Glaberish: Generalizing the continuously-valued Lenia framework to arbitrary Life-like cellular automata

TL;DR

This paper extends the Lenia framework to support all Life-like cellular automata by splitting the growth function into genesis and persistence, enabling the implementation of diverse CA patterns and dynamics.

Contribution

It introduces Glaberish, a generalization of Lenia that allows arbitrary Life-like CA, broadening the scope of patterns and behaviors that can be modeled.

Findings

Implemented a puffer pattern from Life-like CA Morley/Move.

Compared dynamics of Hydrogeminium natans and s613 CA in Lenia and Glaberish.

Found s613 CA exhibits higher variability in spatial entropy, indicating more dynamic behavior.

Abstract

Recent work with Lenia, a continuously-valued cellular automata (CA) framework, has yielded $\sim$100s of compelling, bioreminiscent and mobile patterns. Lenia can be viewed as a continuously-valued generalization of the Game of Life, a seminal cellular automaton developed by John Conway that exhibits complex and universal behavior based on simple birth and survival rules. Life's framework of totalistic CA based on the Moore neighborhood includes many other interesting, Life-like, CA. A simplification introduced in Lenia limits the types of Life-like CA that are expressible in Lenia to a specific subset. This work recovers the ability to easily implement any Life-like CA by splitting Lenia's growth function into genesis and persistence functions, analogous to Life's birth and survival rules. We demonstrate the capabilities of this new CA variant by implementing a puffer pattern from Life-like CA Morley/Move, and examine differences between related CA in Lenia and Glaberish frameworks: Hydrogeminium natans and s613, respectively. These CA exhibit marked differences in dynamics and character based on spatial entropy over time, and both support several persistent mobile patterns. The CA s613, implemented in the Glaberish framework, is more dynamic than the Hydrogeminium CA in terms of a consistently high variance in spatial entropy over time. These results suggest there may be a wide variety of interesting CA that can be implemented in the Glaberish variant of the Lenia framework, analogous to the many interesting Life-like CA outside of Conway's Life.