This repository contains a collection of interactive, browser-based implementations of three-dimensional totalistic cellular automata, developed as part of the AlgorithmicDynamics project.
The focus is on rule-space exploration, emergent structure, and visual analysis of discrete dynamical systems in 3D.
➡ Source repository:
github.com/AlgorithmicDynamics/totalistic-3d-cellular-automata
All implementations run entirely in the browser and are available via GitHub Pages and algorithmicdynamics.com.
A minimal 3D totalistic automaton based on the Von Neumann neighborhood (center cell + 6 axis-aligned neighbors).
- Rule size: 14 bits
- 7 conditions for empty → alive
- 7 conditions for alive → alive
- Neighborhood: center + faces
- Rule space: strongly compressed, symmetric
Live demo
An extended neighborhood including faces and edges, but excluding corners (center + 18 neighbors).
This variant significantly increases structural richness while remaining fully totalistic and isotropic.
- Rule size: 38 bits
- 19 conditions for empty → alive
- 19 conditions for alive → alive
- Neighborhood: center + faces + edges
- Rule space: large but still tractable
Live demo
A manual genetic algorithm layered on top of the 19-cell totalistic automaton.
Instead of editing rules directly, the user selects visually interesting behaviors, which are then evolved through selection, crossover, and mutation.
- Genome: 38-bit totalistic rule
- Population: persistent via local storage
- Fitness: user-driven (visual selection)
- Purpose: discovery of unexpected or complex dynamics
Live demo
All systems in this repository share the following principles:
- Three-dimensional cubic lattice
- Binary cell states (alive / empty)
- Synchronous updates
- Totalistic rules
(depend only on the number of active cells, not their arrangement) - Toroidal boundary conditions
- 2D Z-slice visualization for inspection of 3D structure
The goal is not physical simulation, but algorithmic exploration of emergent form.
Because full 3D rendering is intentionally avoided, all systems expose:
- Adjustable lattice size
- Adjustable pixel scale
- Real-time iteration
- Interactive Z-slice navigation
- Direct rule manipulation (or evolutionary selection)
This keeps the tools fast, inspectable, and suitable for static hosting.
This repository is intended for:
- Exploration of 3D cellular automata behavior
- Study of compressed rule spaces
- Investigation of stability, extinction, oscillation, and structure formation
- Educational and research-oriented experimentation
It is not a game and not a physical model.
- Plain HTML, CSS, and JavaScript
- No external libraries
- Runs fully in the browser
- Designed for GitHub Pages and static hosting
Each subdirectory is a self-contained system.
AlgorithmicDynamics is an open research initiative focused on:
- Cellular automata
- Symbolic dynamics
- Fractals
- Genetic and evolutionary systems
- Algorithmic structure and emergence
MIT License. See LICENSE for details.