Are chaotic systems computable in polynomial time Suppose the parameters/inputs of the computation include the time at which the configuration of a particular deterministic chaotic system needs to be computed. 

Say, for instance, as input we have a start configuration of the chaotic Rule 30 cellular automata and a time-step $t$, and as output, we require the configuration at time-step $t$.

What can be said about the computational complexity of such a computation?
Wolfram's rule 30 is a one dimensional cellular automaton.
If you want to know the state of the CA at step $t$, given the initial configuration, you just need to run the rule for $t$ steps. At every step the computation consist in no more than a bunch of if's, so the time complexity of such  CA is linear in $t$.