Simulation of First-Order Chemical Kinetics Using Cellular Automata

Cellular automata are dynamical systems composed of arrays of cells that change their states in a discrete manner following local, but globally applied, rules. It is shown that a two-dimensional asynchronous cellular automaton simulates both the deterministic and the stochastic features of first-order chemical kinetic processes in an especially simple manner, avoiding the chore of solving either the deterministic coupled differential rate equations or the stochastic master equation. Processes illustrated include first-order decay, opposing first-order reactions, consecutive reactions, the steady-state approximation, a rate-limiting step, pre-equilibrium, and parallel competing reactions. The deterministic solutions are seen to emerge as statistical averages in the limit of large cell numbers. Some additional stochastic and statistical features of the solutions are examined.