The messy red path in the picture is a “loop-erased random walk” on the Sierpinski triangle, a very famous fractal.

Stochastic processes like this one are of interest to researchers working in fractal analysis, probability theory, combinatorics, and mathematical physics. The path was generated by first constructing a random spanning tree (black); at our level of approximation, there were about 5.19 * 10^4480 such spanning trees to pick from (the number of atoms in the observable universe is only about 10^80) – a typical case of “combinatorial explosion”.

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