Symbol processing systems, automata, symbolic dynamics for dynamical systems, strings of DNA. Finite state markov machines. syntactic machines. Systems of strings of symbols.
The Turing machine is a classic example, but there are many ways of operating on strings of symbols.
For metrics, see spaces of strings.
For some esoteric generalisations as models of chemistry, see artificial chemistry.
Especially string rewriting but you can do almost-anything rewriting