2005/03/31 by Marcus Pivato · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algorithm #Cellular Automata and Applications #Cellular automaton #Combinatorics #Conjecture #DNA and Biological Computing #Euclidean geometry #Geometry #Infinity #Limit (mathematics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #math.DS #msc:37B15 #msc:68Q80
paper · pdf · doi:10.1016/j.tcs.2006.11.019
published as Theoretical Computer Science, 372 (#1), March 2007, pp. 46-68 · 22 pages, 3 figures. Final Version
openalex publication_date 2006/12/03 · arxiv created 2007/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let A:=0,1. A `cellular automaton' (CA) is a shift-commuting transformation of AZD determined by a local rule. Likewise, a `Euclidean automaton' is a shift-commuting transformation of ARD determined by a local rule. `Larger than Life' (LtL) CA are long-range generalizations of J.H. Conway's Game of Life CA, proposed by K.M. Evans. We prove a conjecture of Evans: as their radius grows to infinity, LtL CA converge to a `continuum limit' Euclidean automaton, which we call `RealLife'. We also show that the `life forms' (fixed points, periodic orbits, and propagating structures) of LtL CA converge to life forms of RealLife. Finally we prove a number of existence results for fixed points of RealLife.