# Example of complex system, whose components have string etc. valued properties?

Complex systems are branch of physics, Phys. Rev. E has section about them. Complex systems consist from interacting components, each component has some set of properties whose values can change due to interaction or external force. System of interacting particles is example of complex system, particles can have properties such as position, charge, flavour, etc.

So far I have heard about complex systems whose components has numerical properties - continuous or discrete. But does physics and complex system research consider systems whose components have properties with different domain:

1. string valued property, whose values are generated from same formal grammark;

2. element valued property whose value is taken from some lattice from the combinatory algebra;

3. graph valued property whose value is taken from set of graphs having some property;

4. function valued property whose value is taken from some function space;

5. operator valued property whose value is taken from some space of operators.

Has anyone considered such unusual complex system?

E.g. it could be naturally to research emergence of language in system where communication with string occur. It would be very interesting to consider the system whose interaction change no only some numerical parameters of some component, but change entire essence or structure of component by changing function or graph valued property. Are there some works?

The question is a bit too broad, but I guess some pointers can be given.

1. string valued

For the most part, strings should be encode-able as numerical values, so there shouldn't be any fundamental difference between both.

Slightly related to that idea (in a somewhat backwards way) is the representation of a system's dynamics by means of symbolic dynamics, which connects trajectories in phase space to sequences of symbols.

1. element valued property whose value is taken from some lattice from the combinatorics algebra

A walker on a lattice would be an example of such system. In general, specific nodes may be chosen by any sort of dynamical process taking place on a lattice.

1. graph valued

That's a case of network dynamics, such as coevolutionary networks, where there's an interplay between a dynamical process taking place over the network and the network structure itself.

1. function valued

In the renormalization group approach to critical systems, we have a flow in a space of Hamiltonians (i.e., functions). In this approach, a universality class corresponds to the basin of attraction of a given (attractive) fixed point.

1. operator valued

Similarly, in quantum field theory the renormalization group approach can be seen as describing a flow in a space of operators.

• Thanx a lot! I could have created separate question for each type of system (I know, how rigorous the moderation are) but I had no idea whether there can be at least one answer to such question. Now it appears, that every such question has some answer!
– TomR
Commented Jan 28, 2020 at 16:51
• @TomR I think it's fine - no one voted to close it yet. ;-) In particular it's better like that than as 5 separate questions. Commented Jan 28, 2020 at 16:52