Selecting Continuous Life-Like Cellular Automata for Halting Unpredictability: Evolving for Abiogenesis

TL;DR

This paper introduces a method for evolving continuous cellular automata that support complex, unpredictable patterns like gliders, demonstrating the discovery of new CA with diverse dynamics and providing open-source code for reproduction.

Contribution

The work presents a novel two-step evolution strategy for continuous CA that promotes complex, unpredictable behaviors, and rediscoveries of gliders in Lenia CA with new variants.

Findings

Successfully rediscovered gliders in all tested Lenia CA

Evolved 4 new CA supporting novel glider patterns

Evolved CA exhibit a wider range of dynamics than Lenia counterparts

Abstract

Substantial efforts have been applied to engineer CA with desired emergent properties, such as supporting gliders. Recent work in continuous CA has generated a wide variety of compelling bioreminiscent patterns, and the expansion of CA research into continuously-valued domains, multiple channels, and higher dimensions complicates their study. In this work we devise a strategy for evolving CA and CA patterns in two steps, based on the simple idea that CA are likely to be complex and computationally capable if they support patterns that grow indefinitely as well as patterns that vanish completely, and are difficult to predict the difference in advance. The second part of our strategy evolves patterns by selecting for mobility and conservation of mean cell value. We validate our pattern evolution method by re-discovering gliders in 17 of 17 Lenia CA, and also report 4 new evolved CA and 1 randomly evolved CA that support novel evolved glider patterns. The CA reported here share neighborhood kernels with previously described Lenia CA, but exhibit a wider range of typical dynamics than their Lenia counterparts. Code for evolving continuous CA is made available under an MIT License (https://github.com/rivesunder/yuca).