Cellular Automata Describing Non-equilibrium Fluids with Non-mixing Substances

The chapter begins with an introduction to cellular automata (CA), highlighting their ability to model complex systems through simple interactions. It then discusses Wolfram's classification of CA into four distinct classes based on their dynamical behavior. The main focus is on the application of CA to model non-equilibrium fluids, particularly those with non-mixing substances. The text introduces evolutionary methods, such as genetic algorithms, to efficiently obtain CA rules with specific characteristics. The primary contribution is the development of an assembly method to determine CA code rules of increasing complexity, allowing for the study of singular perturbations and interactions between similar fluids leading to global phase transitions. The chapter also provides a detailed computation of the canonical assembly of a specific CA rule and simulations of its perturbations, offering a comprehensive guide to understanding and applying CA in fluid dynamics.