The Arctic Circle

This Markov Chain Monte Carlo simulation converges at large enough times to the uniform distribution over tilings of the hexagon by 60° rhombuses. It has been shown by Cohn, Larsen, and Propp that in the limit of large hexagons, the tiles outside the inscribed circle are frozen, forming an arctic circle

N = redraws =

MC steps per redraw =

show limit shape show means

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