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.
Highlights
First introduced by Conway [1], the ‘game of life’, a cellular automaton algorithm proposed to simulate real life patterns with simple rules, quickly drew the attention of scientists in various fields [2,3,4,5]
We simulate a game of life following non-local rules on an aperiodic grid, the Penrose tiling [9], a two-dimensional quasicrystal (QC)
We review below some key concepts used by the cut-and-project method and we give a graphic example in Figure 1 for a simple case, the LS configuration, a vertex type in the Fibonacci chain
Summary
First introduced by Conway [1], the ‘game of life’, a cellular automaton algorithm proposed to simulate real life patterns with simple rules, quickly drew the attention of scientists in various fields [2,3,4,5]. We simulate a game of life following non-local rules on an aperiodic grid, the Penrose tiling [9], a two-dimensional quasicrystal (QC). The special properties of quasicrystals, their aperiodic order and their non-local nature dictated from higher dimensions [13], make them an interesting research subject not just in the field of material science, but in many other fields, including more recently quantum computing They are an interesting candidate for modeling game of life algorithms. We simulate and track the evolution of this configuration, dynamically, in several scenarios, finding patterns like rotations, quasi-translations and oscillations These patterns are dictated by the interaction of the quasiparticle with its own empire field, a self-interaction.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
