Post #3016949

As a follow up to last week's post on Markov partitions for Hat (hat and turtle) and Spectre (hats in turtles and turtles in hats) tilings (https://mathstodon.xyz/@pieter/116484517078239617), here is a way of colouring such tilings. For each control point, we colour the tile according to its distance from the boundary of the fractal window it lies in. The first image shows a patch of a turtle tiling using the colour map in the second. Control points that lie near the boundary of the fractal window are close to flipping between the two states of a Conway worm, so this is a nice way of highlighting subsets of tiles that are 'close' to being Conway worms. One of the things on my to-do list is to create an animation of a patch as the triangular grid moves slowly relative to the underlying pattern, but if anyone wants to take a stab at this, please do. (1/2) #TilingTuesday #AperiodicMonotile