Glider Dynamics on the Sphere: Exploring Cellular Automata on Geodesic Grids
This paper describes the dynamics of mobile structures (gliders) in 2D cellular automata (CA) on geodesic grids. 2D CA are typically arranged on regular grids with periodic boundary conditions – equivalent to the topology of a torus. This paper describes an alternative topology – the sphere, with an underlying agenda to better understand natural closed systems. The positive curvature of the sphere as manifested in geodesic grids is described as a rich environment for CA. The necessary grid discontinuities are accepted as integral components of the environment. They are not considered as defects but rather as environmental features to be exploited. To explore the potential for a uniquely spherical computational space, a novel XOR gate built on Conway’s Game of Life is demonstrated, utilizing the double-crossing of glider paths following geodesic great circles.
Keywords: glider, geodesic grid, sphere curvature, topology, torus, logical gate, XOR, polyhedra, irregular grid