Cellular Automata — Grid-Based Emergence from Local Rules

A cellular automaton fixes agents (cells) to positions on a regular grid; each cell's state and update rule are uniform across the grid, and interaction is strictly local. An agent-based model allows agents to be mobile, heterogeneous, and to interact through flexible topologies. Use CA when the spatial process is inherently grid-like and the cells themselves do not move or make complex decisions; use ABM when individual heterogeneity, mobility, and decision-making are central to the phenomenon.

Synchronous updating applies the transition rule to all cells simultaneously at each time step and is the classical CA formulation. Asynchronous updating applies rules one cell at a time, in a defined or random sequence. The choice can qualitatively alter the emergent dynamics. Synchronous updating is standard for physical spread processes (fire, diffusion); asynchronous is often more realistic for biological or social processes where agents act sequentially. The choice must be justified and documented.

Calibration typically involves defining a goodness-of-fit metric — such as the figure-of-merit or kappa statistic comparing simulated and observed land-use maps — and then searching the rule parameter space to minimize the discrepancy. Because multiple rule sets can produce similar output (equifinality), calibration should be accompanied by sensitivity analysis across a range of plausible rule configurations, not just optimization to a single best-fit point.

No minimum empirical sample is required. States and rules can be specified theoretically and the model run as a pure simulation. However, if the goal is to model a specific real-world spatial process — urban growth in a particular city, fire spread in a particular landscape — then calibrating the rule set and initial configuration to observed reference data substantially increases the model's credibility and predictive usefulness.