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

  • Nathaniel Johnston


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 2×2 blocks are analyzed and used to show that there exist oscillators with period 2 (2 k −1) for any integers k,≥1.


Cellular Automaton Speed Limit Birth Condition Block Partition Alive Cell 
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© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada

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