Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2205.12728

Step Size is a Consequential Parameter in Continuous Cellular Automata

Q. Tyrell Davis·Josh Bongard
View original source ↗Read source document ↗Export metadata ↓

Abstract

Step size in continuous cellular automata (CA) plays an important role in the stability and behavior of self-organizing patterns. Continous CA dynamics are defined by formula very similar to numerical estimation of physics-based ordinary differential equations, specifically Euler's method, for which a large step size is often inaccurate and unstable. Rather than asymptotically approaching more accurate estimates of CA dynamics with decreasing step size, continuous CA may support different self-organizing patterns at different ranges of step size. We discuss several examples of mobile patterns that become unstable at step sizes that are too small as well as too large. Additionally, an individual mobile pattern may exhibit qualitatively different behavior across a range of step sizes. We demonstrate examples of the effects of step size in pattern stability and qualitative behavior in continuous CA implemented in the Lenia framework and its variant, Glaberish.

Explore related subjects

nlin.CGcs.OHnlin.AO

Keep this discovery

BibTeXRIS

Q. Tyrell Davis, Josh Bongard. 2022-05-20. Step Size is a Consequential Parameter in Continuous Cellular Automata. https://arxiv.org/abs/2205.12728

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Optical free space extreme learning machine for the implementation of emergent complex systems

Cellular automata conform a set of computational models which evolve with a reduced set of simple rules, yet still are able to show extremely complex emergent phenomena such as fractals and universal computation. Despite their apparent simplicity, they have shown great potential in simulating natural systems and solving challenging computational tasks such as classification and image generation. Instead of implementing cellular automata purely at the software level, it is desirable to design novel analog computing platforms that physically evolve following the automata's underlying rules, thereby reducing power requirements and latency. Here, we introduce an optical extreme learning machine for the simulation of a wide range of cellular automata. Our system operates in free space, and uses a spatial light modulator to encode the evolution rules of the system, while coherent wave propagation performs the corresponding computations. Our results demonstrate a simple, fully-programmable, cost and power efficient, and easy to build and align platform for the implementation of a wide range of complex computational systems such as elementary cellular automata, Conway's Game of Life, and two-dimensional Turing machines.

nlin.CG↗
arXiv2026

The istr-graph: Interactive Visualisation of any Classic-Graph in DDLab

Any type of attractor basin (classic-graph) created in DDLab can now be visualised, manipulated, and deconstructed as a drag/drop ``interactive state transition graph'' (istr-graph). The new istr-graph applies to subtrees, single basins, the basin of attraction field, compression, and all other classic-graph parameters. This is an important update on the pre-existing ``interactive basin of attraction field graph'' (ibaf-graph) specific to just the complete uncompressed field, but the ibaf-graph is nevertheless retained for some of its unique attributes. These issues are discussed with a focus on the scope and implementation of the new istr-graph.

nlin.CG↗
arXiv2026

Game of Life on Archimedean Lattices: Glider Guns and Phase Dynamics

I explore Conway's Game of Life (GoL) on six composite Archimedean lattices. On the Kagome lattice, on which small gliders and puffers appear particularly frequently across inputs, I use the output of a symmetry-constrained evolutionary search algorithm to construct a novel glider gun. The glider gun comprises four interacting bouncers and stably emits a small glider every 276th generation. Serving as an extension of classical GoL, I also propose cells with a phase degree of freedom and an associated local phase rule, which on the Kagome lattice is demonstrated to host phase-periodic gliders. This enables the possibility of phase-sensitive and interference-based computations.

nlin.CG↗