Systems which allow interacting particles with string representations. Is there a name for this family of systems? Probably “artificial chemsitry” comes close.
Kauffman’s legacy - a minimal model of gene fitness based on random functions of a specified number of letters in the string.
Related to the NK model, although containing both some extensions and some specifications of variable choice.
Fontana’s model of chemistry using a “Turing Gas” based on lambda calculus.
John Holland’s candidate Genetic Algorithm system whcih is supposed o be Turing complete.
In the sense of evolving electrical circuits. Brian Arthur has done some of this.
Minimal equivalent representations of a given stochastic process, due to Crutchfield.