The Sierpiski triangle (also know as the Sierpiski gasket or sieve) is a fractal first described by Sierpiski in 1915. To construct it, draw the outline of an equilateral triangle on white paper. In its middle draw a black upside down triangle with side length 1/3 the side of the original. Now there are 3 small white right side up triangles inside the large one. In the middle of each of these triangles draw a black upside down triangle. Repeat this process for the 9 small white triangle that are left. Continue this process forever to get the Sierpiski triangle.

Here is a way to obtain something that is a lot like Sierpiski's triangle. Start with any object whatsoever. Make three copies of it and place them one of them symmetrically above the other two. Now shrink all three object by half and make...