Modeling with Cellular Automaton

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

Seen as discrete simulations of dynamic systems, the 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:

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