Modeling with cellular automata

Cellular automaton are mathematical and computational discrete models created by John von Neumann and Stanislaw Ulam. CA is represented as a grid where in each cell a small computation is performed. In CA we will share the process through all the small cells in the grid. CA shows behavior similar to biological reproduction and evolution. In this case, we can say that each cell is an individual in our population (grid) that will switch between states depending on its social interaction (contact rate). (Refer to SIR and SIRS models).

Seen as discrete simulations of dynamical systems, CA has been used for modeling in different areas such as traffic flow, encryption, growth of crystals, bird migration, and epidemic outbreaks. Stephen Wolfram, one of the most influential researchers in CA describes CA as follows:

"Cellular automata are sufficiently simple to allow detailed mathematical analysis, yet sufficiently complex to exhibit a wide variety of complicated phenomena...