Math applications

In this article, we’ll walk through the implementation of a one-dimensional, binary-state cellular automaton built on top of the parametric CA framework I introduced in a previous post. The single-page app is split into two pieces: the cellular-automaton engine itself, and a graphical user interface (GUI). The GUI includes two PixiJS renderers—one for the rule and one for the grid.

Cellular automata are mathematical models built on a finite population of cells. Each cell holds a state selected from a predefined set—finite for discrete automata and potentially continuous for analog variants. In the classic binary case, every cell is either ALIVE or DEAD. At each time step the system advances in lockstep: the new state of every cell is computed by applying a simple local rule that considers the current state of the cell and those of its neighbors. Repeated iterations of this rule generate successive “generations,” allowing intricate global patterns to emerge from straightforward local interactions.