Direct Construction of Aperiodic Tilings with the Hat Monotile
Ulrich Reitebuch
TL;DR
This paper introduces a method for directly constructing aperiodic tilings using the hat monotile, revealing new structures that enable computation akin to Penrose tilings.
Contribution
It presents a novel direct construction technique for aperiodic tilings with the hat monotile, advancing understanding of their structure and computation.
Findings
Discovered structures enabling direct tiling computation
Established parallels with Penrose tilings
Enhanced methods for aperiodic tiling construction
Abstract
In 2023, the quest for an aperiodic monotile was answered by the hat monotile. In this article, structures in this aperiodic tiling are discovered, which allow for a direct computation of the tiling, similar to well-known methods for the Penrose tilings.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Advanced Materials and Mechanics · graph theory and CDMA systems