Conway's game of life is a near-critical metastable state in the multiverse of cellular automata

TL;DR

This paper investigates Conway's Game of LIFE within the broader context of cellular automata, revealing it as a near-critical, metastable state characterized by a nucleation process on the brink of extinction rather than chaos.

Contribution

The study classifies mean-field maps for over 6000 cellular automata, showing LIFE's unique near-critical metastable behavior as a nucleation process rather than a traditional critical transition.

Findings

LIFE's mean-field predictions align with lattice behavior in many cases.

The transition in rule space appears as a discontinuous phase transition.

LIFE operates on the border of extinction, not chaos.

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."