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".

Iteration:

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