This is a Sierpinski Gasket drawn using an Iterated Function System. This fractal was originally thought up by W. Sierpinski and predates the Mandelbrot Set. It was originally produced by starting with a triangle, cutting out the middle, and repeating the process infinitely.

In this way, you can see that at each iteration, one quater of
the original triangle is removed. That is, three quaters of the
area of the original triangle is left after the first iteration.
From this observation, it is not hard to infer that after n
iterations, the area of the gasket would be (0.75)^{n}
times the area of the original triangle. So after an infinite
number of iterations, you would find there was no area at all.

Of course, this generator uses an IFS system instead of the above mentioned method, because it gives a beter picture quicker, and this is a demonstration of my IFS applet.

Copyright © 2005 — James Henstridge <james@jamesh.id.au>