I am very interested in giving mathematical structures "life" by having them change and interact according to certain sets of rules. I already love cellular automata and have looked into dynamical systems, but actual research in dynamical systems seems too broad in a sense. It steers away from experimenting with the behaviors of concrete specific systems. Even thinking about the Collatz Conjecture could fit under this umbrella, since it is about the behavior of a number under the iteration of a rule.
2026-04-25 11:50:47.1777117847
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Area of math dealing with the behavior of structures under iteration of some rule?
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You might be interested in Arithmetic dynamics which is a relatively new field which combines dynamics and arithmetical systems.
You might be interested in evolutionary game theory!, and specifically replicator equations. This field deals with how systems change under iteration and the math can be applied to far more than biological systems.