Dynamical system
Dynamical systems
A set of possible states together with a fixed rule determining how a state evolves over time.
What is usually left out
The rule is deterministic, yet determinism does not imply predictability. Systems with sensitive dependence on initial conditions produce trajectories that diverge exponentially from starting points too close together to distinguish, which is why weather is deterministic in principle and unforecastable in practice beyond a couple of weeks. Time may be continuous, giving a differential equation, or discrete, giving repeated application of a map — the Collatz rule is a dynamical system in exactly this second sense.