Distortion Reversal in Aperiodic Tilings
Louisa Barnsley, Michael Barnsley, Andrew Vince
TL;DR
This paper proves that certain aperiodic tilings remain recognizable under homeomorphic transformations, enabling the detection of distorted aperiodic structures in natural settings.
Contribution
It establishes the recognizability of homeomorphic images of specific aperiodic tilings, extending understanding of their structural properties.
Findings
Homeomorphic images of Ammann-A2 tilings are recognizable.
Recognition applies in both mathematical and practical contexts.
Potential to identify distorted aperiodic structures in nature.
Abstract
It is proved that homeomorphic images of certain two-dimensional aperiodic tilings, such as Ammann-A2 tilings, are recognizable, in both mathematical and practical senses. One implication of the results is that it is possible to search for distorted aperiodic structures in nature, where they may be hiding in plain sight.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Cellular Automata and Applications · Mathematics and Applications