The program that generates all these pictures has a long geneology of lesser programs, dating back almost 10 years. These started out as 2-D attractor drawing programs which drew Henon attractors, so these programs tended to have "henon" in their name. Three to four years ago, I mada a version of this program to produce high-resolution renderings of various 2-D attractors, to be printed on my laser printer.
At about the same time, I visited a friend's house, and one of the other people living there was an artist who was stongly influenced by the art of Roger Dean (the Yes album covers...). He had some sketches on the wall that he had done of abstract objects that I thought looked amazingly similar to some of the attractors I had been generating, except that his drawings were of 3-D objects.
This caused me to think about how to do 3-D attractors. I had recently bought Pickover's "Computers, Pattern. Chaos and Beauty", which had an equation for a 3-D attractor, so I modified the above-mentioned program to handle this 3-D attractor (the name stayed "henon", now called "henon3d", although the attractor was no longer henon).
white gray gray black
This gave the illusion of the sphere shaded with lightsource to the upperleft. I also placed the gray and black pixels at a slightly larger depth than the white pixel, so that when a bunch of "spheres" overlapped to produce a smooth surface, the surface would look smooth, otherwise the most recently calculated points would seem to sit on top of the previous points instead of blending into the surface.
I called the outputs of this program "henon3dh1", "henon3dh2", etc. (the "h" meant "shaded")
1 0 0 -1(scaled by some appropriate factor)
I first tried this by generating an image of the Z-buffer, with intensity representing height, and using the "Custom" filter in Photoshop to perform the convolution. This worked, but to get a satisfactory illusion of depth, the 8 bits used to represent depth were unsatisfactory, because the 256 discrete depths were visible in the picture, as if it had been sliced up and stacked together again. So I instead wrote some code to do the same calculation on the original floating-point Z-buffer data. These pictures were surprisingly good.
As a side note, I later realized that the above shading did not have to be a post-processing step. The image could be calculated at the same time the zbuffer was being filled: since each Z-buffer value affects only two pixels (see the convolution kernel above), each time a Z-buffer value is changed, the two pixels it affects can be recalculated (simply a subtraction and scaling for each pixel). This because my standard preview method (used when selecting parameters and viewpoint).
I called the pictures calculated using this method "fsh1", "fsh2", etc. for "Floating-point, SHadows".
The program was now essentially in the state it is in now: the program that calculated all the pictures on the previous page. Recent additions have been minor compared to how the prgram was before (new attractors, upgraded lighting model, pathetic attempts at a user interface, etc.).
I soon decided to try other attractors, especially when I found Sprott's book. Thus I had to name the pictures of attractors which used the other equations "chaos", "julia", etc. But I kept the name "fsh" for the attractors which used the original formula, a very small variation on the formula in Pickover's book. So I call those attractors "fsh".