Gliders in Cellular Automata on Penrose Tilings
Adam P. Goucher
In this paper, we present the first glider capable of navigating an aperiodic tiling. It inhabits a four-state outer-totalistic cellular automaton, and operates on generic tilings of quadrilaterals. We investigate its behaviour on both the P2 (kite and dart) and P3 (rhombus) Penrose tilings, and characterise the different types of path it can follow. Further, we note that the path followed by the glider on the P2 tiling is a fractal curve generated by a simple Lindenmayer system, and compute its Hausdorff dimension.
Keywords: Penrose tiling, gliders, tessellations, fractals, L-systems