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John MacCormick

Registered: Apr 2011
Posts: 1

A biological or chemical process that truly mimics an arbitrary automaton?

Hi, I'm wondering if anyone can point out to me one or more biological or chemical processes that truly mimic an arbitrary cellular automaton, or one of the other types of automata discussed in NKS. Usually, these automata are motivated as being simplified models of biological processes. But I am interested in whether this claim can be pushed further, and we can find in nature a genuinely discrete system that can be set up to follow the rules of an arbitrary automaton.

The reason for my question is as follows. As part of an undergraduate course on computational theory that I am currently giving, I want to give a lecture on NKS topics, in particular discussing the existence of universal computation in nature. Clearly, the original NKS book describes the *potential* for universal computation to exist in very simple systems. But as far as I am aware, it does not demonstrate the actual existence of such systems. Examples such as leaves and shells do not count for my purposes. I view these -- and please correct me if I'm wrong -- as examples where the automaton which produces the same structures observed on leaves/shells is a simplified model of the underlying biological process, which on a more detailed level might be even better modeled by a continuous differential equation of some kind.

In contrast, I'm interested in examples where a biological or chemical process has genuinely discrete states in genuinely discrete cells. I am particularly interested in examples that can be set up to follow the rules of an arbitrary automaton, or at least there is some potential for implementing different sets of rules.

Ideally, I guess I'm hoping that some expert on molecular biology can chime in with a comment along the lines of “sure, a chain of suitable amino acids (or whatever) can act on a strand of DNA (or whatever) in a way that precisely mimics a mobile automaton with 4 colors/a Turing machine with 4 symbols and 5 states/(or whatever)”. If there are no known examples that precisely mimic an automaton, I would also be interested to know what people would consider the closest approximation.

Many thanks in advance for any advice.

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