title: Conway's Game of Life is a near-critical metastable state in the multiverse of cellular automata.
abstract: 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."
authors.affiliation: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, São Paulo, Brazil.
authors.forename: Sandro M
authors.initials: SM
authors.lastname: Reia
authors.affiliation: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, São Paulo, Brazil.
authors.forename: Osame
authors.initials: O
authors.lastname: Kinouchi
mesh_terms: D000465:Algorithms; D000818:Animals; D032701:Biomimetics / Q000379:methods*; D002468:Cell Physiological Phenomena; D003198:Computer Simulation; D005716:Game Theory; D006801:Humans; D015233:Models, Statistical