Complex Systems

A Game of Life Shifted toward a Critical Point Download PDF

Tomoko Sakiyama
Soka University
1 Chome-236 Tangimachi
Hachioji, Tokyo 192-8577, Japan


The Game of Life (GoL), which produces complex patterns of life, has been employed to describe biological systems through self-organized criticality and scale-free properties. This paper develops two novel GoL models. One model allows each cell to update the time for the state update following interactions with other local cells using parameter tuning. Thus, individual cells replace their behaviors from intermittent state updates with continuous ones. The system evolves unpredictably close to a critical point and occasionally close to extinction for the alive population if an adequate parameter is chosen. This event occurs with a power-law tailed time interval and presents synchronous behaviors, since individual cells modify their state-update intervals and create time continuity. The other model is the same except that the system evolves unpredictably without any parameter tuning. In the second model, actions of individual cells are tuned not by a fixed parameter but by the surrounding situation. We found that the GoL system in the second model behaved in a similar manner in the first model, which suggests that that model shifts toward a critical point autonomously.

Keywords: Game of Life; critical point; power-laws; phase transition

Cite this publication as:
T. Sakiyama, “A Game of Life Shifted toward a Critical Point,” Complex Systems, 32(1), 2023 pp. 57–70.