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Crystals 2018, 8(11), 416; https://doi.org/10.3390/cryst8110416

Non-Local Game of Life in 2D Quasicrystals

Quantum Gravity Research, Los Angeles, CA 90290, USA
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Received: 25 September 2018 / Revised: 25 October 2018 / Accepted: 31 October 2018 / Published: 6 November 2018
(This article belongs to the Collection Structure and Properties of Quasicrystals)
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Abstract

On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at all distances, the empires. Considering the emperor and its local patch as a quasiparticle, in this case a glider, its empire represents its field and the interaction between quasiparticles can be modeled as the interaction between their empires. Following a set of rules, we model the walk of life in different setups and we present examples of self-interaction and two-particle interactions in several scenarios. This dynamic is influenced by both higher dimensional representations and local choice of hinge variables. We discuss our results in the broader context of particle physics and quantum field theory, as a first step in building a geometrical model that bridges together higher dimensional representations, quasicrystals and fundamental particles interactions. View Full-Text
Keywords: non-local; game of life; quasicrystals; empires; forced tiles; possibility space; cut-and-project; particle self-interaction; particle interaction; higher dimensions non-local; game of life; quasicrystals; empires; forced tiles; possibility space; cut-and-project; particle self-interaction; particle interaction; higher dimensions
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Fang, F.; Paduroiu, S.; Hammock, D.; Irwin, K. Non-Local Game of Life in 2D Quasicrystals. Crystals 2018, 8, 416.

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