The B36/S125 “2x2 ” Life-Like Cellular Automaton

Summary. The B36/S125 (or “2x2”) cellular automaton is one that takes place on a 2D lattice much like Conway’s Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but stable evolution, and the ex-istence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way – for example, it is shown that the speed limits for diagonal spaceships and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular au-tomaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 × 2 blocks are analyzed and used to show that there exist oscillators with period 2`(2k − 1) for any integers k, ` ≥ 1.