Reia Sandro M, Kinouchi Osame
Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 May;89(5):052123. doi: 10.1103/PhysRevE.89.052123. Epub 2014 May 16.
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."
康威的细胞自动机生命游戏被推测为一个临界（或准临界）动力系统。这种临界性通常被视为细胞自动机（CA）规则空间中的连续有序-无序转变。生命游戏的平均场返回映射预测了一个吸收性真空相（ρ = 0）和一个活性相密度，其中ρ = 0.37，这与正方形晶格中生命游戏的吸收态形成对比，其静止密度为ρ(2D) ≈ 0.03。在这里，我们研究并分类了6144种外全同细胞自动机的平均场映射，并将它们与正方形晶格中发现的相应行为进行比较。我们表明，单点平均场方法对其中大多数给出了定性（甚至定量）预测。规则空间中的转变区域似乎对应于一个非平衡不连续吸收相变，而不是连续的有序-无序相变。我们声称生命游戏是一个准临界成核过程，其中真空相域侵入活性相。因此，生命游戏并不处于“混沌边缘”，而是在“灭绝边缘”蓬勃发展。
