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 ($\rho =0$) and an active phase density, with $\rho =0.37$, which contrasts with LIFE's absorbing states in a square lattice, which have a stationary density ${\rho }_{2D}\approx 0.03$. 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."

References in corpus (4)

• Higgs mass and vacuum stability in the Standard Model at NNLO
• Investigating the near-criticality of the Higgs boson
• Self-organization without conservation: true or just apparent scale-invariance?
• On the robustness of scale invariance in SOC models

Cited by in corpus (6)

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