ABSTRACT
Randomness and chaos in physical systems are usually ultimately attributed to external noise. There are, however, systems which can also generate apparent randomness internally, without external random input. Different degrees of randomness can be defined in terms of the computational complexity of the procedures used. Sequences generated by chaotic physical systems often show some redundancy or determinism under simple statistical procedures. A sequence can be considered "simple" if it has small Θ. Θ provides a measure of "complexity," "effective randomness," or "computational unpredictability". The simplest mathematical and physical systems can be decomposed into essentially uncoupled components, and cannot increase Θ. The polynomial-time process of cellular automaton evolution thus increases Θ, and generates effective randomness. Despite extensive empirical evidence, almost nothing has, however, been proved about the randomness of such sequences. Autoplectism is expected to be responsible for apparent randomness-in many physical systems.
