Fermion picture for cellular automata

Understand

How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful methods exist for this type of problem.

• Indeed, many cellular automata admit an interpretation in terms of fermionic particles.
• Reversible automata on space-lattices with a local updating rule can be described by a partition function or Grassmann functional integral for interacting fermions moving in this space.
• We discuss large classes of automata that are equivalent to discretized fermionic quantum field theories with various types of interactions.