RealLife: the continuum limit of Larger than Life cellular automata

摘要

Let A := {0, 1}. A cellular automaton (CA) is a shift-commuting transformation of A{sup}Z{sup}D determined by a local rule. Likewise, a Euclidean automaton (EA) is a shift-commuting transformation of A{sup}R{sup}D 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' EA, 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.