Example 7.  Morphological Stability in Anti-Color and Super-Color Diffusion

The 40-frame animated gif shown (7.1) below was produced by anti-color and super-color effects (similar to Example 6) from a single tuple of three numbers picked from a set of four numbers: {-9.01,-1.,4.5, 9.0}, i.e., 64 possibilities aligned as color guns on perpendicular axis.  With the extreme range of negative (-9) and positive (+9) numbers in the resultant 64 RGB triples, the initial image is black (i.e., all colors lie outside of the visible 0-1 R, G, B ranges.  However, after a few frames of averaging with a 3 x 3 convolution kernel (all elements are 1/9), real color begins to develop.

After real color has developed in the first few frames of this animated gif, some 'evolution' of the image occurs until about half way through the loop at frame number 20.  From approximately frame 20 through the end of the animation (frame 40), there is very little change in the morphology of the triangular-shaped hierarchy of structures.  Although the (averaging) convolution of the 3x3 kernel is still running, the morphology appears to have reached a stasis or equilibrium in which anti-color and super-color continue to create real color that is not averaged to grey, as expected.  This finding is somewhat perplexing and more study is needed for a fuller explanation of this phenomenon.  We are fairly certain that the code is correct, as it has been independently written three different times.  The convolution code is almost identical to the next example in which diffusion is clearly seen, albeit with a larger kernel.

Source code is given here in .nb and .PDF formats.  The PDF file has high resolution images for all 40 frames of the diffusion.