Visualizing the Structure of Lenia Parameter Space

2026-01-05

AI Summary

This study addresses the lack of a systematic understanding of soliton definitions, the global structure of the parameter space, and their distribution regions in the continuous cellular automaton Lenia. To this end, the work proposes an automated classification method that categorizes Lenia’s dynamical behaviors into four distinct classes, effectively identifying mobile solitons. An interactive visualization platform for the parameter space is also developed, enabling structured exploration. The approach reveals multiple previously unknown regions harboring new soliton families and demonstrates that the phase-space structure exhibits universality across different kernel functions. These contributions provide both a novel computational tool and deeper insights into self-organizing patterns in complex systems, significantly advancing the structured investigation of Lenia’s parameter landscape.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Continuous cellular automata are rocketing in popularity, yet developing a theoretical understanding of their behaviour remains a challenge. In the case of Lenia, a few fundamental open problems include determining what exactly constitutes a soliton, what is the overall structure of the parameter space, and where do the solitons occur in it. In this abstract, we present a new method to automatically classify Lenia systems into four qualitatively different dynamical classes. This allows us to detect moving solitons, and to provide an interactive visualization of Lenia's parameter space structure on our website https://lenia-explorer.vercel.app/. The results shed new light on the above-mentioned questions and lead to several observations: the existence of new soliton families for parameters where they were not believed to exist, or the universality of the phase space structure across various kernels.

Problem

• Lenia
• soliton
• parameter space
• continuous cellular automata
• dynamical classes

Innovation

• Lenia
• soliton detection
• parameter space visualization
• dynamical classification
• continuous cellular automata