2010/01/01 by Nathaniel Johnston · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Automaton #Block cellular automaton #Cellular Automata and Applications #Cellular automaton #Chaotic #Combinatorics #Computer science #Diagonal #Discrete mathematics #Geometry #Lattice gas automaton #Mathematics #Mobile automaton #Natural number #Nonlinear Dynamics and Pattern Formation #Stochastic cellular automaton #Theoretical and Computational Physics #Theoretical computer science #nlin.CG
paper · pdf · doi:10.1007/978-1-84996-217-9_7
published as Springer-Verlag, 2010, pp. 99-114 · 18 pages, 19 figures
openalex publication_date 2010/01/01 · arxiv created 2012/03/07 · arxiv updated 2012/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence 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, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2m(2k - 1) for any integers m,k ≥ 1.