synthesizer. The motif is found in Illuminated Music, e.g. where it divides the screen into bilateral symmetry. Beck, however, chooses to let these occur along with false instances of the gulf, which seek to camouflage the distinction between natural and unnatural occurrences. In this, his use differs from O'Neill's use of symmetry as an abstraction strategy. O'Neill's use of the prominence for abstraction seems, in 7362, to be promoted by the optical printer because he uses the effect in interaction with other of the printer's abstracting features, notably multi-exposure and colorful solarization. Later, in the digital environment, the gap has also found a popular spread in the form of "mirror effect" in Apple's PhotoBooth program.

The wave is a central motif, both in Lye's A Color Box and at Beck. At Lye, the subject is a variation of the strip, which is an applied revitalization in direct film that confronts the viewer with the reality of the strip as it runs vertically through the projector. As Lye deflects the continuous line to make it wave, he revitalizes another aspect of the projector, namely that it engages the continuous film strip in successive frames. At the same time, the wave creates another appearance where the line appears to vibrate on the spot. As a result, the arrangement of paint on the strip is not only based on static optical predicates, but also creates new forms of motion. In comparison, the wave at Beck is almost opposite to Lye's frantic fragmentation. Beck's waves are calm and stable in the image, and they serve as demonstrations of the VtP module's ability to translate the oscillator signal from rolling, horizontal lines to graphical waves reminiscent of the oscilloscope's screen. Their propensity to wave only vertically is due to advances in the horizontal loading principle of the environment. Thus, a possible genealogy in the chemical-mechanical environment does not point to Lye's striping, but to weary scan photography, whose wave effects are horizontally oriented, due to the vertical loading principle of the camera shutter.

The color blending of the filmmakers is yet another motif that goes across multiple environments, although it is not a figure in the same sense as the dot, chasm and wave. Nevertheless, the use of color holds deep traces of the filmmakers' algorithm. In Rainbow Dance, Lye used Gasparcolor as a filmmaker, considering the system's strips as three separate algorithm inputs rather than as one unified rendering system. The algorithmic practice leads him to an unreal and synthetic use of color, where he exchanges color channels in color fantasy. But in addition, the process also allows him to release the color as an independent image element, for example. expresses kinetic energy as the three tennis players hit the ball, or contradict spatial dimensions, using Gasparcolor's color layer like the spatial stratification of the cell animation, but letting the front, middle and background collapse through color changes. Contrary to Lye's practice, color is embedded in the image structure of the DVS, where it necessarily comes by form and motion, with the color chord module of the film machine filling in the surfaces first drawn by the VtP module. On the video screen, these colors are created by the additive color blend (as opposed to the subtractive of the strip) of red, green and blue, and it causes its blends to escape the pure light as substance. But, crucially, the DVS is not bound in this color process because Beck, with the VtP module, can program how to express specific interactions between surfaces in color. In this way, the film machine introduces a break with both Gasparcolor and the color printer of the optical printer, which in many ways prejudges the programmability of the digital environment.

Closely related is the dynamic free scraping used by Lye in Rainbow Dance. The appearance is based on the optical printer's matte technique, e.g. promotes turning the silhouette of a figure into an abstract texture, with Lye using the figure as a hole in the background for a new space. Where this practice reflects the DVS's dynamic filling of shapes with texture, Lye's use includes an algorithmic conveyance of the optical printer. For where the free scraping of a character has not been associated with transitions in normal cinematic practice, Lye uses it as a transition, where e.g. the figure remains constant while the background changes, and vice versa. This practice is obvious if one considers it from the optical printer's algorithm: Here both collage and "wipe" appearances are made by using the matte parameter, and in the work with the optical printer this relationship can foster the fusion of the two appearances so that the scraping takes over the function of the flip-flop and becomes a stage transition. This use is particularly linked to the optical printer, and continues to be unlike many digital film machines, where the matte-based wipes and exposure-based dissolves and fades have all become intersectional parameters used in most editors' interfaces. .

In continuation of this problem is also the split screen appearance, which as a technique goes back in both optical printer, video synthesizer and digital TV graphics. However, in the genealogy of this motif between the environments, we see an increasing spatial dynamics of the picture-in-picture, reflecting a changing parametric embedding in their algorithms. In the optical printer, the appearance comes from the math parameter, and this elaborate process is dynamized into "raster scan" synthesizers like Scanimate, where the cut, position, size and skew become the new parameters that let the artist model and even animate each input signal. with immediate effect. The final limitation of the video synthesizer is that it can only modulate the image as a surface. By contrast, digital 3D programs allow graphics to be reshaped and adapt to curved surfaces and spaces - a trend that can still be seen in the augmented reality-like integration of graphics into TV's photographic space, e.g. in the TV newspaper on DR1.

The echo effect is seen in Lye's Rainbow Dance, where the bouncing silhouette exposes colored traces of the movement, and in Illuminated Music, where the dancing dots multiply toward the center of the image and merge to form a star. In Lye, the motif extends by Marey's photographs, where one stage of motion is exposed on the same photograph, so the result is a figure stretched in time and space. The appearance here comes from the optical printer, which exposes the subject several times on the same frame, but therefore it must also allow the movement to unfold in the surface so that it remains clear. Also in Beck, whose echoes are made by video feedback, the subject holds both space and time dimensions, with the repetition in space being a delay in time as the camera films the screen displaying its own image. But here, the video format reveals its essence in that it projects the echo into the depths of the image. The echo gradually merges and becomes a new figure, and its strident movements are direct traces of the feedback technique's cybernetic system, which is about to re-balance itself.

== The machine genealogy as a film-historiographical approach ==
As the six lead motif analyzes show, the question of the motive versus historical motivation of the motif is complex, and will probably rarely be answered as either / or. It is, on the other hand, a question that we can ask to examine the nuances of origin. Of course, we cannot isolate the artist from the influence of cinematic history - let alone the influence of reality, psychology and other arts - and although a motif is widely conveyed by a filmmaker, it also requires an artist who has a hand on the machine or who makes it a work. However, the analyzes show that we can, however, strengthen our sensitivity to what new features in the subject may indicate the film machine's agent.

The issue has been discussed in modern art history since Semper and Riegl's time, and it may not stand as such to solve. On the other hand, our analytical search for demonstrable traces in the specific film works opens up to rephrase the issue into a film archaeological issue. What history would account for instead changing the focus to investigate the filmmakers' own history and to map their imitations, transformations and fractures?

For this project, the algorithm acts as an obvious model that can form the basis for this study. First, it allows us to distinguish between a appearance and a parameter-based imitation of a subject, and secondly, the algorithm gives an expectation of what practice will be associated with a given film machine.

However, this requires a broader historical study that takes into account: (1) the economic and cultural motivations and conditions for new film machines to be invented and developed, (2) a mapping of the concrete imitations and exchanges that occur between film machines, and what improvements, refinements and streamlining they bring, and (3) how these film machines' changing algorithms manifest themselves historically in the film language, since the canonized film story's invisibility of the machines at significant points could be challenged by the film history (s) of the filmmakers.

== The digital filmmaker ==
However, the formulation of the film machine method's further possibility as a genealogical project is not purely a historical matter. It is as much a matter of understanding the mechanical dynamics that have become even more relevant with the spread of the digital environment.

Finally, I will grab the ball from Chapter 2 and ask how the filmmaker can explain (mis) the use of analog noise in the DR documentary Skeletons in Tax. Considered static, the series is problematic because it (1) mixes noise from separate environments and (2) consistently associates visible framelines with clips in the movie - two features that both indicate that the previous indexes are being detached from their machine context in the digital environment.

These errors also become evident if you consider them from the film machine's method. But on the contrary, they can now also be considered as traces of the digital editing program if one wants to look for a deeper root cause than the creators are just ignorant or playing postmodern.

The typical digital editor's interface is built on a timeline where clips are sequenced and cropped. These clips that come from outside are the program's inputs. In addition, I want to highlight two parameters: First, filters that you put over one (or more) clip, e.g. to make the clip black and white, slow motion, out of focus, etc. Second, transitions that you put between two clips to determine a transition - more or less like the transitions between slides in PowerPoint.

Having identified the program algorithm, it is now possible to demonstrate that the DR series use of noise is a practice promoted by the program algorithm. The first type of error may indicate that the emulsion film scratches and error exposure and the flicker and scanlines of the video are all appearances for the filter parameter. Ie those in the interface are presented as the same tool - e.g. as an effect that adds graphic depth or texture to the image. Similarly, we can assume that the second error with visible framelines is an appearance on the transition parameter, that is, along with the optical printer wipes, Scanimate's skewed "raster scan" transitions and digital 3D cubes - in which case the film machine even promotes it. consistent use of the effect of clips.
However, these problems must not lead to a general condemnation of the digital environment, because it is precisely a practice associated with specific film machines (programs) and not, for example. the computer as such.

In the history of filmmakers, we have seen that these imitations where some aspects are reduced while others are expanded are terms. However, these genealogies at the same time require that we become aware of these processes. In particular, the spread of digital film (and image) machines has a huge impact on creative practice. An example could be the Instagram photo app, which offers filters such as polaroid, pixelation, solarization, etc. These terms were originally associated with special apparatus and developing techniques that required money, time and technical talent to use. But with apps and software, there is a landslide where the appearances become economized, streamlined and automated so everyone can use them. Ie the appearances that were initially technical and experimental become democratized when acquired by users through their own creative practices.

The algorithmic model of the filmmaker method can then add that the appearances in Instagram are also being conventionalized. Because just like in the editor, the algorithmic scheme in filters has an impact on practice. But in addition to the mixing of machines and environments as the filter risks, there is also a significant parametric reduction. For instead of imitating e.g. the parameters of the dark chamber, such as the temperature, concentration and application times of the chemicals, are merely imitated the end products, ie appearances such as solarization, sepia, 8mm noise, etc.

However, when comparing Instagram with Adobe Photoshop, it becomes clear that digital cannot be generalized into one category. For in Photoshop, there is precisely a similarly wide range of parameters that can be used. Ift. the film machines here could point to Adobe AfterEffects, which is a key-frame-based editor. The program thus promotes a practice that is full of parameters and just as cumbersome as working with the optical printer. And many of its algorithmic capabilities are not just imitations and simulations of previous filmmakers' techniques - they even go so far into the digital environment that the user can program plug-ins for their effects themselves.

Here, the algorithm model can become a critical tool for accessing these interfaces, as the method contributes to a central distinction between input, parameter, output and appearance, as well as principles for how these conditions can be detected and influenced in works.

The film machine method is in opposition to both digital aesthetics and traditional film studies. Ift. aforementioned, because the subject field is fundamentally expanded to include all four environments. And according to the latter, because the method challenges the traditional concept of works, since works are now empirical to illuminate the film machine as an object. With these two crucial differences, it is possible with the history of the film machine not to read digital as a newcomer, but as a return to 19th-century optomechanical film machines, where (rich) children and adults also owned zoetropes, laterna magica, flip books and kaleidoscopes , and spent hours exploring and imprisoning them.

The use here was recreational and playful, and it was not intended to create works, but merely a diversion for the individual user. But the aesthetic exploration that lay in this process was not fruitless for this reason. For example. a large part of the apparatus was categorized as "philosophical toys" with reference to e.g. the thaumatrope and zoetrope made newly discovered perceptual phenomena such as the phi effect and the inertia of the eye experience for the user, in that you can turn the disc or drum yourself and watch the figures merge and come alive.

Thus, while the perceptual and the substantive are mediated by an artist or operator in traditional works, the digital interactivity promotes a possible return of the user, who himself acquires the perceptual and substantive behavior of the algorithm and seeks their association. The finished works can in this light be seen as a "frozen play", which the archaeological study of the film machine behind can "animate". With this, the theory of the filmmaker not only becomes a checklist for whether this or that motive is now also used in the work of a specific filmmaker, but also a question that the work can be brought back to life when we know its filmmaking origins and can enter into dialogue with the poetics that the artist has explored.

In addition, this aesthetically-creative supplement to the filmmaker method can illuminate how the acquisition of an algorithm allows us to experience the legalities contained in the individual technologies and environments. For man, not only interact with film machines, but also through them. They let us interact with algorithms that we acquire, whatever this algorithm derives from a geometric equation (Whitney), projector and strip synthesis (Lye), analog electronic systems (Beck), optics laws (Wilfred), simulations of our own reality (3D programs), alternate realities, or our perception (Zoetropen). And while these topics are as diverse as there are different filmmakers, they do share a principle: that the filmmaker lets algorithms become experienced cinematographically.

Kzxpr: /* Animation */

In this chapter, I will analyze John Whitney's Arabesque software as a film machine, and set out the first principles of an algorithm model that can be used in the further work on the film machines. Next, I will briefly analyze how the algorithm is animated in Whitney's early computer film ''Arabesque'' (1975) and outline what issues it raises.

Specifically, the film machine uses a geometric equation that generates images by defining the 360 dots position on the screen. Whitney has also used this dot technique in films such as ''Permutations'' (1965), but in Arabesque, the dot is merged with the environment's own minority, the pixel.

Whitney's film machine is exemplary because in his work with the computer he built his films on some relatively simple geometric algorithms. His book ''Digital Harmony'' (1980) even includes a "Do it yourself" chapter in which he shares the program code underlying ''Arabesque'' (Whitney: 136) and discusses the musical principles that have inspired the making of the film.

Through the descriptions in ''Digital Harmony'', I have succeeded in creating a program that can simulate the algorithm used by Whitney in ''Arabesque''. '''{G}''' In addition to the characteristics below, this simulation can also give the reader an idea of the basic geometric principles that has guided the film’s imaging and movement patterns.

== Arabesque algorithm's three parameters ==
The starting point for Whitney's ''Arabesque'' algorithm is a simple circle derived from a polar equation. He makes the computer draw 360 dots that are evenly spaced 360 degrees around a a particular point (center of the circle) with a fixed distance (radius). A polar equation for this circle would then read:
p = r
or rewritten into a Cartesian coordinate system:
x (t) = cx + r * cos (t)
y (t) = cy + r * sin (t)
where cx and cy are the coordinates of the center of the circle, r is the radius of the circle and t is each degree.

Now each dot has an individual number that allows the computer to move them individually. The first dot drawn in the circle is named # 1, the next dot is named # 2, and so on, up to dot # 360, which is the last in the circle and is next to dot # 1. This numbering allows Whitney to transform the circular shape by manipulating a dot's position through three new parameters.

I have called the simplest parameter ''yinv'' (y inversion), which causes the figure to be reflected vertically across the x-axis, since each dot's y coordinate can be "inverted" from its distance from the center. The ''yinv'' parameter has a value between 0% and 100%, where 0% would mean that dot # 1 is at the top of the circle and 100% that dot # 1 is at the bottom of the circle. The numbering goes clockwise. Between these two extremes, there are a number of intermediate points where the mirroring is underway. First, the figure is compressed until it becomes completely flat (50%), and then inflated again to straighten out completely like a mirror.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Yinv-0.png|100px|thumb]]
||
[[File:Yinv-25.png|100px|thumb]]
||
[[File:Yinv50.png|100px|thumb]]
||
[[File:Yinv-75.png|100px|thumb]]
||
[[File:Yinv-100.png|100px|thumb]]
|-
|colspan="5"|yinv from 0% to 100% (pinv = 0%, step = 0)
|}

In the opening of ''Arabesque'' '''{H}''', yinv initially has a value of 100%, so the opening of the circle is at the bottom, but in the middle of the sequence, yinv changes from 100% to 0%, thereby compressing and mirroring the current figure (a kind of rounded triangle) across the x-axis in the same way we have seen it with the circle.

The next parameter I have called ''pinv'' (polar inversion) and it is similar to yinv, in that it's value range is also between 0% and 100% and the parameter similarly determines a mirroring. But instead of mirroring the figure across a mid-axis, the pinv uses the center of the circle as the point of reflection, so that each x-coordinate of a dot is "crossed over" the center of the circle and is diametrically opposite to it's starting point.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv1-0.png|100px|thumb]]
||
[[File:Pinv1-20.png|100px|thumb]]
||
[[File:Pinv1-50.png|100px|thumb]]
||
[[File:Pinv1-75.png|100px|thumb]]
||
[[File:Pinv1-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 0)
|}

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv2-0.png|100px|thumb]]
||
[[File:Pinv2-25.png|100px|thumb]]
||
[[File:Pinv2-50.png|100px|thumb]]
||
[[File:Pinv2-75.png|100px|thumb]]
||
[[File:Pinv2-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 1/360)
|}

If the base figure is a circle, a transformation from pinv = 0% to pinv = 100% will be similar to a horizontal reflection of the figure in the y-axis. However, if a pinv transformation is applied to the figure, e.g. when step = 1/360 then the pinv mirroring is much more complex. Initially the shape looks like a tooth, which gradually turns out to form an arc (25%), then a wave (50%), and eventually the line ties a knot on itself (75%) and ends as a loop (100%).

As attractive as this reflection can be, it is equally unpredictable. In comparison to a yinv transformation that just squeezes the figure and straightens it out in a mirrored form, the results of pinv are harder to anticipate, even though the transformation is mathematically consistent.

To understand the complex mirroring, one must also look at the ''step'' which is the last of the parameters. Unlike yinv and pinv, step is not based on a mirror, but on the principle Whitney calls "differential motion". In ''Digital Harmony'', he illustrates this by drawing a line of 60 dots. He labels these dots from left to right (so they are called 1,2,3 ... 60), and then tells the computer that for each "step" in the animation, each dot must move upwards by a number of pixels corresponding to the dot's number. While the dots are on a horizontal line at step # 0, the dots on the right will gradually move up faster, making the line animated to appear skewed at ever increasing speed (Whitney: 48-49).

{| class="wikitable"
|-
! step = 0 !! step = 1 !! step = 2 !! step = 3 !! step = 4
|-
|
[[File:line0.png|100px|thumb]]
||
[[File:line1.png|100px|thumb]]
||
[[File:line2.png|100px|thumb]]
||
[[File:line3.png|100px|thumb]]
||
[[File:line4.png|100px|thumb]]
|-
|colspan="5"|Example of "differential motion" based on a line (cf. Whitney: 50)
|}

In such "differential motion", the dots initially line up. At step = 1, dot # 1 has moved 1 pixel up, dot # 2 has moved 2 pixels up, etc. up to dot # 60 which has moved 60 pixels up. At step = 2, dot # 1 has moved 2 pixels up compared to the starting point, dot # 2 has moved 4 pixels up, and dot # 60 has moved 120 pixels up. Continuing this line, at step = 4 dot # 1 has moved 4 pixels up (1 * 4), while dot # 60 has moved 240 pixels up (60 * 4).

As the figure above shows, we do not perceive these movements as individual dots moving - we perceive the dots as a coherent figure, as if it is a line that is gradually tilting and extending.

In ''Arabesque'', Whitney applies the same principle to the circle figure. Having already numbered the dots in the circle, he programs dot # 1 to move 1 pixel to the right of each step, dot # 2 to move 2 pixels to the right of each step, and so on, until dot # 360 that moves 360 pixels to right for each step.

As the dots will quickly move beyond the edge of the screen as they move to the right, Whitney adds a modulus function to each dot, meaning that if the computer calculates a an off-screen position for a dot, it jumps to the left edge of the screen and continues to the right again (ibid: 97). This principle can e.g. can be seen in the figure below, where the figure cuts the edge by 50%, but appears on the left side. Here's how it goes on for 75%, up to 100%, where half of the figure has crossed the edge of the screen and now forms a "tooth" figure.

{| class="wikitable"
|-
! step = 0/360 !! step = 1 * 25% !! step = 1 * 50% !! step = 1 * 75% !! step = 1 * 100%
|-
|
[[File:step1-0.png|100px|thumb]]
||
[[File:step1-25.png|100px|thumb]]
||
[[File:step1-50.png|100px|thumb]]
||
[[File:step1-75.png|100px|thumb]]
||
[[File:step1-100.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 1/360 (yinv = 0%, pinv = 0%)
|}

In the last frame of the table, each dot has moved an amount that corresponds to one step. In other words, dot # 1 has moved 1 pixel to the right, dot # 2 has moved 2 pixels to the right, and dot # 360 has moved 360 pixels to the right.

Note that while the tables showing the differential motion of the line has a distance of 1 step between each frame, the Arabesque circle requires a much lower increase in order for us to perceive the change between the frames as a single movement. If I only showed the first and last frames, few would be able to figure out how the movement between them is going - and this problem only increase if we continue to change the step parameter by an increase of 1:

{| class="wikitable"
|-
! step = 0/360 !! step = 1/360 !! step = 2/360 !! step = 3/360 !! step = 4/360
|-
|
[[File:Step3-0.png|100px|thumb]]
||
[[File:Step3-1.png|100px|thumb]]
||
[[File:Step3-2.png|100px|thumb]]
||
[[File:Step3-3.png|100px|thumb]]
||
[[File:Step3-4.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 4/360 (yinv = 0%, pinv = 0%)
|}

I have chosen to list the whole step value as numbers between 0/360 and 360/360. This notation should reflect that after 360 steps, the differential motion of the circle will cause each dot to be displaced so much that they occupy their original position on the screen. This is comparable to a clock where all three hands point to twelve when it is midnight. During the day, they will move around the disc at different speeds, but after 12 hours they will point to twelve again. Similarly, step = 360/360 corresponds to step = 0/360, where all dots have run through a full cycle at least once. Dot # 1 is the slowest and has only completed one cycle. Dot # 2 will be the second-slowest and has completed two cycles. And finally, Dot # 360 will have completed 360 full cycles. (Whitney: 98)

Because the program requires only numeric values to generate output, there are no signal inputs, but only parameters in this algorithm. We can summarize its algorithm with this diagram, also including x and y position to move the circle and radius to change the size:

[[File:Arab-chart01.png|thumb|center]]

== Variations over the algorithm ==
Appropriately, the opening scene in ''Arabesque'' also serves as an introduction to the algorithm's behavior. First, the step goes from 0 to 1/360, while the y-inv from the start is set to 100%. Then pinv goes from 0 to 100%. Step from 1/360 to 2/360. And y-inv from 100% to 0%. While this last movement is midway and the circle is compressed, a new, vertically mirrored figure emerges above the first one that performs the same movements synchronously. Together they now play the same sequence in reverse - step from 2/360 to 1/360, pinv from 100% to 0% and step from 1/360 to 0/360 - whereby the two figures simultaneously fold in to form two circles that lie on top of each other.

The scene is like an exposition that presents the shape to the viewer and demonstrates it's algorithmic behavior based on the three basic parameters. We can already see how Whitney not only uses an algorithm for the shapes in his animation, but also animates the shapes algorithmically.

In the following sections, however, he does not adhere to the simple operations. Instead, he lets the circle - now in a horizontally stretched variation - do a sprint by the step parameter that dissolves the contiguous line of the circle, letting the dots run into a frantic flicker. Just before the circle gathers, a new circle emerges and sets off, resulting in a kind of musical canon of voices repeating the same melody line.

Subsequently, Whitney continues this musical exploration of the algorithm's simple theme. In the next section, several circles with slightly delayed temporal offsets form a new canon in which they perform the same composite choreography: They set off in motion, and are multiplied into five circles when they return to start. They rotate a few times, set off again, and eventually gather in one circle, and then gradually disappear. In the next section, the shapes are even freer animated, forming little trajectories in the image at intersections, running in different sizes, colors, directions and tempi. Especially in this section, the title's arabesque connotations become obvious, resembling the shapes and motifs of an Islamic rug.

In the film's climax, the circle returns to its round starting point at the top of the screen in a slightly diminished size. It slowly transform the step parameter from 0/360 to 1/360, whereupon a new, skewed circle appears diagonally below it. The new circle performs the same movement and is then supplemented by another new, skewed circle until 5 circles (unfolded to 1/360) form a five-club in the center of the screen.

[image?]

Then all 5 circles' pinv parameters are animated synchronously to 100%, where the configuration along the way resembles 5-pointed star and eventually a buttercup. Then the step parameters change from 1 to 2, and a whirl appears within the flower, swapping the space of their leaves, and forming a new pointed-leaf flower. With a y-inv transformation, the flower collapses, but stops halfway just when it forms a pentagon and the sequence is played backwards.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:2-1.png|100px|thumb]]
||
[[File:2-2.png|100px|thumb]]
||
[[File:2-3.png|100px|thumb]]
||
[[File:2-4.png|100px|thumb]]
||
[[File:2-5.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 100, step = 1)
|}

{| class="wikitable"
|-
! step = 1/360 !! step = 1/360 + 25% !! step = 1/360 + 50% !! step = 1/360 + 75% !! step = 1/360 + 100%
|-
|
[[File:3-1.png|100px|thumb]]
||
[[File:3-2.png|100px|thumb]]
||
[[File:3-3.png|100px|thumb]]
||
[[File:3-4.png|100px|thumb]]
||
[[File:3-5.png|100px|thumb]]
|-
|colspan="5"|steps from 1 to 2 (yinv = 100%, pinv = 100%)
|}

Because the circles only have to go from step = 1 to step = 0, they do this in a slightly delayed canon where each shape disappears just as it forms a circle again.



== Animation ==
In animating the algorithm in the film, Whitney also uses other techniques, such as changing the positions, sizes and proportions of the figures (using the x, y and r parameters). In addition, he uses spatial amplification, where multiple of the same figure are seen synchronously side by side, and he rotates the figures to form a flower at the climax. With these techniques, Whitney manages to turn the simple theme of the Arabesque algorithm into a varied and expressive animation film.

Furthermore, we should also note that he makes tempo changes and often let's the dots condense into configurations of other shapes than just the circle. As we saw above, the gap is too wide if you increase the step value from 1/360 to 2/360 to see the movement, and the selection of tempo is therefore crucial, as Whitney hereby can structure the algorithm for a human recipient. In this way, he performs a necessary supplement to the machine, which does not know when the viewer perceives a movement rather than a jump or just a standstill.

This relationship is a central theme in Whitney's poetics in uniting visual and musical expression in a complementary relation. In addition to the aforementioned "differential motion", "harmony" is another concept of musical strategies that he explores. The term relates to his early films, such as ''Permutations'', which, like ''Arabesque'', consisted of a series of dots that occasionally condense and form perceptibly stable configurations using a geometric rose curve algorithm. Here the harmony consists precisely in "the dynamics of graphic pattern arrays" (ibid: 42), which he calls the moving dots that sometimes form stable patterns. These works, Whitney believes, create a sense of tension and relaxation when stable patterns suddenly appear or gradually emerge and disappear. In this way, they form a "graphic "scale"", which is modeled on musical harmony, where some tones are grouped into scales because they sound good to the human ear, and can create excitement by perceptually attracting and repelling each other. Similarly, Whitney sees in his film machines: "a diversity of rise and fall of tension, of highs and lows of tension, and a metrical rhythm and order" (ibid: 44)

[examples of condensed dots in the flicker?]

Here we can not go into further depth regarding the harmonies implemented in Arabesque and how they are arranged temporarily in the sequences. Instead, we will pursue the interesting point regarding the use of the algorithm, namely that there is a significant difference between the perceptual and substantive experience of the algorithm's graphical output. On the one hand, the human recipient perceives by the laws of perception and can only see patterns in the Arabesque flicker in the certain cases when it forms a recognizable or rather perceptually stable pattern. We can see how the algorithm's output makes ''appearances'' for the human eye. On the other hand is the machine that interprets all the screen outputs according to the algorithm that produced them. The film ''Arabesque'' is, in other words, a substantial imprint of both the algorithm and it's parametric values. This substantive understanding of the film does not see the screen output as appearances of patterns, but as an indexical imprint of the algorithm. If the computer already knows the algorithm, it can analyze what values the parameters were set to for that particular frame at the moment of creation. We could even imagine that a computer (and perhaps also a human) would be able to calculate the underlying algorithm if only the final film was given, by reverse engineering the geometry based on the work's figures and movement patterns.

By letting a software program draw the connections between the dots of the pattern (i.e. from dot # 1 to dot # 360) we see the difference between a substantial and perceptual interpretation, when we compare this to how a human might perceive the design of the dots in pattern:

{| class="wikitable"
|-
|rowspan="2"|'''Human vs. machine:'''
[[File:Tom-44.png|thumb]]
An example of a figure in Arabesque (step = 44, pinv = 0%, yinv = 0%)
|A possible perceptual interpretation of this figure:
[[File:percept-44.png|thumb]]
|-
|A substantial interpretation of this figure
[[File:substans-44.png|thumb]]
|}

Between the perceptual/human and substantial/machine poles of the algorithm, the artist stands as a mediator. In some cases, film machines are used for a narrative function where they simply have to be decorative, draw a circle, etc. But in some works, the film technician may use and explore the film machine algorithmically like Whitney has done. Here, there is a crucial accentuation of the substantive pole, but a successful musicalization of a film machine's algorithm requires an understanding of both perception and substance.

In the following two chapters we will see how two other artists use their film machine in an algorithmic practice, where the substantial also plays a crucial part in the works. The relationship between perceptual and substantial understanding will be further unfolded in the conclusion.

Cine-Machine as Method: Algorithm and Animation in the Digital Environment

2020-04-20T15:36:08Z

Kzxpr: /* Animation */

In this chapter, I will analyze John Whitney's Arabesque software as a film machine, and set out the first principles of an algorithm model that can be used in the further work on the film machines. Next, I will briefly analyze how the algorithm is animated in Whitney's early computer film ''Arabesque'' (1975) and outline what issues it raises.

Specifically, the film machine uses a geometric equation that generates images by defining the 360 dots position on the screen. Whitney has also used this dot technique in films such as ''Permutations'' (1965), but in Arabesque, the dot is merged with the environment's own minority, the pixel.

Whitney's film machine is exemplary because in his work with the computer he built his films on some relatively simple geometric algorithms. His book ''Digital Harmony'' (1980) even includes a "Do it yourself" chapter in which he shares the program code underlying ''Arabesque'' (Whitney: 136) and discusses the musical principles that have inspired the making of the film.

Through the descriptions in ''Digital Harmony'', I have succeeded in creating a program that can simulate the algorithm used by Whitney in ''Arabesque''. '''{G}''' In addition to the characteristics below, this simulation can also give the reader an idea of the basic geometric principles that has guided the film’s imaging and movement patterns.

== Arabesque algorithm's three parameters ==
The starting point for Whitney's ''Arabesque'' algorithm is a simple circle derived from a polar equation. He makes the computer draw 360 dots that are evenly spaced 360 degrees around a a particular point (center of the circle) with a fixed distance (radius). A polar equation for this circle would then read:
p = r
or rewritten into a Cartesian coordinate system:
x (t) = cx + r * cos (t)
y (t) = cy + r * sin (t)
where cx and cy are the coordinates of the center of the circle, r is the radius of the circle and t is each degree.

Now each dot has an individual number that allows the computer to move them individually. The first dot drawn in the circle is named # 1, the next dot is named # 2, and so on, up to dot # 360, which is the last in the circle and is next to dot # 1. This numbering allows Whitney to transform the circular shape by manipulating a dot's position through three new parameters.

I have called the simplest parameter ''yinv'' (y inversion), which causes the figure to be reflected vertically across the x-axis, since each dot's y coordinate can be "inverted" from its distance from the center. The ''yinv'' parameter has a value between 0% and 100%, where 0% would mean that dot # 1 is at the top of the circle and 100% that dot # 1 is at the bottom of the circle. The numbering goes clockwise. Between these two extremes, there are a number of intermediate points where the mirroring is underway. First, the figure is compressed until it becomes completely flat (50%), and then inflated again to straighten out completely like a mirror.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Yinv-0.png|100px|thumb]]
||
[[File:Yinv-25.png|100px|thumb]]
||
[[File:Yinv50.png|100px|thumb]]
||
[[File:Yinv-75.png|100px|thumb]]
||
[[File:Yinv-100.png|100px|thumb]]
|-
|colspan="5"|yinv from 0% to 100% (pinv = 0%, step = 0)
|}

In the opening of ''Arabesque'' '''{H}''', yinv initially has a value of 100%, so the opening of the circle is at the bottom, but in the middle of the sequence, yinv changes from 100% to 0%, thereby compressing and mirroring the current figure (a kind of rounded triangle) across the x-axis in the same way we have seen it with the circle.

The next parameter I have called ''pinv'' (polar inversion) and it is similar to yinv, in that it's value range is also between 0% and 100% and the parameter similarly determines a mirroring. But instead of mirroring the figure across a mid-axis, the pinv uses the center of the circle as the point of reflection, so that each x-coordinate of a dot is "crossed over" the center of the circle and is diametrically opposite to it's starting point.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv1-0.png|100px|thumb]]
||
[[File:Pinv1-20.png|100px|thumb]]
||
[[File:Pinv1-50.png|100px|thumb]]
||
[[File:Pinv1-75.png|100px|thumb]]
||
[[File:Pinv1-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 0)
|}

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv2-0.png|100px|thumb]]
||
[[File:Pinv2-25.png|100px|thumb]]
||
[[File:Pinv2-50.png|100px|thumb]]
||
[[File:Pinv2-75.png|100px|thumb]]
||
[[File:Pinv2-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 1/360)
|}

If the base figure is a circle, a transformation from pinv = 0% to pinv = 100% will be similar to a horizontal reflection of the figure in the y-axis. However, if a pinv transformation is applied to the figure, e.g. when step = 1/360 then the pinv mirroring is much more complex. Initially the shape looks like a tooth, which gradually turns out to form an arc (25%), then a wave (50%), and eventually the line ties a knot on itself (75%) and ends as a loop (100%).

As attractive as this reflection can be, it is equally unpredictable. In comparison to a yinv transformation that just squeezes the figure and straightens it out in a mirrored form, the results of pinv are harder to anticipate, even though the transformation is mathematically consistent.

To understand the complex mirroring, one must also look at the ''step'' which is the last of the parameters. Unlike yinv and pinv, step is not based on a mirror, but on the principle Whitney calls "differential motion". In ''Digital Harmony'', he illustrates this by drawing a line of 60 dots. He labels these dots from left to right (so they are called 1,2,3 ... 60), and then tells the computer that for each "step" in the animation, each dot must move upwards by a number of pixels corresponding to the dot's number. While the dots are on a horizontal line at step # 0, the dots on the right will gradually move up faster, making the line animated to appear skewed at ever increasing speed (Whitney: 48-49).

{| class="wikitable"
|-
! step = 0 !! step = 1 !! step = 2 !! step = 3 !! step = 4
|-
|
[[File:line0.png|100px|thumb]]
||
[[File:line1.png|100px|thumb]]
||
[[File:line2.png|100px|thumb]]
||
[[File:line3.png|100px|thumb]]
||
[[File:line4.png|100px|thumb]]
|-
|colspan="5"|Example of "differential motion" based on a line (cf. Whitney: 50)
|}

In such "differential motion", the dots initially line up. At step = 1, dot # 1 has moved 1 pixel up, dot # 2 has moved 2 pixels up, etc. up to dot # 60 which has moved 60 pixels up. At step = 2, dot # 1 has moved 2 pixels up compared to the starting point, dot # 2 has moved 4 pixels up, and dot # 60 has moved 120 pixels up. Continuing this line, at step = 4 dot # 1 has moved 4 pixels up (1 * 4), while dot # 60 has moved 240 pixels up (60 * 4).

As the figure above shows, we do not perceive these movements as individual dots moving - we perceive the dots as a coherent figure, as if it is a line that is gradually tilting and extending.

In ''Arabesque'', Whitney applies the same principle to the circle figure. Having already numbered the dots in the circle, he programs dot # 1 to move 1 pixel to the right of each step, dot # 2 to move 2 pixels to the right of each step, and so on, until dot # 360 that moves 360 pixels to right for each step.

As the dots will quickly move beyond the edge of the screen as they move to the right, Whitney adds a modulus function to each dot, meaning that if the computer calculates a an off-screen position for a dot, it jumps to the left edge of the screen and continues to the right again (ibid: 97). This principle can e.g. can be seen in the figure below, where the figure cuts the edge by 50%, but appears on the left side. Here's how it goes on for 75%, up to 100%, where half of the figure has crossed the edge of the screen and now forms a "tooth" figure.

{| class="wikitable"
|-
! step = 0/360 !! step = 1 * 25% !! step = 1 * 50% !! step = 1 * 75% !! step = 1 * 100%
|-
|
[[File:step1-0.png|100px|thumb]]
||
[[File:step1-25.png|100px|thumb]]
||
[[File:step1-50.png|100px|thumb]]
||
[[File:step1-75.png|100px|thumb]]
||
[[File:step1-100.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 1/360 (yinv = 0%, pinv = 0%)
|}

In the last frame of the table, each dot has moved an amount that corresponds to one step. In other words, dot # 1 has moved 1 pixel to the right, dot # 2 has moved 2 pixels to the right, and dot # 360 has moved 360 pixels to the right.

Note that while the tables showing the differential motion of the line has a distance of 1 step between each frame, the Arabesque circle requires a much lower increase in order for us to perceive the change between the frames as a single movement. If I only showed the first and last frames, few would be able to figure out how the movement between them is going - and this problem only increase if we continue to change the step parameter by an increase of 1:

{| class="wikitable"
|-
! step = 0/360 !! step = 1/360 !! step = 2/360 !! step = 3/360 !! step = 4/360
|-
|
[[File:Step3-0.png|100px|thumb]]
||
[[File:Step3-1.png|100px|thumb]]
||
[[File:Step3-2.png|100px|thumb]]
||
[[File:Step3-3.png|100px|thumb]]
||
[[File:Step3-4.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 4/360 (yinv = 0%, pinv = 0%)
|}

I have chosen to list the whole step value as numbers between 0/360 and 360/360. This notation should reflect that after 360 steps, the differential motion of the circle will cause each dot to be displaced so much that they occupy their original position on the screen. This is comparable to a clock where all three hands point to twelve when it is midnight. During the day, they will move around the disc at different speeds, but after 12 hours they will point to twelve again. Similarly, step = 360/360 corresponds to step = 0/360, where all dots have run through a full cycle at least once. Dot # 1 is the slowest and has only completed one cycle. Dot # 2 will be the second-slowest and has completed two cycles. And finally, Dot # 360 will have completed 360 full cycles. (Whitney: 98)

Because the program requires only numeric values to generate output, there are no signal inputs, but only parameters in this algorithm. We can summarize its algorithm with this diagram, also including x and y position to move the circle and radius to change the size:

[[File:Arab-chart01.png|thumb|center]]

== Variations over the algorithm ==
Appropriately, the opening scene in ''Arabesque'' also serves as an introduction to the algorithm's behavior. First, the step goes from 0 to 1/360, while the y-inv from the start is set to 100%. Then pinv goes from 0 to 100%. Step from 1/360 to 2/360. And y-inv from 100% to 0%. While this last movement is midway and the circle is compressed, a new, vertically mirrored figure emerges above the first one that performs the same movements synchronously. Together they now play the same sequence in reverse - step from 2/360 to 1/360, pinv from 100% to 0% and step from 1/360 to 0/360 - whereby the two figures simultaneously fold in to form two circles that lie on top of each other.

The scene is like an exposition that presents the shape to the viewer and demonstrates it's algorithmic behavior based on the three basic parameters. We can already see how Whitney not only uses an algorithm for the shapes in his animation, but also animates the shapes algorithmically.

In the following sections, however, he does not adhere to the simple operations. Instead, he lets the circle - now in a horizontally stretched variation - do a sprint by the step parameter that dissolves the contiguous line of the circle, letting the dots run into a frantic flicker. Just before the circle gathers, a new circle emerges and sets off, resulting in a kind of musical canon of voices repeating the same melody line.

Subsequently, Whitney continues this musical exploration of the algorithm's simple theme. In the next section, several circles with slightly delayed temporal offsets form a new canon in which they perform the same composite choreography: They set off in motion, and are multiplied into five circles when they return to start. They rotate a few times, set off again, and eventually gather in one circle, and then gradually disappear. In the next section, the shapes are even freer animated, forming little trajectories in the image at intersections, running in different sizes, colors, directions and tempi. Especially in this section, the title's arabesque connotations become obvious, resembling the shapes and motifs of an Islamic rug.

In the film's climax, the circle returns to its round starting point at the top of the screen in a slightly diminished size. It slowly transform the step parameter from 0/360 to 1/360, whereupon a new, skewed circle appears diagonally below it. The new circle performs the same movement and is then supplemented by another new, skewed circle until 5 circles (unfolded to 1/360) form a five-club in the center of the screen.

[image?]

Then all 5 circles' pinv parameters are animated synchronously to 100%, where the configuration along the way resembles 5-pointed star and eventually a buttercup. Then the step parameters change from 1 to 2, and a whirl appears within the flower, swapping the space of their leaves, and forming a new pointed-leaf flower. With a y-inv transformation, the flower collapses, but stops halfway just when it forms a pentagon and the sequence is played backwards.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:2-1.png|100px|thumb]]
||
[[File:2-2.png|100px|thumb]]
||
[[File:2-3.png|100px|thumb]]
||
[[File:2-4.png|100px|thumb]]
||
[[File:2-5.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 100, step = 1)
|}

{| class="wikitable"
|-
! step = 1/360 !! step = 1/360 + 25% !! step = 1/360 + 50% !! step = 1/360 + 75% !! step = 1/360 + 100%
|-
|
[[File:3-1.png|100px|thumb]]
||
[[File:3-2.png|100px|thumb]]
||
[[File:3-3.png|100px|thumb]]
||
[[File:3-4.png|100px|thumb]]
||
[[File:3-5.png|100px|thumb]]
|-
|colspan="5"|steps from 1 to 2 (yinv = 100%, pinv = 100%)
|}

Because the circles only have to go from step = 1 to step = 0, they do this in a slightly delayed canon where each shape disappears just as it forms a circle again.



== Animation ==
In animating the algorithm in the film, Whitney also uses other techniques, such as changing the positions, sizes and proportions of the figures (using the x, y and r parameters). In addition, he uses spatial amplification, where multiple of the same figure are seen synchronously side by side, and he rotates the figures to form a flower at the climax. With these techniques, Whitney manages to turn the simple theme of the Arabesque algorithm into a varied and expressive animation film.

Furthermore, we should also note that he makes tempo changes and often let's the dots condense into configurations of other shapes than just the circle. As we saw above, the gap is too wide if you increase the step value from 1/360 to 2/360 to see the movement, and the selection of tempo is therefore crucial, as Whitney hereby can structure the algorithm for a human recipient. In this way, he performs a necessary supplement to the machine, which does not know when the viewer perceives a movement rather than a jump or just a standstill.

This relationship is a central theme in Whitney's poetics in uniting visual and musical expression in a complementary relation. In addition to the aforementioned "differential motion", "harmony" is another concept of musical strategies that he explores. The term relates to his early films, such as ''Permutations'', which, like ''Arabesque'', consisted of a series of dots that occasionally condense and form perceptibly stable configurations using a geometric rose curve algorithm. Here the harmony consists precisely in "the dynamics of graphic pattern arrays" (ibid: 42), which he calls the moving dots that sometimes form stable patterns. These works, Whitney believes, create a sense of tension and relaxation when stable patterns suddenly appear or gradually emerge and disappear. In this way, they form a "graphic "scale"", which is modeled on musical harmony, where some tones are grouped into scales because they sound good to the human ear, and can create excitement by perceptually attracting and repelling each other. Similarly, Whitney sees in his film machines: "a diversity of rise and fall of tension, of highs and lows of tension, and a metrical rhythm and order" (ibid: 44)

[examples of condensed dots in the flicker?]

Here we can not go into further depth regarding the harmonies implemented in Arabesque and how they are arranged temporarily in the sequences. Instead, we will pursue the interesting point regarding the use of the algorithm, namely that there is a significant difference between the perceptual and substantive experience of the algorithm's graphical output. On the one hand, the human recipient perceives by the laws of perception and can only see patterns in the Arabesque flicker in the certain cases when it forms a recognizable or rather perceptually stable pattern. We can see how the algorithm's output makes ''appearances'' for the human eye. On the other hand is the machine that interprets all the screen outputs according to the algorithm that produced them. The film ''Arabesque'' is, in other words, a substantial imprint of both the algorithm and it's parametric values. This substantive understanding of the film does not see the screen output as appearances of patterns, but as an indexical imprint of the algorithm. If the computer already knows the algorithm, it can analyze what values the parameters were set to for that particular frame at the moment of creation. We could even imagine that a computer (and perhaps also a human) would be able to calculate the underlying algorithm if only the final film was given, by reverse engineering the geometry based on the work's figures and movement patterns.

By letting a software program draw the connections between the dots of the pattern (i.e. from dot # 1 to dot # 360) we see the difference between a substantial and perceptual interpretation, when we compare this to how a human might perceive the design of the dots in pattern:

{| class="wikitable"
|-
|rowspan="2"|
[[File:Tom-44.png|thumb]]
|[[File:percept-44.png|thumb]]
|-
|[[File:substans-44.png|thumb]]
|}

[table]
Human vs. machine:
An example of a figure in Arabesque
(step = 44, pinv = 0%, yinv = 0%)

Between the perceptual/human and substantial/machine poles of the algorithm, the artist stands as a mediator. In some cases, film machines are used for a narrative function where they simply have to be decorative, draw a circle, etc. But in some works, the film technician may use and explore the film machine algorithmically like Whitney has done. Here, there is a crucial accentuation of the substantive pole, but a successful musicalization of a film machine's algorithm requires an understanding of both perception and substance.

In the following two chapters we will see how two other artists use their film machine in an algorithmic practice, where the substantial also plays a crucial part in the works. The relationship between perceptual and substantial understanding will be further unfolded in the conclusion.

File:Percept-44.png

2020-04-20T15:35:07Z

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File:Substans-44.png

2020-04-20T15:35:07Z

Kzxpr: Uploaded with SimpleBatchUpload

File:Tom-44.png

2020-04-20T15:35:07Z

Kzxpr: Uploaded with SimpleBatchUpload

Cine-Machine as Method: Algorithm and Animation in the Digital Environment

2020-04-20T15:34:03Z

Kzxpr: /* Animation */

In this chapter, I will analyze John Whitney's Arabesque software as a film machine, and set out the first principles of an algorithm model that can be used in the further work on the film machines. Next, I will briefly analyze how the algorithm is animated in Whitney's early computer film ''Arabesque'' (1975) and outline what issues it raises.

Specifically, the film machine uses a geometric equation that generates images by defining the 360 dots position on the screen. Whitney has also used this dot technique in films such as ''Permutations'' (1965), but in Arabesque, the dot is merged with the environment's own minority, the pixel.

Whitney's film machine is exemplary because in his work with the computer he built his films on some relatively simple geometric algorithms. His book ''Digital Harmony'' (1980) even includes a "Do it yourself" chapter in which he shares the program code underlying ''Arabesque'' (Whitney: 136) and discusses the musical principles that have inspired the making of the film.

Through the descriptions in ''Digital Harmony'', I have succeeded in creating a program that can simulate the algorithm used by Whitney in ''Arabesque''. '''{G}''' In addition to the characteristics below, this simulation can also give the reader an idea of the basic geometric principles that has guided the film’s imaging and movement patterns.

== Arabesque algorithm's three parameters ==
The starting point for Whitney's ''Arabesque'' algorithm is a simple circle derived from a polar equation. He makes the computer draw 360 dots that are evenly spaced 360 degrees around a a particular point (center of the circle) with a fixed distance (radius). A polar equation for this circle would then read:
p = r
or rewritten into a Cartesian coordinate system:
x (t) = cx + r * cos (t)
y (t) = cy + r * sin (t)
where cx and cy are the coordinates of the center of the circle, r is the radius of the circle and t is each degree.

Now each dot has an individual number that allows the computer to move them individually. The first dot drawn in the circle is named # 1, the next dot is named # 2, and so on, up to dot # 360, which is the last in the circle and is next to dot # 1. This numbering allows Whitney to transform the circular shape by manipulating a dot's position through three new parameters.

I have called the simplest parameter ''yinv'' (y inversion), which causes the figure to be reflected vertically across the x-axis, since each dot's y coordinate can be "inverted" from its distance from the center. The ''yinv'' parameter has a value between 0% and 100%, where 0% would mean that dot # 1 is at the top of the circle and 100% that dot # 1 is at the bottom of the circle. The numbering goes clockwise. Between these two extremes, there are a number of intermediate points where the mirroring is underway. First, the figure is compressed until it becomes completely flat (50%), and then inflated again to straighten out completely like a mirror.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Yinv-0.png|100px|thumb]]
||
[[File:Yinv-25.png|100px|thumb]]
||
[[File:Yinv50.png|100px|thumb]]
||
[[File:Yinv-75.png|100px|thumb]]
||
[[File:Yinv-100.png|100px|thumb]]
|-
|colspan="5"|yinv from 0% to 100% (pinv = 0%, step = 0)
|}

In the opening of ''Arabesque'' '''{H}''', yinv initially has a value of 100%, so the opening of the circle is at the bottom, but in the middle of the sequence, yinv changes from 100% to 0%, thereby compressing and mirroring the current figure (a kind of rounded triangle) across the x-axis in the same way we have seen it with the circle.

The next parameter I have called ''pinv'' (polar inversion) and it is similar to yinv, in that it's value range is also between 0% and 100% and the parameter similarly determines a mirroring. But instead of mirroring the figure across a mid-axis, the pinv uses the center of the circle as the point of reflection, so that each x-coordinate of a dot is "crossed over" the center of the circle and is diametrically opposite to it's starting point.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv1-0.png|100px|thumb]]
||
[[File:Pinv1-20.png|100px|thumb]]
||
[[File:Pinv1-50.png|100px|thumb]]
||
[[File:Pinv1-75.png|100px|thumb]]
||
[[File:Pinv1-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 0)
|}

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv2-0.png|100px|thumb]]
||
[[File:Pinv2-25.png|100px|thumb]]
||
[[File:Pinv2-50.png|100px|thumb]]
||
[[File:Pinv2-75.png|100px|thumb]]
||
[[File:Pinv2-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 1/360)
|}

If the base figure is a circle, a transformation from pinv = 0% to pinv = 100% will be similar to a horizontal reflection of the figure in the y-axis. However, if a pinv transformation is applied to the figure, e.g. when step = 1/360 then the pinv mirroring is much more complex. Initially the shape looks like a tooth, which gradually turns out to form an arc (25%), then a wave (50%), and eventually the line ties a knot on itself (75%) and ends as a loop (100%).

As attractive as this reflection can be, it is equally unpredictable. In comparison to a yinv transformation that just squeezes the figure and straightens it out in a mirrored form, the results of pinv are harder to anticipate, even though the transformation is mathematically consistent.

To understand the complex mirroring, one must also look at the ''step'' which is the last of the parameters. Unlike yinv and pinv, step is not based on a mirror, but on the principle Whitney calls "differential motion". In ''Digital Harmony'', he illustrates this by drawing a line of 60 dots. He labels these dots from left to right (so they are called 1,2,3 ... 60), and then tells the computer that for each "step" in the animation, each dot must move upwards by a number of pixels corresponding to the dot's number. While the dots are on a horizontal line at step # 0, the dots on the right will gradually move up faster, making the line animated to appear skewed at ever increasing speed (Whitney: 48-49).

{| class="wikitable"
|-
! step = 0 !! step = 1 !! step = 2 !! step = 3 !! step = 4
|-
|
[[File:line0.png|100px|thumb]]
||
[[File:line1.png|100px|thumb]]
||
[[File:line2.png|100px|thumb]]
||
[[File:line3.png|100px|thumb]]
||
[[File:line4.png|100px|thumb]]
|-
|colspan="5"|Example of "differential motion" based on a line (cf. Whitney: 50)
|}

In such "differential motion", the dots initially line up. At step = 1, dot # 1 has moved 1 pixel up, dot # 2 has moved 2 pixels up, etc. up to dot # 60 which has moved 60 pixels up. At step = 2, dot # 1 has moved 2 pixels up compared to the starting point, dot # 2 has moved 4 pixels up, and dot # 60 has moved 120 pixels up. Continuing this line, at step = 4 dot # 1 has moved 4 pixels up (1 * 4), while dot # 60 has moved 240 pixels up (60 * 4).

As the figure above shows, we do not perceive these movements as individual dots moving - we perceive the dots as a coherent figure, as if it is a line that is gradually tilting and extending.

In ''Arabesque'', Whitney applies the same principle to the circle figure. Having already numbered the dots in the circle, he programs dot # 1 to move 1 pixel to the right of each step, dot # 2 to move 2 pixels to the right of each step, and so on, until dot # 360 that moves 360 pixels to right for each step.

As the dots will quickly move beyond the edge of the screen as they move to the right, Whitney adds a modulus function to each dot, meaning that if the computer calculates a an off-screen position for a dot, it jumps to the left edge of the screen and continues to the right again (ibid: 97). This principle can e.g. can be seen in the figure below, where the figure cuts the edge by 50%, but appears on the left side. Here's how it goes on for 75%, up to 100%, where half of the figure has crossed the edge of the screen and now forms a "tooth" figure.

{| class="wikitable"
|-
! step = 0/360 !! step = 1 * 25% !! step = 1 * 50% !! step = 1 * 75% !! step = 1 * 100%
|-
|
[[File:step1-0.png|100px|thumb]]
||
[[File:step1-25.png|100px|thumb]]
||
[[File:step1-50.png|100px|thumb]]
||
[[File:step1-75.png|100px|thumb]]
||
[[File:step1-100.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 1/360 (yinv = 0%, pinv = 0%)
|}

In the last frame of the table, each dot has moved an amount that corresponds to one step. In other words, dot # 1 has moved 1 pixel to the right, dot # 2 has moved 2 pixels to the right, and dot # 360 has moved 360 pixels to the right.

Note that while the tables showing the differential motion of the line has a distance of 1 step between each frame, the Arabesque circle requires a much lower increase in order for us to perceive the change between the frames as a single movement. If I only showed the first and last frames, few would be able to figure out how the movement between them is going - and this problem only increase if we continue to change the step parameter by an increase of 1:

{| class="wikitable"
|-
! step = 0/360 !! step = 1/360 !! step = 2/360 !! step = 3/360 !! step = 4/360
|-
|
[[File:Step3-0.png|100px|thumb]]
||
[[File:Step3-1.png|100px|thumb]]
||
[[File:Step3-2.png|100px|thumb]]
||
[[File:Step3-3.png|100px|thumb]]
||
[[File:Step3-4.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 4/360 (yinv = 0%, pinv = 0%)
|}

I have chosen to list the whole step value as numbers between 0/360 and 360/360. This notation should reflect that after 360 steps, the differential motion of the circle will cause each dot to be displaced so much that they occupy their original position on the screen. This is comparable to a clock where all three hands point to twelve when it is midnight. During the day, they will move around the disc at different speeds, but after 12 hours they will point to twelve again. Similarly, step = 360/360 corresponds to step = 0/360, where all dots have run through a full cycle at least once. Dot # 1 is the slowest and has only completed one cycle. Dot # 2 will be the second-slowest and has completed two cycles. And finally, Dot # 360 will have completed 360 full cycles. (Whitney: 98)

Because the program requires only numeric values to generate output, there are no signal inputs, but only parameters in this algorithm. We can summarize its algorithm with this diagram, also including x and y position to move the circle and radius to change the size:

[[File:Arab-chart01.png|thumb|center]]

== Variations over the algorithm ==
Appropriately, the opening scene in ''Arabesque'' also serves as an introduction to the algorithm's behavior. First, the step goes from 0 to 1/360, while the y-inv from the start is set to 100%. Then pinv goes from 0 to 100%. Step from 1/360 to 2/360. And y-inv from 100% to 0%. While this last movement is midway and the circle is compressed, a new, vertically mirrored figure emerges above the first one that performs the same movements synchronously. Together they now play the same sequence in reverse - step from 2/360 to 1/360, pinv from 100% to 0% and step from 1/360 to 0/360 - whereby the two figures simultaneously fold in to form two circles that lie on top of each other.

The scene is like an exposition that presents the shape to the viewer and demonstrates it's algorithmic behavior based on the three basic parameters. We can already see how Whitney not only uses an algorithm for the shapes in his animation, but also animates the shapes algorithmically.

In the following sections, however, he does not adhere to the simple operations. Instead, he lets the circle - now in a horizontally stretched variation - do a sprint by the step parameter that dissolves the contiguous line of the circle, letting the dots run into a frantic flicker. Just before the circle gathers, a new circle emerges and sets off, resulting in a kind of musical canon of voices repeating the same melody line.

Subsequently, Whitney continues this musical exploration of the algorithm's simple theme. In the next section, several circles with slightly delayed temporal offsets form a new canon in which they perform the same composite choreography: They set off in motion, and are multiplied into five circles when they return to start. They rotate a few times, set off again, and eventually gather in one circle, and then gradually disappear. In the next section, the shapes are even freer animated, forming little trajectories in the image at intersections, running in different sizes, colors, directions and tempi. Especially in this section, the title's arabesque connotations become obvious, resembling the shapes and motifs of an Islamic rug.

In the film's climax, the circle returns to its round starting point at the top of the screen in a slightly diminished size. It slowly transform the step parameter from 0/360 to 1/360, whereupon a new, skewed circle appears diagonally below it. The new circle performs the same movement and is then supplemented by another new, skewed circle until 5 circles (unfolded to 1/360) form a five-club in the center of the screen.

[image?]

Then all 5 circles' pinv parameters are animated synchronously to 100%, where the configuration along the way resembles 5-pointed star and eventually a buttercup. Then the step parameters change from 1 to 2, and a whirl appears within the flower, swapping the space of their leaves, and forming a new pointed-leaf flower. With a y-inv transformation, the flower collapses, but stops halfway just when it forms a pentagon and the sequence is played backwards.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:2-1.png|100px|thumb]]
||
[[File:2-2.png|100px|thumb]]
||
[[File:2-3.png|100px|thumb]]
||
[[File:2-4.png|100px|thumb]]
||
[[File:2-5.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 100, step = 1)
|}

{| class="wikitable"
|-
! step = 1/360 !! step = 1/360 + 25% !! step = 1/360 + 50% !! step = 1/360 + 75% !! step = 1/360 + 100%
|-
|
[[File:3-1.png|100px|thumb]]
||
[[File:3-2.png|100px|thumb]]
||
[[File:3-3.png|100px|thumb]]
||
[[File:3-4.png|100px|thumb]]
||
[[File:3-5.png|100px|thumb]]
|-
|colspan="5"|steps from 1 to 2 (yinv = 100%, pinv = 100%)
|}

Because the circles only have to go from step = 1 to step = 0, they do this in a slightly delayed canon where each shape disappears just as it forms a circle again.



== Animation ==
In animating the algorithm in the film, Whitney also uses other techniques, such as changing the positions, sizes and proportions of the figures (using the x, y and r parameters). In addition, he uses spatial amplification, where multiple of the same figure are seen synchronously side by side, and he rotates the figures to form a flower at the climax. With these techniques, Whitney manages to turn the simple theme of the Arabesque algorithm into a varied and expressive animation film.

Furthermore, we should also note that he makes tempo changes and often let's the dots condense into configurations of other shapes than just the circle. As we saw above, the gap is too wide if you increase the step value from 1/360 to 2/360 to see the movement, and the selection of tempo is therefore crucial, as Whitney hereby can structure the algorithm for a human recipient. In this way, he performs a necessary supplement to the machine, which does not know when the viewer perceives a movement rather than a jump or just a standstill.

This relationship is a central theme in Whitney's poetics in uniting visual and musical expression in a complementary relation. In addition to the aforementioned "differential motion", "harmony" is another concept of musical strategies that he explores. The term relates to his early films, such as ''Permutations'', which, like ''Arabesque'', consisted of a series of dots that occasionally condense and form perceptibly stable configurations using a geometric rose curve algorithm. Here the harmony consists precisely in "the dynamics of graphic pattern arrays" (ibid: 42), which he calls the moving dots that sometimes form stable patterns. These works, Whitney believes, create a sense of tension and relaxation when stable patterns suddenly appear or gradually emerge and disappear. In this way, they form a "graphic "scale"", which is modeled on musical harmony, where some tones are grouped into scales because they sound good to the human ear, and can create excitement by perceptually attracting and repelling each other. Similarly, Whitney sees in his film machines: "a diversity of rise and fall of tension, of highs and lows of tension, and a metrical rhythm and order" (ibid: 44)

[examples of condensed dots in the flicker?]

Here we can not go into further depth regarding the harmonies implemented in Arabesque and how they are arranged temporarily in the sequences. Instead, we will pursue the interesting point regarding the use of the algorithm, namely that there is a significant difference between the perceptual and substantive experience of the algorithm's graphical output. On the one hand, the human recipient perceives by the laws of perception and can only see patterns in the Arabesque flicker in the certain cases when it forms a recognizable or rather perceptually stable pattern. We can see how the algorithm's output makes ''appearances'' for the human eye. On the other hand is the machine that interprets all the screen outputs according to the algorithm that produced them. The film ''Arabesque'' is, in other words, a substantial imprint of both the algorithm and it's parametric values. This substantive understanding of the film does not see the screen output as appearances of patterns, but as an indexical imprint of the algorithm. If the computer already knows the algorithm, it can analyze what values the parameters were set to for that particular frame at the moment of creation. We could even imagine that a computer (and perhaps also a human) would be able to calculate the underlying algorithm if only the final film was given, by reverse engineering the geometry based on the work's figures and movement patterns.

By letting a software program draw the connections between the dots of the pattern (i.e. from dot # 1 to dot # 360) we see the difference between a substantial and perceptual interpretation, when we compare this to how a human might perceive the design of the dots in pattern:

{| class="wikitable"
|-
|rowspan="2"|LOL
|Example
|-
|Hej
|}

[table]
Human vs. machine:
An example of a figure in Arabesque
(step = 44, pinv = 0%, yinv = 0%)

Between the perceptual/human and substantial/machine poles of the algorithm, the artist stands as a mediator. In some cases, film machines are used for a narrative function where they simply have to be decorative, draw a circle, etc. But in some works, the film technician may use and explore the film machine algorithmically like Whitney has done. Here, there is a crucial accentuation of the substantive pole, but a successful musicalization of a film machine's algorithm requires an understanding of both perception and substance.

In the following two chapters we will see how two other artists use their film machine in an algorithmic practice, where the substantial also plays a crucial part in the works. The relationship between perceptual and substantial understanding will be further unfolded in the conclusion.

Cine-Machine as Method: Algorithm and Animation in the Digital Environment

2020-04-20T15:33:34Z

Kzxpr: /* Animation */

In this chapter, I will analyze John Whitney's Arabesque software as a film machine, and set out the first principles of an algorithm model that can be used in the further work on the film machines. Next, I will briefly analyze how the algorithm is animated in Whitney's early computer film ''Arabesque'' (1975) and outline what issues it raises.

Specifically, the film machine uses a geometric equation that generates images by defining the 360 dots position on the screen. Whitney has also used this dot technique in films such as ''Permutations'' (1965), but in Arabesque, the dot is merged with the environment's own minority, the pixel.

Whitney's film machine is exemplary because in his work with the computer he built his films on some relatively simple geometric algorithms. His book ''Digital Harmony'' (1980) even includes a "Do it yourself" chapter in which he shares the program code underlying ''Arabesque'' (Whitney: 136) and discusses the musical principles that have inspired the making of the film.

Through the descriptions in ''Digital Harmony'', I have succeeded in creating a program that can simulate the algorithm used by Whitney in ''Arabesque''. '''{G}''' In addition to the characteristics below, this simulation can also give the reader an idea of the basic geometric principles that has guided the film’s imaging and movement patterns.

== Arabesque algorithm's three parameters ==
The starting point for Whitney's ''Arabesque'' algorithm is a simple circle derived from a polar equation. He makes the computer draw 360 dots that are evenly spaced 360 degrees around a a particular point (center of the circle) with a fixed distance (radius). A polar equation for this circle would then read:
p = r
or rewritten into a Cartesian coordinate system:
x (t) = cx + r * cos (t)
y (t) = cy + r * sin (t)
where cx and cy are the coordinates of the center of the circle, r is the radius of the circle and t is each degree.

Now each dot has an individual number that allows the computer to move them individually. The first dot drawn in the circle is named # 1, the next dot is named # 2, and so on, up to dot # 360, which is the last in the circle and is next to dot # 1. This numbering allows Whitney to transform the circular shape by manipulating a dot's position through three new parameters.

I have called the simplest parameter ''yinv'' (y inversion), which causes the figure to be reflected vertically across the x-axis, since each dot's y coordinate can be "inverted" from its distance from the center. The ''yinv'' parameter has a value between 0% and 100%, where 0% would mean that dot # 1 is at the top of the circle and 100% that dot # 1 is at the bottom of the circle. The numbering goes clockwise. Between these two extremes, there are a number of intermediate points where the mirroring is underway. First, the figure is compressed until it becomes completely flat (50%), and then inflated again to straighten out completely like a mirror.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Yinv-0.png|100px|thumb]]
||
[[File:Yinv-25.png|100px|thumb]]
||
[[File:Yinv50.png|100px|thumb]]
||
[[File:Yinv-75.png|100px|thumb]]
||
[[File:Yinv-100.png|100px|thumb]]
|-
|colspan="5"|yinv from 0% to 100% (pinv = 0%, step = 0)
|}

In the opening of ''Arabesque'' '''{H}''', yinv initially has a value of 100%, so the opening of the circle is at the bottom, but in the middle of the sequence, yinv changes from 100% to 0%, thereby compressing and mirroring the current figure (a kind of rounded triangle) across the x-axis in the same way we have seen it with the circle.

The next parameter I have called ''pinv'' (polar inversion) and it is similar to yinv, in that it's value range is also between 0% and 100% and the parameter similarly determines a mirroring. But instead of mirroring the figure across a mid-axis, the pinv uses the center of the circle as the point of reflection, so that each x-coordinate of a dot is "crossed over" the center of the circle and is diametrically opposite to it's starting point.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv1-0.png|100px|thumb]]
||
[[File:Pinv1-20.png|100px|thumb]]
||
[[File:Pinv1-50.png|100px|thumb]]
||
[[File:Pinv1-75.png|100px|thumb]]
||
[[File:Pinv1-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 0)
|}

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv2-0.png|100px|thumb]]
||
[[File:Pinv2-25.png|100px|thumb]]
||
[[File:Pinv2-50.png|100px|thumb]]
||
[[File:Pinv2-75.png|100px|thumb]]
||
[[File:Pinv2-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 1/360)
|}

If the base figure is a circle, a transformation from pinv = 0% to pinv = 100% will be similar to a horizontal reflection of the figure in the y-axis. However, if a pinv transformation is applied to the figure, e.g. when step = 1/360 then the pinv mirroring is much more complex. Initially the shape looks like a tooth, which gradually turns out to form an arc (25%), then a wave (50%), and eventually the line ties a knot on itself (75%) and ends as a loop (100%).

As attractive as this reflection can be, it is equally unpredictable. In comparison to a yinv transformation that just squeezes the figure and straightens it out in a mirrored form, the results of pinv are harder to anticipate, even though the transformation is mathematically consistent.

To understand the complex mirroring, one must also look at the ''step'' which is the last of the parameters. Unlike yinv and pinv, step is not based on a mirror, but on the principle Whitney calls "differential motion". In ''Digital Harmony'', he illustrates this by drawing a line of 60 dots. He labels these dots from left to right (so they are called 1,2,3 ... 60), and then tells the computer that for each "step" in the animation, each dot must move upwards by a number of pixels corresponding to the dot's number. While the dots are on a horizontal line at step # 0, the dots on the right will gradually move up faster, making the line animated to appear skewed at ever increasing speed (Whitney: 48-49).

{| class="wikitable"
|-
! step = 0 !! step = 1 !! step = 2 !! step = 3 !! step = 4
|-
|
[[File:line0.png|100px|thumb]]
||
[[File:line1.png|100px|thumb]]
||
[[File:line2.png|100px|thumb]]
||
[[File:line3.png|100px|thumb]]
||
[[File:line4.png|100px|thumb]]
|-
|colspan="5"|Example of "differential motion" based on a line (cf. Whitney: 50)
|}

In such "differential motion", the dots initially line up. At step = 1, dot # 1 has moved 1 pixel up, dot # 2 has moved 2 pixels up, etc. up to dot # 60 which has moved 60 pixels up. At step = 2, dot # 1 has moved 2 pixels up compared to the starting point, dot # 2 has moved 4 pixels up, and dot # 60 has moved 120 pixels up. Continuing this line, at step = 4 dot # 1 has moved 4 pixels up (1 * 4), while dot # 60 has moved 240 pixels up (60 * 4).

As the figure above shows, we do not perceive these movements as individual dots moving - we perceive the dots as a coherent figure, as if it is a line that is gradually tilting and extending.

In ''Arabesque'', Whitney applies the same principle to the circle figure. Having already numbered the dots in the circle, he programs dot # 1 to move 1 pixel to the right of each step, dot # 2 to move 2 pixels to the right of each step, and so on, until dot # 360 that moves 360 pixels to right for each step.

As the dots will quickly move beyond the edge of the screen as they move to the right, Whitney adds a modulus function to each dot, meaning that if the computer calculates a an off-screen position for a dot, it jumps to the left edge of the screen and continues to the right again (ibid: 97). This principle can e.g. can be seen in the figure below, where the figure cuts the edge by 50%, but appears on the left side. Here's how it goes on for 75%, up to 100%, where half of the figure has crossed the edge of the screen and now forms a "tooth" figure.

{| class="wikitable"
|-
! step = 0/360 !! step = 1 * 25% !! step = 1 * 50% !! step = 1 * 75% !! step = 1 * 100%
|-
|
[[File:step1-0.png|100px|thumb]]
||
[[File:step1-25.png|100px|thumb]]
||
[[File:step1-50.png|100px|thumb]]
||
[[File:step1-75.png|100px|thumb]]
||
[[File:step1-100.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 1/360 (yinv = 0%, pinv = 0%)
|}

In the last frame of the table, each dot has moved an amount that corresponds to one step. In other words, dot # 1 has moved 1 pixel to the right, dot # 2 has moved 2 pixels to the right, and dot # 360 has moved 360 pixels to the right.

Note that while the tables showing the differential motion of the line has a distance of 1 step between each frame, the Arabesque circle requires a much lower increase in order for us to perceive the change between the frames as a single movement. If I only showed the first and last frames, few would be able to figure out how the movement between them is going - and this problem only increase if we continue to change the step parameter by an increase of 1:

{| class="wikitable"
|-
! step = 0/360 !! step = 1/360 !! step = 2/360 !! step = 3/360 !! step = 4/360
|-
|
[[File:Step3-0.png|100px|thumb]]
||
[[File:Step3-1.png|100px|thumb]]
||
[[File:Step3-2.png|100px|thumb]]
||
[[File:Step3-3.png|100px|thumb]]
||
[[File:Step3-4.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 4/360 (yinv = 0%, pinv = 0%)
|}

I have chosen to list the whole step value as numbers between 0/360 and 360/360. This notation should reflect that after 360 steps, the differential motion of the circle will cause each dot to be displaced so much that they occupy their original position on the screen. This is comparable to a clock where all three hands point to twelve when it is midnight. During the day, they will move around the disc at different speeds, but after 12 hours they will point to twelve again. Similarly, step = 360/360 corresponds to step = 0/360, where all dots have run through a full cycle at least once. Dot # 1 is the slowest and has only completed one cycle. Dot # 2 will be the second-slowest and has completed two cycles. And finally, Dot # 360 will have completed 360 full cycles. (Whitney: 98)

Because the program requires only numeric values to generate output, there are no signal inputs, but only parameters in this algorithm. We can summarize its algorithm with this diagram, also including x and y position to move the circle and radius to change the size:

[[File:Arab-chart01.png|thumb|center]]

== Variations over the algorithm ==
Appropriately, the opening scene in ''Arabesque'' also serves as an introduction to the algorithm's behavior. First, the step goes from 0 to 1/360, while the y-inv from the start is set to 100%. Then pinv goes from 0 to 100%. Step from 1/360 to 2/360. And y-inv from 100% to 0%. While this last movement is midway and the circle is compressed, a new, vertically mirrored figure emerges above the first one that performs the same movements synchronously. Together they now play the same sequence in reverse - step from 2/360 to 1/360, pinv from 100% to 0% and step from 1/360 to 0/360 - whereby the two figures simultaneously fold in to form two circles that lie on top of each other.

The scene is like an exposition that presents the shape to the viewer and demonstrates it's algorithmic behavior based on the three basic parameters. We can already see how Whitney not only uses an algorithm for the shapes in his animation, but also animates the shapes algorithmically.

In the following sections, however, he does not adhere to the simple operations. Instead, he lets the circle - now in a horizontally stretched variation - do a sprint by the step parameter that dissolves the contiguous line of the circle, letting the dots run into a frantic flicker. Just before the circle gathers, a new circle emerges and sets off, resulting in a kind of musical canon of voices repeating the same melody line.

Subsequently, Whitney continues this musical exploration of the algorithm's simple theme. In the next section, several circles with slightly delayed temporal offsets form a new canon in which they perform the same composite choreography: They set off in motion, and are multiplied into five circles when they return to start. They rotate a few times, set off again, and eventually gather in one circle, and then gradually disappear. In the next section, the shapes are even freer animated, forming little trajectories in the image at intersections, running in different sizes, colors, directions and tempi. Especially in this section, the title's arabesque connotations become obvious, resembling the shapes and motifs of an Islamic rug.

In the film's climax, the circle returns to its round starting point at the top of the screen in a slightly diminished size. It slowly transform the step parameter from 0/360 to 1/360, whereupon a new, skewed circle appears diagonally below it. The new circle performs the same movement and is then supplemented by another new, skewed circle until 5 circles (unfolded to 1/360) form a five-club in the center of the screen.

[image?]

Then all 5 circles' pinv parameters are animated synchronously to 100%, where the configuration along the way resembles 5-pointed star and eventually a buttercup. Then the step parameters change from 1 to 2, and a whirl appears within the flower, swapping the space of their leaves, and forming a new pointed-leaf flower. With a y-inv transformation, the flower collapses, but stops halfway just when it forms a pentagon and the sequence is played backwards.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:2-1.png|100px|thumb]]
||
[[File:2-2.png|100px|thumb]]
||
[[File:2-3.png|100px|thumb]]
||
[[File:2-4.png|100px|thumb]]
||
[[File:2-5.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 100, step = 1)
|}

{| class="wikitable"
|-
! step = 1/360 !! step = 1/360 + 25% !! step = 1/360 + 50% !! step = 1/360 + 75% !! step = 1/360 + 100%
|-
|
[[File:3-1.png|100px|thumb]]
||
[[File:3-2.png|100px|thumb]]
||
[[File:3-3.png|100px|thumb]]
||
[[File:3-4.png|100px|thumb]]
||
[[File:3-5.png|100px|thumb]]
|-
|colspan="5"|steps from 1 to 2 (yinv = 100%, pinv = 100%)
|}

Because the circles only have to go from step = 1 to step = 0, they do this in a slightly delayed canon where each shape disappears just as it forms a circle again.



== Animation ==
In animating the algorithm in the film, Whitney also uses other techniques, such as changing the positions, sizes and proportions of the figures (using the x, y and r parameters). In addition, he uses spatial amplification, where multiple of the same figure are seen synchronously side by side, and he rotates the figures to form a flower at the climax. With these techniques, Whitney manages to turn the simple theme of the Arabesque algorithm into a varied and expressive animation film.

Furthermore, we should also note that he makes tempo changes and often let's the dots condense into configurations of other shapes than just the circle. As we saw above, the gap is too wide if you increase the step value from 1/360 to 2/360 to see the movement, and the selection of tempo is therefore crucial, as Whitney hereby can structure the algorithm for a human recipient. In this way, he performs a necessary supplement to the machine, which does not know when the viewer perceives a movement rather than a jump or just a standstill.

This relationship is a central theme in Whitney's poetics in uniting visual and musical expression in a complementary relation. In addition to the aforementioned "differential motion", "harmony" is another concept of musical strategies that he explores. The term relates to his early films, such as ''Permutations'', which, like ''Arabesque'', consisted of a series of dots that occasionally condense and form perceptibly stable configurations using a geometric rose curve algorithm. Here the harmony consists precisely in "the dynamics of graphic pattern arrays" (ibid: 42), which he calls the moving dots that sometimes form stable patterns. These works, Whitney believes, create a sense of tension and relaxation when stable patterns suddenly appear or gradually emerge and disappear. In this way, they form a "graphic "scale"", which is modeled on musical harmony, where some tones are grouped into scales because they sound good to the human ear, and can create excitement by perceptually attracting and repelling each other. Similarly, Whitney sees in his film machines: "a diversity of rise and fall of tension, of highs and lows of tension, and a metrical rhythm and order" (ibid: 44)

[examples of condensed dots in the flicker?]

Here we can not go into further depth regarding the harmonies implemented in Arabesque and how they are arranged temporarily in the sequences. Instead, we will pursue the interesting point regarding the use of the algorithm, namely that there is a significant difference between the perceptual and substantive experience of the algorithm's graphical output. On the one hand, the human recipient perceives by the laws of perception and can only see patterns in the Arabesque flicker in the certain cases when it forms a recognizable or rather perceptually stable pattern. We can see how the algorithm's output makes ''appearances'' for the human eye. On the other hand is the machine that interprets all the screen outputs according to the algorithm that produced them. The film ''Arabesque'' is, in other words, a substantial imprint of both the algorithm and it's parametric values. This substantive understanding of the film does not see the screen output as appearances of patterns, but as an indexical imprint of the algorithm. If the computer already knows the algorithm, it can analyze what values the parameters were set to for that particular frame at the moment of creation. We could even imagine that a computer (and perhaps also a human) would be able to calculate the underlying algorithm if only the final film was given, by reverse engineering the geometry based on the work's figures and movement patterns.

By letting a software program draw the connections between the dots of the pattern (i.e. from dot # 1 to dot # 360) we see the difference between a substantial and perceptual interpretation, when we compare this to how a human might perceive the design of the dots in pattern:

{| class="wikitable"
|-
| rowspan="2" |LOL| Example
|-
| Hej
|}

[table]
Human vs. machine:
An example of a figure in Arabesque
(step = 44, pinv = 0%, yinv = 0%)

Between the perceptual/human and substantial/machine poles of the algorithm, the artist stands as a mediator. In some cases, film machines are used for a narrative function where they simply have to be decorative, draw a circle, etc. But in some works, the film technician may use and explore the film machine algorithmically like Whitney has done. Here, there is a crucial accentuation of the substantive pole, but a successful musicalization of a film machine's algorithm requires an understanding of both perception and substance.

In the following two chapters we will see how two other artists use their film machine in an algorithmic practice, where the substantial also plays a crucial part in the works. The relationship between perceptual and substantial understanding will be further unfolded in the conclusion.

Cine-Machine as Method: Algorithm and Animation in the Digital Environment

2020-04-20T15:32:23Z

Kzxpr: /* Variations over the algorithm */

In this chapter, I will analyze John Whitney's Arabesque software as a film machine, and set out the first principles of an algorithm model that can be used in the further work on the film machines. Next, I will briefly analyze how the algorithm is animated in Whitney's early computer film ''Arabesque'' (1975) and outline what issues it raises.

Specifically, the film machine uses a geometric equation that generates images by defining the 360 dots position on the screen. Whitney has also used this dot technique in films such as ''Permutations'' (1965), but in Arabesque, the dot is merged with the environment's own minority, the pixel.

Whitney's film machine is exemplary because in his work with the computer he built his films on some relatively simple geometric algorithms. His book ''Digital Harmony'' (1980) even includes a "Do it yourself" chapter in which he shares the program code underlying ''Arabesque'' (Whitney: 136) and discusses the musical principles that have inspired the making of the film.

Through the descriptions in ''Digital Harmony'', I have succeeded in creating a program that can simulate the algorithm used by Whitney in ''Arabesque''. '''{G}''' In addition to the characteristics below, this simulation can also give the reader an idea of the basic geometric principles that has guided the film’s imaging and movement patterns.

== Arabesque algorithm's three parameters ==
The starting point for Whitney's ''Arabesque'' algorithm is a simple circle derived from a polar equation. He makes the computer draw 360 dots that are evenly spaced 360 degrees around a a particular point (center of the circle) with a fixed distance (radius). A polar equation for this circle would then read:
p = r
or rewritten into a Cartesian coordinate system:
x (t) = cx + r * cos (t)
y (t) = cy + r * sin (t)
where cx and cy are the coordinates of the center of the circle, r is the radius of the circle and t is each degree.

Now each dot has an individual number that allows the computer to move them individually. The first dot drawn in the circle is named # 1, the next dot is named # 2, and so on, up to dot # 360, which is the last in the circle and is next to dot # 1. This numbering allows Whitney to transform the circular shape by manipulating a dot's position through three new parameters.

I have called the simplest parameter ''yinv'' (y inversion), which causes the figure to be reflected vertically across the x-axis, since each dot's y coordinate can be "inverted" from its distance from the center. The ''yinv'' parameter has a value between 0% and 100%, where 0% would mean that dot # 1 is at the top of the circle and 100% that dot # 1 is at the bottom of the circle. The numbering goes clockwise. Between these two extremes, there are a number of intermediate points where the mirroring is underway. First, the figure is compressed until it becomes completely flat (50%), and then inflated again to straighten out completely like a mirror.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Yinv-0.png|100px|thumb]]
||
[[File:Yinv-25.png|100px|thumb]]
||
[[File:Yinv50.png|100px|thumb]]
||
[[File:Yinv-75.png|100px|thumb]]
||
[[File:Yinv-100.png|100px|thumb]]
|-
|colspan="5"|yinv from 0% to 100% (pinv = 0%, step = 0)
|}

In the opening of ''Arabesque'' '''{H}''', yinv initially has a value of 100%, so the opening of the circle is at the bottom, but in the middle of the sequence, yinv changes from 100% to 0%, thereby compressing and mirroring the current figure (a kind of rounded triangle) across the x-axis in the same way we have seen it with the circle.

The next parameter I have called ''pinv'' (polar inversion) and it is similar to yinv, in that it's value range is also between 0% and 100% and the parameter similarly determines a mirroring. But instead of mirroring the figure across a mid-axis, the pinv uses the center of the circle as the point of reflection, so that each x-coordinate of a dot is "crossed over" the center of the circle and is diametrically opposite to it's starting point.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv1-0.png|100px|thumb]]
||
[[File:Pinv1-20.png|100px|thumb]]
||
[[File:Pinv1-50.png|100px|thumb]]
||
[[File:Pinv1-75.png|100px|thumb]]
||
[[File:Pinv1-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 0)
|}

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv2-0.png|100px|thumb]]
||
[[File:Pinv2-25.png|100px|thumb]]
||
[[File:Pinv2-50.png|100px|thumb]]
||
[[File:Pinv2-75.png|100px|thumb]]
||
[[File:Pinv2-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 1/360)
|}

If the base figure is a circle, a transformation from pinv = 0% to pinv = 100% will be similar to a horizontal reflection of the figure in the y-axis. However, if a pinv transformation is applied to the figure, e.g. when step = 1/360 then the pinv mirroring is much more complex. Initially the shape looks like a tooth, which gradually turns out to form an arc (25%), then a wave (50%), and eventually the line ties a knot on itself (75%) and ends as a loop (100%).

As attractive as this reflection can be, it is equally unpredictable. In comparison to a yinv transformation that just squeezes the figure and straightens it out in a mirrored form, the results of pinv are harder to anticipate, even though the transformation is mathematically consistent.

To understand the complex mirroring, one must also look at the ''step'' which is the last of the parameters. Unlike yinv and pinv, step is not based on a mirror, but on the principle Whitney calls "differential motion". In ''Digital Harmony'', he illustrates this by drawing a line of 60 dots. He labels these dots from left to right (so they are called 1,2,3 ... 60), and then tells the computer that for each "step" in the animation, each dot must move upwards by a number of pixels corresponding to the dot's number. While the dots are on a horizontal line at step # 0, the dots on the right will gradually move up faster, making the line animated to appear skewed at ever increasing speed (Whitney: 48-49).

{| class="wikitable"
|-
! step = 0 !! step = 1 !! step = 2 !! step = 3 !! step = 4
|-
|
[[File:line0.png|100px|thumb]]
||
[[File:line1.png|100px|thumb]]
||
[[File:line2.png|100px|thumb]]
||
[[File:line3.png|100px|thumb]]
||
[[File:line4.png|100px|thumb]]
|-
|colspan="5"|Example of "differential motion" based on a line (cf. Whitney: 50)
|}

In such "differential motion", the dots initially line up. At step = 1, dot # 1 has moved 1 pixel up, dot # 2 has moved 2 pixels up, etc. up to dot # 60 which has moved 60 pixels up. At step = 2, dot # 1 has moved 2 pixels up compared to the starting point, dot # 2 has moved 4 pixels up, and dot # 60 has moved 120 pixels up. Continuing this line, at step = 4 dot # 1 has moved 4 pixels up (1 * 4), while dot # 60 has moved 240 pixels up (60 * 4).

As the figure above shows, we do not perceive these movements as individual dots moving - we perceive the dots as a coherent figure, as if it is a line that is gradually tilting and extending.

In ''Arabesque'', Whitney applies the same principle to the circle figure. Having already numbered the dots in the circle, he programs dot # 1 to move 1 pixel to the right of each step, dot # 2 to move 2 pixels to the right of each step, and so on, until dot # 360 that moves 360 pixels to right for each step.

As the dots will quickly move beyond the edge of the screen as they move to the right, Whitney adds a modulus function to each dot, meaning that if the computer calculates a an off-screen position for a dot, it jumps to the left edge of the screen and continues to the right again (ibid: 97). This principle can e.g. can be seen in the figure below, where the figure cuts the edge by 50%, but appears on the left side. Here's how it goes on for 75%, up to 100%, where half of the figure has crossed the edge of the screen and now forms a "tooth" figure.

{| class="wikitable"
|-
! step = 0/360 !! step = 1 * 25% !! step = 1 * 50% !! step = 1 * 75% !! step = 1 * 100%
|-
|
[[File:step1-0.png|100px|thumb]]
||
[[File:step1-25.png|100px|thumb]]
||
[[File:step1-50.png|100px|thumb]]
||
[[File:step1-75.png|100px|thumb]]
||
[[File:step1-100.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 1/360 (yinv = 0%, pinv = 0%)
|}

In the last frame of the table, each dot has moved an amount that corresponds to one step. In other words, dot # 1 has moved 1 pixel to the right, dot # 2 has moved 2 pixels to the right, and dot # 360 has moved 360 pixels to the right.

Note that while the tables showing the differential motion of the line has a distance of 1 step between each frame, the Arabesque circle requires a much lower increase in order for us to perceive the change between the frames as a single movement. If I only showed the first and last frames, few would be able to figure out how the movement between them is going - and this problem only increase if we continue to change the step parameter by an increase of 1:

{| class="wikitable"
|-
! step = 0/360 !! step = 1/360 !! step = 2/360 !! step = 3/360 !! step = 4/360
|-
|
[[File:Step3-0.png|100px|thumb]]
||
[[File:Step3-1.png|100px|thumb]]
||
[[File:Step3-2.png|100px|thumb]]
||
[[File:Step3-3.png|100px|thumb]]
||
[[File:Step3-4.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 4/360 (yinv = 0%, pinv = 0%)
|}

I have chosen to list the whole step value as numbers between 0/360 and 360/360. This notation should reflect that after 360 steps, the differential motion of the circle will cause each dot to be displaced so much that they occupy their original position on the screen. This is comparable to a clock where all three hands point to twelve when it is midnight. During the day, they will move around the disc at different speeds, but after 12 hours they will point to twelve again. Similarly, step = 360/360 corresponds to step = 0/360, where all dots have run through a full cycle at least once. Dot # 1 is the slowest and has only completed one cycle. Dot # 2 will be the second-slowest and has completed two cycles. And finally, Dot # 360 will have completed 360 full cycles. (Whitney: 98)

Because the program requires only numeric values to generate output, there are no signal inputs, but only parameters in this algorithm. We can summarize its algorithm with this diagram, also including x and y position to move the circle and radius to change the size:

[[File:Arab-chart01.png|thumb|center]]

== Variations over the algorithm ==
Appropriately, the opening scene in ''Arabesque'' also serves as an introduction to the algorithm's behavior. First, the step goes from 0 to 1/360, while the y-inv from the start is set to 100%. Then pinv goes from 0 to 100%. Step from 1/360 to 2/360. And y-inv from 100% to 0%. While this last movement is midway and the circle is compressed, a new, vertically mirrored figure emerges above the first one that performs the same movements synchronously. Together they now play the same sequence in reverse - step from 2/360 to 1/360, pinv from 100% to 0% and step from 1/360 to 0/360 - whereby the two figures simultaneously fold in to form two circles that lie on top of each other.

The scene is like an exposition that presents the shape to the viewer and demonstrates it's algorithmic behavior based on the three basic parameters. We can already see how Whitney not only uses an algorithm for the shapes in his animation, but also animates the shapes algorithmically.

In the following sections, however, he does not adhere to the simple operations. Instead, he lets the circle - now in a horizontally stretched variation - do a sprint by the step parameter that dissolves the contiguous line of the circle, letting the dots run into a frantic flicker. Just before the circle gathers, a new circle emerges and sets off, resulting in a kind of musical canon of voices repeating the same melody line.

Subsequently, Whitney continues this musical exploration of the algorithm's simple theme. In the next section, several circles with slightly delayed temporal offsets form a new canon in which they perform the same composite choreography: They set off in motion, and are multiplied into five circles when they return to start. They rotate a few times, set off again, and eventually gather in one circle, and then gradually disappear. In the next section, the shapes are even freer animated, forming little trajectories in the image at intersections, running in different sizes, colors, directions and tempi. Especially in this section, the title's arabesque connotations become obvious, resembling the shapes and motifs of an Islamic rug.

In the film's climax, the circle returns to its round starting point at the top of the screen in a slightly diminished size. It slowly transform the step parameter from 0/360 to 1/360, whereupon a new, skewed circle appears diagonally below it. The new circle performs the same movement and is then supplemented by another new, skewed circle until 5 circles (unfolded to 1/360) form a five-club in the center of the screen.

[image?]

Then all 5 circles' pinv parameters are animated synchronously to 100%, where the configuration along the way resembles 5-pointed star and eventually a buttercup. Then the step parameters change from 1 to 2, and a whirl appears within the flower, swapping the space of their leaves, and forming a new pointed-leaf flower. With a y-inv transformation, the flower collapses, but stops halfway just when it forms a pentagon and the sequence is played backwards.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:2-1.png|100px|thumb]]
||
[[File:2-2.png|100px|thumb]]
||
[[File:2-3.png|100px|thumb]]
||
[[File:2-4.png|100px|thumb]]
||
[[File:2-5.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 100, step = 1)
|}

{| class="wikitable"
|-
! step = 1/360 !! step = 1/360 + 25% !! step = 1/360 + 50% !! step = 1/360 + 75% !! step = 1/360 + 100%
|-
|
[[File:3-1.png|100px|thumb]]
||
[[File:3-2.png|100px|thumb]]
||
[[File:3-3.png|100px|thumb]]
||
[[File:3-4.png|100px|thumb]]
||
[[File:3-5.png|100px|thumb]]
|-
|colspan="5"|steps from 1 to 2 (yinv = 100%, pinv = 100%)
|}

Because the circles only have to go from step = 1 to step = 0, they do this in a slightly delayed canon where each shape disappears just as it forms a circle again.



== Animation ==
In animating the algorithm in the film, Whitney also uses other techniques, such as changing the positions, sizes and proportions of the figures (using the x, y and r parameters). In addition, he uses spatial amplification, where multiple of the same figure are seen synchronously side by side, and he rotates the figures to form a flower at the climax. With these techniques, Whitney manages to turn the simple theme of the Arabesque algorithm into a varied and expressive animation film.

Furthermore, we should also note that he makes tempo changes and often let's the dots condense into configurations of other shapes than just the circle. As we saw above, the gap is too wide if you increase the step value from 1/360 to 2/360 to see the movement, and the selection of tempo is therefore crucial, as Whitney hereby can structure the algorithm for a human recipient. In this way, he performs a necessary supplement to the machine, which does not know when the viewer perceives a movement rather than a jump or just a standstill.

This relationship is a central theme in Whitney's poetics in uniting visual and musical expression in a complementary relation. In addition to the aforementioned "differential motion", "harmony" is another concept of musical strategies that he explores. The term relates to his early films, such as ''Permutations'', which, like ''Arabesque'', consisted of a series of dots that occasionally condense and form perceptibly stable configurations using a geometric rose curve algorithm. Here the harmony consists precisely in "the dynamics of graphic pattern arrays" (ibid: 42), which he calls the moving dots that sometimes form stable patterns. These works, Whitney believes, create a sense of tension and relaxation when stable patterns suddenly appear or gradually emerge and disappear. In this way, they form a "graphic "scale"", which is modeled on musical harmony, where some tones are grouped into scales because they sound good to the human ear, and can create excitement by perceptually attracting and repelling each other. Similarly, Whitney sees in his film machines: "a diversity of rise and fall of tension, of highs and lows of tension, and a metrical rhythm and order" (ibid: 44)

[examples of condensed dots in the flicker?]

Here we can not go into further depth regarding the harmonies implemented in Arabesque and how they are arranged temporarily in the sequences. Instead, we will pursue the interesting point regarding the use of the algorithm, namely that there is a significant difference between the perceptual and substantive experience of the algorithm's graphical output. On the one hand, the human recipient perceives by the laws of perception and can only see patterns in the Arabesque flicker in the certain cases when it forms a recognizable or rather perceptually stable pattern. We can see how the algorithm's output makes ''appearances'' for the human eye. On the other hand is the machine that interprets all the screen outputs according to the algorithm that produced them. The film ''Arabesque'' is, in other words, a substantial imprint of both the algorithm and it's parametric values. This substantive understanding of the film does not see the screen output as appearances of patterns, but as an indexical imprint of the algorithm. If the computer already knows the algorithm, it can analyze what values the parameters were set to for that particular frame at the moment of creation. We could even imagine that a computer (and perhaps also a human) would be able to calculate the underlying algorithm if only the final film was given, by reverse engineering the geometry based on the work's figures and movement patterns.

By letting a software program draw the connections between the dots of the pattern (i.e. from dot # 1 to dot # 360) we see the difference between a substantial and perceptual interpretation, when we compare this to how a human might perceive the design of the dots in pattern:

[table]
Human vs. machine:
An example of a figure in Arabesque
(step = 44, pinv = 0%, yinv = 0%)

Between the perceptual/human and substantial/machine poles of the algorithm, the artist stands as a mediator. In some cases, film machines are used for a narrative function where they simply have to be decorative, draw a circle, etc. But in some works, the film technician may use and explore the film machine algorithmically like Whitney has done. Here, there is a crucial accentuation of the substantive pole, but a successful musicalization of a film machine's algorithm requires an understanding of both perception and substance.

In the following two chapters we will see how two other artists use their film machine in an algorithmic practice, where the substantial also plays a crucial part in the works. The relationship between perceptual and substantial understanding will be further unfolded in the conclusion.

Cine-Machine as Method: Algorithm and Animation in the Digital Environment

2020-04-20T15:31:47Z

Kzxpr: /* Variations over the algorithm */

In this chapter, I will analyze John Whitney's Arabesque software as a film machine, and set out the first principles of an algorithm model that can be used in the further work on the film machines. Next, I will briefly analyze how the algorithm is animated in Whitney's early computer film ''Arabesque'' (1975) and outline what issues it raises.

Specifically, the film machine uses a geometric equation that generates images by defining the 360 dots position on the screen. Whitney has also used this dot technique in films such as ''Permutations'' (1965), but in Arabesque, the dot is merged with the environment's own minority, the pixel.

Whitney's film machine is exemplary because in his work with the computer he built his films on some relatively simple geometric algorithms. His book ''Digital Harmony'' (1980) even includes a "Do it yourself" chapter in which he shares the program code underlying ''Arabesque'' (Whitney: 136) and discusses the musical principles that have inspired the making of the film.

Through the descriptions in ''Digital Harmony'', I have succeeded in creating a program that can simulate the algorithm used by Whitney in ''Arabesque''. '''{G}''' In addition to the characteristics below, this simulation can also give the reader an idea of the basic geometric principles that has guided the film’s imaging and movement patterns.

== Arabesque algorithm's three parameters ==
The starting point for Whitney's ''Arabesque'' algorithm is a simple circle derived from a polar equation. He makes the computer draw 360 dots that are evenly spaced 360 degrees around a a particular point (center of the circle) with a fixed distance (radius). A polar equation for this circle would then read:
p = r
or rewritten into a Cartesian coordinate system:
x (t) = cx + r * cos (t)
y (t) = cy + r * sin (t)
where cx and cy are the coordinates of the center of the circle, r is the radius of the circle and t is each degree.

Now each dot has an individual number that allows the computer to move them individually. The first dot drawn in the circle is named # 1, the next dot is named # 2, and so on, up to dot # 360, which is the last in the circle and is next to dot # 1. This numbering allows Whitney to transform the circular shape by manipulating a dot's position through three new parameters.

I have called the simplest parameter ''yinv'' (y inversion), which causes the figure to be reflected vertically across the x-axis, since each dot's y coordinate can be "inverted" from its distance from the center. The ''yinv'' parameter has a value between 0% and 100%, where 0% would mean that dot # 1 is at the top of the circle and 100% that dot # 1 is at the bottom of the circle. The numbering goes clockwise. Between these two extremes, there are a number of intermediate points where the mirroring is underway. First, the figure is compressed until it becomes completely flat (50%), and then inflated again to straighten out completely like a mirror.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Yinv-0.png|100px|thumb]]
||
[[File:Yinv-25.png|100px|thumb]]
||
[[File:Yinv50.png|100px|thumb]]
||
[[File:Yinv-75.png|100px|thumb]]
||
[[File:Yinv-100.png|100px|thumb]]
|-
|colspan="5"|yinv from 0% to 100% (pinv = 0%, step = 0)
|}

In the opening of ''Arabesque'' '''{H}''', yinv initially has a value of 100%, so the opening of the circle is at the bottom, but in the middle of the sequence, yinv changes from 100% to 0%, thereby compressing and mirroring the current figure (a kind of rounded triangle) across the x-axis in the same way we have seen it with the circle.

The next parameter I have called ''pinv'' (polar inversion) and it is similar to yinv, in that it's value range is also between 0% and 100% and the parameter similarly determines a mirroring. But instead of mirroring the figure across a mid-axis, the pinv uses the center of the circle as the point of reflection, so that each x-coordinate of a dot is "crossed over" the center of the circle and is diametrically opposite to it's starting point.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv1-0.png|100px|thumb]]
||
[[File:Pinv1-20.png|100px|thumb]]
||
[[File:Pinv1-50.png|100px|thumb]]
||
[[File:Pinv1-75.png|100px|thumb]]
||
[[File:Pinv1-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 0)
|}

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:Pinv2-0.png|100px|thumb]]
||
[[File:Pinv2-25.png|100px|thumb]]
||
[[File:Pinv2-50.png|100px|thumb]]
||
[[File:Pinv2-75.png|100px|thumb]]
||
[[File:Pinv2-100.png|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 0%, step = 1/360)
|}

If the base figure is a circle, a transformation from pinv = 0% to pinv = 100% will be similar to a horizontal reflection of the figure in the y-axis. However, if a pinv transformation is applied to the figure, e.g. when step = 1/360 then the pinv mirroring is much more complex. Initially the shape looks like a tooth, which gradually turns out to form an arc (25%), then a wave (50%), and eventually the line ties a knot on itself (75%) and ends as a loop (100%).

As attractive as this reflection can be, it is equally unpredictable. In comparison to a yinv transformation that just squeezes the figure and straightens it out in a mirrored form, the results of pinv are harder to anticipate, even though the transformation is mathematically consistent.

To understand the complex mirroring, one must also look at the ''step'' which is the last of the parameters. Unlike yinv and pinv, step is not based on a mirror, but on the principle Whitney calls "differential motion". In ''Digital Harmony'', he illustrates this by drawing a line of 60 dots. He labels these dots from left to right (so they are called 1,2,3 ... 60), and then tells the computer that for each "step" in the animation, each dot must move upwards by a number of pixels corresponding to the dot's number. While the dots are on a horizontal line at step # 0, the dots on the right will gradually move up faster, making the line animated to appear skewed at ever increasing speed (Whitney: 48-49).

{| class="wikitable"
|-
! step = 0 !! step = 1 !! step = 2 !! step = 3 !! step = 4
|-
|
[[File:line0.png|100px|thumb]]
||
[[File:line1.png|100px|thumb]]
||
[[File:line2.png|100px|thumb]]
||
[[File:line3.png|100px|thumb]]
||
[[File:line4.png|100px|thumb]]
|-
|colspan="5"|Example of "differential motion" based on a line (cf. Whitney: 50)
|}

In such "differential motion", the dots initially line up. At step = 1, dot # 1 has moved 1 pixel up, dot # 2 has moved 2 pixels up, etc. up to dot # 60 which has moved 60 pixels up. At step = 2, dot # 1 has moved 2 pixels up compared to the starting point, dot # 2 has moved 4 pixels up, and dot # 60 has moved 120 pixels up. Continuing this line, at step = 4 dot # 1 has moved 4 pixels up (1 * 4), while dot # 60 has moved 240 pixels up (60 * 4).

As the figure above shows, we do not perceive these movements as individual dots moving - we perceive the dots as a coherent figure, as if it is a line that is gradually tilting and extending.

In ''Arabesque'', Whitney applies the same principle to the circle figure. Having already numbered the dots in the circle, he programs dot # 1 to move 1 pixel to the right of each step, dot # 2 to move 2 pixels to the right of each step, and so on, until dot # 360 that moves 360 pixels to right for each step.

As the dots will quickly move beyond the edge of the screen as they move to the right, Whitney adds a modulus function to each dot, meaning that if the computer calculates a an off-screen position for a dot, it jumps to the left edge of the screen and continues to the right again (ibid: 97). This principle can e.g. can be seen in the figure below, where the figure cuts the edge by 50%, but appears on the left side. Here's how it goes on for 75%, up to 100%, where half of the figure has crossed the edge of the screen and now forms a "tooth" figure.

{| class="wikitable"
|-
! step = 0/360 !! step = 1 * 25% !! step = 1 * 50% !! step = 1 * 75% !! step = 1 * 100%
|-
|
[[File:step1-0.png|100px|thumb]]
||
[[File:step1-25.png|100px|thumb]]
||
[[File:step1-50.png|100px|thumb]]
||
[[File:step1-75.png|100px|thumb]]
||
[[File:step1-100.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 1/360 (yinv = 0%, pinv = 0%)
|}

In the last frame of the table, each dot has moved an amount that corresponds to one step. In other words, dot # 1 has moved 1 pixel to the right, dot # 2 has moved 2 pixels to the right, and dot # 360 has moved 360 pixels to the right.

Note that while the tables showing the differential motion of the line has a distance of 1 step between each frame, the Arabesque circle requires a much lower increase in order for us to perceive the change between the frames as a single movement. If I only showed the first and last frames, few would be able to figure out how the movement between them is going - and this problem only increase if we continue to change the step parameter by an increase of 1:

{| class="wikitable"
|-
! step = 0/360 !! step = 1/360 !! step = 2/360 !! step = 3/360 !! step = 4/360
|-
|
[[File:Step3-0.png|100px|thumb]]
||
[[File:Step3-1.png|100px|thumb]]
||
[[File:Step3-2.png|100px|thumb]]
||
[[File:Step3-3.png|100px|thumb]]
||
[[File:Step3-4.png|100px|thumb]]
|-
|colspan="5"|steps from 0/360 to 4/360 (yinv = 0%, pinv = 0%)
|}

I have chosen to list the whole step value as numbers between 0/360 and 360/360. This notation should reflect that after 360 steps, the differential motion of the circle will cause each dot to be displaced so much that they occupy their original position on the screen. This is comparable to a clock where all three hands point to twelve when it is midnight. During the day, they will move around the disc at different speeds, but after 12 hours they will point to twelve again. Similarly, step = 360/360 corresponds to step = 0/360, where all dots have run through a full cycle at least once. Dot # 1 is the slowest and has only completed one cycle. Dot # 2 will be the second-slowest and has completed two cycles. And finally, Dot # 360 will have completed 360 full cycles. (Whitney: 98)

Because the program requires only numeric values to generate output, there are no signal inputs, but only parameters in this algorithm. We can summarize its algorithm with this diagram, also including x and y position to move the circle and radius to change the size:

[[File:Arab-chart01.png|thumb|center]]

== Variations over the algorithm ==
Appropriately, the opening scene in ''Arabesque'' also serves as an introduction to the algorithm's behavior. First, the step goes from 0 to 1/360, while the y-inv from the start is set to 100%. Then pinv goes from 0 to 100%. Step from 1/360 to 2/360. And y-inv from 100% to 0%. While this last movement is midway and the circle is compressed, a new, vertically mirrored figure emerges above the first one that performs the same movements synchronously. Together they now play the same sequence in reverse - step from 2/360 to 1/360, pinv from 100% to 0% and step from 1/360 to 0/360 - whereby the two figures simultaneously fold in to form two circles that lie on top of each other.

The scene is like an exposition that presents the shape to the viewer and demonstrates it's algorithmic behavior based on the three basic parameters. We can already see how Whitney not only uses an algorithm for the shapes in his animation, but also animates the shapes algorithmically.

In the following sections, however, he does not adhere to the simple operations. Instead, he lets the circle - now in a horizontally stretched variation - do a sprint by the step parameter that dissolves the contiguous line of the circle, letting the dots run into a frantic flicker. Just before the circle gathers, a new circle emerges and sets off, resulting in a kind of musical canon of voices repeating the same melody line.

Subsequently, Whitney continues this musical exploration of the algorithm's simple theme. In the next section, several circles with slightly delayed temporal offsets form a new canon in which they perform the same composite choreography: They set off in motion, and are multiplied into five circles when they return to start. They rotate a few times, set off again, and eventually gather in one circle, and then gradually disappear. In the next section, the shapes are even freer animated, forming little trajectories in the image at intersections, running in different sizes, colors, directions and tempi. Especially in this section, the title's arabesque connotations become obvious, resembling the shapes and motifs of an Islamic rug.

In the film's climax, the circle returns to its round starting point at the top of the screen in a slightly diminished size. It slowly transform the step parameter from 0/360 to 1/360, whereupon a new, skewed circle appears diagonally below it. The new circle performs the same movement and is then supplemented by another new, skewed circle until 5 circles (unfolded to 1/360) form a five-club in the center of the screen.

[image?]

Then all 5 circles' pinv parameters are animated synchronously to 100%, where the configuration along the way resembles 5-pointed star and eventually a buttercup. Then the step parameters change from 1 to 2, and a whirl appears within the flower, swapping the space of their leaves, and forming a new pointed-leaf flower. With a y-inv transformation, the flower collapses, but stops halfway just when it forms a pentagon and the sequence is played backwards.

{| class="wikitable"
|-
! 0% !! 25% !! 50% !! 75% !! 100%
|-
|
[[File:2-1.png|100px|thumb]]
||
[[File:2-2.png|100px|thumb]]
||
[[File:2-3.png|100px|thumb]]
||
[[File:2-4.png|100px|thumb]]
||
[[File:2-5|100px|thumb]]
|-
|colspan="5"|pinv from 0% to 100% (yinv = 100, step = 1)
|}

{| class="wikitable"
|-
! step = 1/360 !! step = 1/360 + 25% !! step = 1/360 + 50% !! step = 1/360 + 75% !! step = 1/360 + 100%
|-
|
[[File:3-1.png|100px|thumb]]
||
[[File:3-2.png|100px|thumb]]
||
[[File:3-3.png|100px|thumb]]
||
[[File:3-4.png|100px|thumb]]
||
[[File:3-5|100px|thumb]]
|-
|colspan="5"|steps from 1 to 2 (yinv = 100%, pinv = 100%)
|}

Because the circles only have to go from step = 1 to step = 0, they do this in a slightly delayed canon where each shape disappears just as it forms a circle again.



== Animation ==
In animating the algorithm in the film, Whitney also uses other techniques, such as changing the positions, sizes and proportions of the figures (using the x, y and r parameters). In addition, he uses spatial amplification, where multiple of the same figure are seen synchronously side by side, and he rotates the figures to form a flower at the climax. With these techniques, Whitney manages to turn the simple theme of the Arabesque algorithm into a varied and expressive animation film.

Furthermore, we should also note that he makes tempo changes and often let's the dots condense into configurations of other shapes than just the circle. As we saw above, the gap is too wide if you increase the step value from 1/360 to 2/360 to see the movement, and the selection of tempo is therefore crucial, as Whitney hereby can structure the algorithm for a human recipient. In this way, he performs a necessary supplement to the machine, which does not know when the viewer perceives a movement rather than a jump or just a standstill.

This relationship is a central theme in Whitney's poetics in uniting visual and musical expression in a complementary relation. In addition to the aforementioned "differential motion", "harmony" is another concept of musical strategies that he explores. The term relates to his early films, such as ''Permutations'', which, like ''Arabesque'', consisted of a series of dots that occasionally condense and form perceptibly stable configurations using a geometric rose curve algorithm. Here the harmony consists precisely in "the dynamics of graphic pattern arrays" (ibid: 42), which he calls the moving dots that sometimes form stable patterns. These works, Whitney believes, create a sense of tension and relaxation when stable patterns suddenly appear or gradually emerge and disappear. In this way, they form a "graphic "scale"", which is modeled on musical harmony, where some tones are grouped into scales because they sound good to the human ear, and can create excitement by perceptually attracting and repelling each other. Similarly, Whitney sees in his film machines: "a diversity of rise and fall of tension, of highs and lows of tension, and a metrical rhythm and order" (ibid: 44)

[examples of condensed dots in the flicker?]

Here we can not go into further depth regarding the harmonies implemented in Arabesque and how they are arranged temporarily in the sequences. Instead, we will pursue the interesting point regarding the use of the algorithm, namely that there is a significant difference between the perceptual and substantive experience of the algorithm's graphical output. On the one hand, the human recipient perceives by the laws of perception and can only see patterns in the Arabesque flicker in the certain cases when it forms a recognizable or rather perceptually stable pattern. We can see how the algorithm's output makes ''appearances'' for the human eye. On the other hand is the machine that interprets all the screen outputs according to the algorithm that produced them. The film ''Arabesque'' is, in other words, a substantial imprint of both the algorithm and it's parametric values. This substantive understanding of the film does not see the screen output as appearances of patterns, but as an indexical imprint of the algorithm. If the computer already knows the algorithm, it can analyze what values the parameters were set to for that particular frame at the moment of creation. We could even imagine that a computer (and perhaps also a human) would be able to calculate the underlying algorithm if only the final film was given, by reverse engineering the geometry based on the work's figures and movement patterns.

By letting a software program draw the connections between the dots of the pattern (i.e. from dot # 1 to dot # 360) we see the difference between a substantial and perceptual interpretation, when we compare this to how a human might perceive the design of the dots in pattern:

[table]
Human vs. machine:
An example of a figure in Arabesque
(step = 44, pinv = 0%, yinv = 0%)

Between the perceptual/human and substantial/machine poles of the algorithm, the artist stands as a mediator. In some cases, film machines are used for a narrative function where they simply have to be decorative, draw a circle, etc. But in some works, the film technician may use and explore the film machine algorithmically like Whitney has done. Here, there is a crucial accentuation of the substantive pole, but a successful musicalization of a film machine's algorithm requires an understanding of both perception and substance.

In the following two chapters we will see how two other artists use their film machine in an algorithmic practice, where the substantial also plays a crucial part in the works. The relationship between perceptual and substantial understanding will be further unfolded in the conclusion.

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