Regular Article: Cellular Automaton Growth on Z2: Theorems, Examples, and Problems
Advances in Applied Mathematics
Probability Theory: An Analytic View
Probability Theory: An Analytic View
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
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Let A@?{0,1}. A cellular automaton (CA) is a shift-commuting transformation of A^Z^^^D determined by a local rule. Likewise, a Euclidean automaton (EA) is a shift-commuting transformation of A^R^^^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.