Abstract:

The B36/S125 (or “2×2”) 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 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 2×2 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 automaton that 2×2 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^k(2^m – 1) for any integers k, m ≥ 1.

Authors:

• Nathaniel Johnston

Download:

• Official chapter from SpringerLink
• Preprint from arXiv:1203.1644 [nlin.CG]
• Local preprint [pdf]

Cite as:

• N. Johnston. The B36/S125 “2×2” Life-Like Cellular Automaton. In Game of Life Cellular Automata chapter 7, A. Adamatzky, Springer-UK, 99–114, 2010.

Supplementary Material:

• Spaceship Speed Limits in “B3” Life-Like Cellular Automata (blog post)
• Rectangular Oscillators in the 2×2 (B36/S125) Cellular Automaton (blog post)