Cosmos3d1.0

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). The limit of this fractal pattern itself would be completely unviewable, even in principle, so it's just as well that it gets stopped at some point.
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.