This is a
recipe for your making your own
fractal shape at home. Take a piece of paper (or a patch of computer screen). Pick three points on the paper; these will be the corners of the triangle. Number them 1, 2, 3. Pick any other point on the paper or screen. Now, roll
1d3, or somehow generate a random integer number of 1, 2, or 3 (with equal probability). Make a point at the
midpoint of the
line between your old point and the corner of the triangle indicated by your
random selection. Now use that point as your starting point for the next roll of the die.
Iterate. You will generate a space-filling form of a triangle, with the central quarter removed, and the central quarter removed from each remaining sub-triangle, and so on
ad infinitum. This is one example of an iterated function system. (Other similar designs will generate the image of
fern leaves.)
There is now an implementation of the above algorithm available in PostScript.