Emergent Dynamics in Heterogeneous Life-Like Cellular Automata

TL;DR

This work addresses the lack of open-ended dynamics in the Game of Life by engineering a heterogeneous life-like cellular automaton with an inner evolutionary loop and an ageing mechanism that decouples aliveness from computation. The authors implement a two-layered substrate where cells carry per-cell life-like rules and age through alive, decay, and quiescent states; rule inheritance and mutations occur locally, expanding genotypic diversity while the Grid State reflects computation under local rules. Through systematic experiments on different ageing budgets and grid sizes, they demonstrate sustained long-term phenotypic dynamics and substantial genotypic innovation, with growth in the number of discovered rules and persistent Grid State fluctuations. The findings highlight the potential of open-ended, ecology-inspired CA substrates for studying evolution-like dynamics and adaptive computation, with future work exploring environmental perturbations and task-based rewards to further drive adaptation.

Abstract

The Game of Life (GoL), one well known 2D cellular automaton, does not typically ensure interesting long-term phenotypic dynamics. Therefore, while being Turing complete, GoL cannot be said to be open-ended. In this work, we extend GoL with the opportunity for local mutations, thus enabling a heterogeneous life-like cellular automaton guided by an evolutionary inner loop. Additionally, we introduce the concept of cell ageing to ensure that cell aliveness (activated by inheritance with variation, and controlled by ageing) and actual cell computation (governed by life-like rules on local neighborhoods) are kept conceptually separated. We conduct an experimental campaign to identify suitable parameters that produce long-term phenotypic dynamics and favor genotypic innovations.

Figures (9)

• Figure 1: States of a glider in Conway's Game of Life
• Figure 2: Life cycle of a cell's Cell State.
• Figure 3: Example of a 3x3 CA substrate, where the genotype is represented by the Transition Rules and the phenotype is composed by three components: Cell Age (a counter), Cell State (alive, decay, quiescent), and Grid State (Boolean cell state representing the ongoing computation).
• Figure 4: Grid Size of 50 $\times$ 50 for 10,000 generations. Averages over 10 runs.
• Figure 5: Grid Size of 500 $\times$ 500 for 1,000 generations. Averages over 10 runs.