Square-Triangle Tilings: Lift & Flip to Sample?
Thomas Fernique (HSE, Moscow, Russia), Olga Mikhailovna Sizova, (Semenov Institute of Chemical Physics, Moscow, Russia)
TL;DR
This paper introduces a simple flip transformation on square-triangle tilings and conjectures it can connect any two tilings of the same region, potentially enabling new methods for sampling and transforming tilings.
Contribution
The paper proposes a new elementary flip operation on square-triangle tilings and conjectures its universality in connecting all tilings of a given region.
Findings
Introduction of flip operation on tilings
Conjecture that flips connect all tilings of the same region
Potential implications for sampling and tiling transformations
Abstract
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.
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