A Universal Semi-totalistic Cellular Automaton on Kite and Dart Penrose Tilings

In this paper we investigate certain properties of semi-totalistic cellular automata (CA) on the well known quasi-periodic kite and dart two dimensional tiling of the plane presented by Roger Penrose. We show that, despite the irregularity of the underlying grid, it is possible to devise a semi-totalistic CA capable of simulating any boolean circuit on this aperiodic tiling.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

The Game of Life on the Robinson Triangle Penrose Tiling: Still Life

We investigate Conway's Game of Life played on the Robinson triangle Penrose tiling. In this paper, we classify all four-cell still lifes

Empires: The Nonlocal Properties of Quasicrystals

In quasicrystals, any given local patch—called an emperor—forces at all distances the existence of accompanying tiles—called the empire—revealing thus their inherent nonlocality. In this chapter, we review and compare the methods currently used for generating the empires, with a focus on the cut-and-project method, which can be generalized to calculate empires for any quasicrystals that are projections of cubic lattices. Projections of non-cubic lattices are more restrictive and some modifications to the cut-and-project method must be made in order to correctly compute the tilings and their empires. Interactions between empires have been modeled in a game-of-life approach governed by nonlocal rules and will be discussed in 2D and 3D quasicrystals. These nonlocal properties and the consequent dynamical evolution have many applications in quasicrystals research, and we will explore the connections with current material science experimental research

Towards aperiodic tesellation: a self-organising particle spring system approach

The derivation of novel programming methods for the generation of aperiodic tiling patterns, predominantly in 2d space, has attracted considerable attention from both researchers and practicing architects. So far L-Systems and quasicrystals are the only tools which can be used for the creation of aperiodic tiling patterns. This project attempts to create a self organizing particle spring system for aperiodic tiling formation on a 2d surface. The proposed method simulates natural dynamic procedures and applies a generative particle spring system for tiling formation. The initial inspiration of the thesis is the realization of tiling patterns for non-planar geometries, by using the previously stated method. The architectural reasoning behind that would be to use a minimal number of types of prefabricated units (e.g. Penrose rhombuses) to create an irregular and complex pattern or geometry