Generative art is produced in a similar way to conventional art.
You start with an idea, and then first sketch out the basic implementation of the idea as a simple sketch, which may be elaborated in place, or by starting anew in a number of versions until the final desired effect is achieved.
Hence, when working with the Processing system, each experiment or trial is also known as a sketch. A collection of sketches is a Sketchbook. We will use the term specifically to mean the collection of sketches relating to the development of a particular idea over a number of experiments.
Each of the topics below is covered in more detail in its own page. Here, the intention is just to give an overview of different approaches that I have employed.
Circular Motion
The first Sketchbook that we look at is "Circular Motion" or "Epicycles" - some of you may remember the child's "Spirograph" toy which also produces attractive traces using epicycles. With Processing, however, we can go much further than a mechanical toy, and produce much more complex and visually interesting diagrams.
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Many of my early explorations with Processing are based on tracing a smooth curve, and then drawing repeated motifs around the curve. The "Circular Motion" series, based on superimposed epicycles constrains the basic curve to have a certain degree of symmetry.
Lissajous Curves
Lissajous curves though mathematically related, have more potential variations of form - mathematicians would say "a larger parameter space". In the case of epicyclic curves, for every cosine of a particular frequency using the calculation of the "x" coordinate of a point on a traced curve, there is a sine contribution of the same frequency and amplitude in the calculation of the "y" coordinate. When tracing a Lissajous curve we do not insist on this type of exact pairing - though it is often to the case that we will look at cases where the ratios of the frequencies used to control the x and y coordinate values on the traced curve will have a simple relationship to each other - such as 3:4 or 5:7 and so on.
The "Waves" series explores various simple forms of the basic Lissajous curve, drawing repeated motifs at each point on the traced curve, which motif is itself also based on a wave form. The form is simpler earlier in the series, and become more complex later.
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Although in this series I have chose only to exploit a wave motif it would be interesting to explore the use of other motifs in combination with these curves.
Chaotic Motions
The explorations of Lissajous Curves - drawing wave motifs emerging from an underlying trace based on regular oscillations in horizontal and vertical directions - suggested that it might be interesting to use a trace based on Chaotic Dynamics, that is a deterministic (i.e. exactly repeatable) evolution that is nevertheless highly sensitive to initial conditions and never repeats. While the outcomes appear distinctly less well ordered there are also patterns of change because the motions are constrained by analogies with physical laws.
The image set below uses exactly the same chaotic evolution algorithm as those above, but with some additional variation of the motifs used at each point on the traced curve.
There are more images in this Gallery page
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Rosette Transformations
The Complex Maps page describes methods of transforming an image on one 2D plane into an image on another 2D plane, treating the pixels of both images as addressed by complex numbers in the Argand/Wessel plane, and the transformation as a, generally, analytic complex function.
The source images, in some of the examples shown in the image slider are simple patterns defined by a trivial mathematical algorithm (for example a regular grid of alternating colours). The following two series of images are from Processing sketchbooks in which the algorithms are based on the "Rosette Transformation" discussed by Frank Farris in his "Creating Symmetry" book.
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We can, however, use source material such as real photographs. What we see is a mathematical transform of the image to induce elements of symmetry. One can either go for strict symmetry or introduce various amounts of asymmetry (which, in my opinion, are ultimately more interesting).
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Also interesting is applying the rosette transformation to original drawings, from my recent life class exercises. Once again, the most intriguing are those which are on the verge of recognisability.
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In some of the above images, I find that the most intriguing are those in which the original image just on the verge of being recognisable, one is not quite sure whether the image is completely abstract or distorted reality.
Use of "Wallpaper" Groups
An exploration of symmetries of patterns on the plane (also known as "Wallpaper Groups") is dealt with on the Wallpaper Symmetries page. The examples below deal only with one symmetry group. More complex symmetries will be investigated as time permits, hopefully covering the full 17 groups. As with earlier
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The Mandelbrot Set
I could not resist doing some image creation around the Mandelbrot set. This is a method of image generation that is somewhat over exercised on the Internet, but is nevertheless worth a look because the techniques open the door to some more interesting and less familiar ways of building abstract images based on fractal geometry.
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In all the galleries above, I am exploring one particular type of technique. It may well be that future work will be based on combinations of the various areas investigated. Further ideas I intend to explore at some point include , random fractals, and virtual 3D sculptures. I still have to learn some of the maths.
Then, of course, there is the entire field of dynamic images at which Processing excels - I have not yet take a close look at this area, though my "Video from Processing" page looks at a rather different approach to creating dynamic images.