Overview

What is a Cellular Automaton, and what is JCAL?

What is a Cellular Automaton?

A Cellular Automaton (CA) is a discrete computational model consisting of a grid of cells, each holding a finite state. At each time step (a generation), every cell updates its state according to a fixed transition function that depends only on the cell’s current state and the states of its immediate neighbors.

Despite deceptively simple rules, cellular automata can generate remarkably complex behavior — making them a powerful tool for modeling natural phenomena such as:

  • Population dynamics
  • Fluid and lava flow
  • Landslide propagation
  • Heat diffusion
  • Crystal growth

Formal Definition

A Cellular Automaton is the quadruple <Zᵈ, S, X, σ>:

Symbol Meaning JCAL type
Zᵈ A d-dimensional grid of cells CellGrid → CellGrid (2D) or CellGrid (3D/4D)
S The finite set of possible cell states CellState instances
X The neighborhood — which cells are “neighbors” Neighborhood subclass
σ The transition function — one step of evolution CellularAutomataRule subclass

Neighborhood Strategies

The two most common neighborhood shapes are:

  • Moore neighborhood — all surrounding cells (orthogonal + diagonal): 8 in 2D, 26 in 3D, 80 in 4D. Use NeighborhoodType.MOORE.
  • Von Neumann neighborhood — orthogonal cells only: 4 in 2D, 6 in 3D, 8 in 4D. Use NeighborhoodType.VON_NEUMANN.

You can also define a custom neighborhood by subclassing Neighborhood (2D) or Neighborhood (3D/4D). See Neighborhoods for details.

Further Reading

What is JCAL?

JCAL was born from the author’s master’s thesis, where a C++ library for Cellular Automata was developed and used by physicists, geologists, and researchers across multiple departments. That library was comprehensive but complex.

JCAL brings the same ideas to Java in a smaller, simpler, and more accessible form.

Design Goals

Goal How JCAL Achieves It
Minimal boilerplate A working CA in a handful of Java lines
Idiomatic Java Fluent builder API, abstract base classes, standard java.util collections
Extensible Swap in custom states, neighborhood shapes, or parallel execution with minimal changes
Complex CA support Custom state objects and a refinements hook enable rich, multi-value simulations
Multi-dimensional 2D, 3D, and 4D grids with matching built-in neighborhood strategies

Key Classes at a Glance

Class Role
CellState A cell’s state. Has a key (String) and a value (any Object).
Cell One cell on the grid. Has a CellState and coordinate(s).
CellularAutomataConfiguration Immutable configuration. Always use the inner Builder.
CellularAutomata The grid. Create from a configuration object.
CellularAutomataRule Extend this to define your transition rule (transition).
Neighborhood Extend this for a custom 2D neighborhood shape.
Neighborhood Extend this for a custom 3D/4D neighborhood shape.
CellularAutomataParallelRule Parallel variant of CellularAutomataRule.

Grid Coordinate Convention

In 2D: map[col][row] where col is the x-axis (left → right) and row is the y-axis (top → bottom).

See Also