Holey hexagons with holes at different heights
Leonid Petrov
What happens if we sample a uniformly random tiling of a hexagon with a hole, but place the hole at different heights? (Thanks to MR for the request to sample these examples.)
Data file format
The data file is a list of lists of lists in Mathematica-readable format, of the form \(\{ \lambda(1),\lambda(2),\ldots,\lambda(T) \},\) where each $\lambda(t)$ is a list of weakly interlacing integer coordinates of the form \(\{ \{ 47,0,0,0,\ldots \},\{ 50,47,0,0,\ldots \} , \{ 50,49,47,0,\ldots \} ,\ldots, \} .\) This list is a square array, and each $\lambda(i)$ is appended by zeroes.
code • (Main GitHub repo)
(note: parameters in the code might differ from the ones in simulation results below)-
https://github.com/lenis2000/Glauber_Simulation/tree/holey-hexagons(python code (Glauber2.py) for simulations, simple Mathematica code (Dynamic.nb) for drawing)
simulation results
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Tiling with a symmetric hole • (data: 57 KB) • (graphics: 8.7 MB)
Hexagon of size 100, hole size 15, shift 0.
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Tiling with a skewed hole • (data: 57 KB) • (graphics: 8.7 MB)
Hexagon of size 100, hole size 15, shift 4.
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Tiling with an even more skewed hole • (data: 57 KB) • (graphics: 8.7 MB)
Hexagon of size 100, hole size 15, shift 8.
