Cosmos3d - This program will allow you to visualize a fractal pattern which was used to render a cosmological model
Version: 1.0Cosmos3d was created to visualize a fractal pattern which was used to render a cosmological model by Hoyle mentioned on page 218 of The Fractal Geometry of Nature by Mandelbrot. The pictures in that book are a bit hard to visualize for the 3-d case, hence this program. Also, this was a good project to do some OpenGL/Objective-C/Cocoa coding.
Operating System: Mac OS X
This program does not show a true fractal (technically no fractal program does) but several iterations of a pattern which, if fleshed out, would be a true fractal geometric figure. The iteration depth is controllable, but that depth is set to a low limit based on the video processing power that exists in most computers.
The pattern is formed by having a cube sub-divided into some number of cells (also controllable to some extent), the exact ones of which are determined at random. What you do see are those cubes which have been selected last in the iteration process, and within which the fractal pattern would continue if you let it.
You'll notice that the pattern is harder and harder to see by itself as you let the iteration depth grow (apart from slowing down while your machine tries to render it). This gets stopped at some point because the limit of this fractal pattern is completely unviewable, even in principle.
To see the construction technique, how the program subdivides cubes within cubes, select "subcells." Besides, it's a beautiful effect. (For reasons of how OpenGL does its rendering, showing subcells often speeds up the drawing to the screen.)
You may want to turn off the automatic rotation of the cube and move it by hand to understand better what's going on. From there zoom in and out, and push it around by hand, and you'll really get a feel for the pattern. The "spheres" option was left in the program purely for aesthetic reasons. It has no good correlation to the fractal being studied here.