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Conway's Game of Life is a near-critical metastable state in the multiverse of cellular automata. | LitMetric

Conway's Game of Life is a near-critical metastable state in the multiverse of cellular automata.

Phys Rev E Stat Nonlin Soft Matter Phys

Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, São Paulo, Brazil.

Published: May 2014

Conway's cellular automaton Game of Life has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. Life's mean-field return map predicts an absorbing vacuum phase (ρ = 0) and an active phase density, with ρ = 0.37, which contrasts with Life's absorbing states in a square lattice, which have a stationary density of ρ(2D) ≈ 0.03. Here, we study and classify mean-field maps for 6144 outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that Life is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, Life is not at the "border of chaos," but thrives on the "border of extinction."

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Source
http://dx.doi.org/10.1103/PhysRevE.89.052123DOI Listing

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