The exact complexity of a Robinson tiling
Ilya Galanov
TL;DR
This paper derives the precise formula for counting the number of unique n-by-n patterns in a Robinson tiling, revealing detailed combinatorial complexity of this aperiodic tiling system.
Contribution
It provides the first exact enumeration formula for patterns in Robinson tilings, advancing understanding of their combinatorial structure.
Findings
Exact formula for pattern count in Robinson tilings
Quantitative analysis of tiling complexity
Insights into aperiodic tiling pattern diversity
Abstract
We find the exact formula for the number of distinct square patterns which appear in a Robinson tiling made of one infinite order supertile.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Advanced Materials and Mechanics · Cellular Automata and Applications