Pearls

The limit set of a two-generator Moebius group, built from traces tr(a) = 1.91 + 0.05i and tr(b) = 1.91 - 0.05i by solving the Markov identity tab^2 - ta tb tab + ta^2 + tb^2 = 0, which forces the commutator to be parabolic. Reduced words in the two generators are expanded without backtracking, each branch stopping once its map contracts below one output pixel. Every plotted point is an image of the parabolic commutator fixed point, coloured by the leading letter of its word.