Instead, through the rule's repeated application the long-term behavior becomes quite complicated. One has to measure the system again to find out where it is. Starting from very close initial conditions a chaotic system very rapidly moves to different states.
Many frequencies are excited.
If this noise is below measurement accuracy, so that an experimenter can't see or control the noise, then the system appears unpredictable. But for the system to consistently produce stable behavior, over long times the set of behaviors must fall back into itself. The tension of these two properties leads to very elegantly structured chaotic attractors. In fact, deterministic chaotic systems are quite ordered and even predictable on short time scales. The goal is to find the hidden order in the apparent chaos.