Enumeration of Number-Conserving Cellular Automata Rules with Two Inputs

Cellular automata (CA) rules possessing additive invariants have been studied since early 90’s. The simplest form of an additive invariant is the sum of all site values over a finite lattice with periodic boundary conditions. Rules with such an invariant are known as number-conserving rules, and they exhibit many interesting properties. For example, they can be viewed as systems of interacting particles [4]. In a finite system, the flux or current of particles in equilibrium depends only on their density. The graph of the current as a function of density characterizes many features of the flow, and is therefore called the fundamental diagram. Fundamental diagrams of numberconserving CA exhibit intriguing singularities, which have been investigated extensively [1, 5].