Frequency-Histogram Coarse Graining in Elementary Cellular Automata and 2D CA

TL;DR

This paper explores a coarse-graining method for cellular automata to identify emergent complexity, aiming to understand and facilitate open-ended evolution in AI systems.

Contribution

It introduces a systematic approach to coarse-graining in cellular automata, providing insights into emergent behaviors and their potential role in developing artificial general intelligence.

Findings

Coarse-graining captures emergent complexity effectively.

Different filtering levels reveal various macrostate behaviors.

Method supports analysis of large-scale cellular automata dynamics.

Abstract

Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial intelligence, thanks to their propensity to support properties such as self-organization, emergence, and open-endedness. However, understanding emergent complexity in large scale systems is an open challenge. How can the important computations leading to emergent complex structures and behaviors be identified? In this work, we systematically investigate a form of dimensionality reduction for 1-dimensional and 2-dimensional cellular automata based on coarse-graining of macrostates into smaller blocks. We discuss selected examples and provide the entire exploration of coarse graining with different filtering levels in the appendix (available also digitally at this link: https://s4nyam.github.io/eca88/). We argue that being able to capture emergent complexity in AI systems may pave the way to open-ended evolution, a plausible path to reach artificial general intelligence.