Flow-Lenia.png: Evolving Multi-Scale Complexity by Means of Compression

TL;DR

This paper introduces a method to quantify and evolve multi-scale complexity in cellular automaton states using compressibility as a proxy, enabling targeted pattern generation and exploration of complexity extremes.

Contribution

It presents a novel fitness measure based on Kolmogorov complexity for evolving cellular automaton patterns with desired complexity levels.

Findings

Evolved patterns match specified complexity targets.

Higher complexity targets produce more intricate patterns.

The method effectively explores the complexity range of Flow Lenia.

Abstract

We propose a fitness measure quantifying multi-scale complexity for cellular automaton states, using compressibility as a proxy for complexity. The use of compressibility is grounded in the concept of Kolmogorov complexity, which defines the complexity of an object by the size of its smallest representation. With this fitness function, we explore the complexity range accessible to the well-known Flow Lenia cellular automaton, using image compression algorithms to assess state compressibility. Using a Genetic Algorithm to evolve Flow Lenia patterns, we conduct experiments with two primary objectives: 1) generating patterns of specific complexity levels, and 2) exploring the extrema of Flow Lenia's complexity domain. Evolved patterns reflect the complexity targets, with higher complexity targets yielding more intricate patterns, consistent with human perceptions of complexity. This demonstrates that our fitness function can effectively evolve patterns that match specific complexity objectives within the bounds of the complexity range accessible to Flow Lenia under a given hyperparameter configuration.