Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1001.0505

Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

A. Nishiyama·T. Tokihiro
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media.

Explore related subjects

nlin.CGnlin.PS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. Nishiyama, T. Tokihiro. 2010-01-04. Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk. https://doi.org/10.1143/jpsj.80.054003

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↗