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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