Take an undamped double pendulum and divide the space up into 2 sections. Suppose you can only check which section the pendulum is every N seconds. Every time you check, you record the value, and over time you build up a sequence of K numbers: 1,0,1,0,0,1,1,1,1,0,0,1,0,...

Suppose you know the exact initial state (dx/dt, x) of the pendulum.

What bounds on K and T are required such that the sequence of numbers is asymptotically indistinguishable from a purely random sequence?

So, because of a silly thought experiment, one might think there is very simple order to the apparent randomness. But, as Pauli would say, "it's not even wrong"...