I'm trying to think of an elegant way to draw Sierpinski Triangles,
perhaps using my screensaver library (see ~kfogel/screensavers/).

        Here's what I've got so far:
--------------------------------------------------------------------------

TRIANGLE (A, B, C)  =>  draws a triangle with corners A, B, C.
                        (Each var is a struct point { int x, y };).

MIDPOINT (N, M)     =>  returns the midpoint of line from N to M.
                        (Each var is a struct point { int x, y };).


        Let us call the number of iterations the "depth" of the
triangle.  So a triangle with a depth of 0 contains 3 lines/1
triangle, a depth of 1 implies 6 lines/5 triangles, depth 2 implies 15
lines/14 triangles... hmm, let's make a table:

depth          triangles          lines
-----          ---------          -----
0                  1                3
1                  5                6
2                 14               15
3                 50
4
5
6

        One triangle becomes five triangles on the next iteration, if
it gets divided, and three out of four triangles *do* get divided.

1
3
6
10
15
21
28