An interesting thing to try is to run the same algorithm as above, except use more than three points. If you run a program with a square, it will just fill up solid. Same with a hexagon. However, any figure with an odd number of sides will give a picture with forbidden areas, much like the triangle does. The area of these forbidden spaces decreases with respect to the total area of the object as you add more and more points. The limit of applying a Sierpinksy type operation to a circle will give a solid circle.

Other fun things to try are fixing the coordinates of two points constant and allowing the third to be some random point within a range of 2-D space. Also try doing four points, where three are the vertices of a triange and the fourth is a point inside the triangle. These all came from a science project I did in highschool many years ago using a Commodore 64 and the LOGO programming language =)