# Sierpiński triangles

See Wikipedia. Extract below.

The Sierpiński triangle (sometimes spelled Sierpinski), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.

The production rules for this curve is:

variables : F G constants : + − start : F−G−G rules : (F → F−G+F+G−F), (G → GG) angle : 120°

Here, F and G both mean "draw forward", + means "turn left by angle", and − means "turn right by angle".