MergeLife

Evolving Continuous Cellular Automata for Aesthetic Objectives

Jeff Heaton

Abstract: We present MergeLife, a genetic algorithm (GA) capable of evolving continuous cellular automata (CA) that generate full color dynamic animations according to aesthetic user specifications. A simple 16-byte update rule is introduced that is evolved through an objective function that requires only initial human aesthetic guidelines. This update rule provides a fixed-length genome that can be successfully optimized by a GA. Also introduced are several novel fitness measures that when given human selected aesthetic guidelines encourage the evolution of complex animations that often include spaceships, oscillators, still life, and other complex emergent behavior. The results of this research are several complex and long running update rules and the objective function parameters that produced them. Several update rules produced from this paper exhibit complex emergent behavior through patterns, such as spaceships, guns, oscillators, and Universal Turing Machines. Because the true animated behavior of these CA cannot be observed from static images, we also present an on-line JavaScript viewer that is capable of animating any MergeLife 16-byte update rule.

Heaton, Jeff. "Evolving continuous cellular automata for aesthetic objectives." Genetic Programming and Evolvable Machines (2018): 1-33. https://doi.org/10.1007/s10710-018-9336-1

Useful Links

• JavaScript Demo
• Binary Downloads

HeatonCA App

HeatonCA is the MergeLife application, built with Unity for iPhone, iPad, macOS, Android, Windows, and the web; its source is in unity/heaton-ca. The app animates any 16-byte MergeLife update rule in full color, offers a gallery of thirty curated rules, decodes a rule into the eight sub-rules that define it, and runs the genetic algorithm of the paper on the device, so new rules can be evolved and saved as PNG images. The app carries a C# copy of the MergeLife engine that replays this repository's conformance vectors, so a rule produces the same lattice in the app as it does in the other implementations here.

Get HeatonCA:

• Apple App Store - iPhone, iPad, and Mac, all on the one listing
• Microsoft Store - Windows 10/11
• Google Play - Android

More about the app:

• HeatonCA user manual
• Building HeatonCA from source
• Binary Downloads, which says what has shipped on each platform

Reference MergeLife Implementations

• MergeLife in JavaScript
• MergeLife in Java
• MergeLife in Python

MergeLife in 3rd Party Software

• Visions of Chaos