Back to the universality of the Billiard ball model
Résumé
A full construction of the universality of the Billiard ball model, a lattice gas model introduced by Margolus in 84 is provided. The BBM is a reversible two-dimensional block cellular automaton with two states. Fredkin's gate and reversible logic can be emulated inside the Billiard ball model. They are use to embed two-counter automata, a model universal for computation.
In the one-dimensional case, there exists a universal block cellular automaton with 11 states