Chaos and randomness

✍ Scribed by F. James

• Book ID: 103981023
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 334 KB
• Volume: 6
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/0960-0779(95)80028-f

✦ Synopsis

It is well-known that a rigorous operational definition of randomness is very hard to formulate in terms of classical mathematical primitives. This difficulty is reflected in the difficulty of deciding whether a given (pseudo-)random number sequence is "sufficiently random". Intuitively, we want the sequence to possess all the properties that a truly random sequence would have, where these properties are well-defined but uncountably infinite in number. This kind of reasoning invariably leads to an infinite number of conditions which must be satisfied, and which in addition are not independent.

A more appealing way to approach the problem is through the concepts of chaos and fractals.

Certainly a sequence of random numbers is the ultimate self-similar set, since it is (statistically) self-similar at all scales and in all permutations. The idea of applying chaos theory to randomness is not new, but as far as I know, it has only recently given rise to demonstrably "good" random number generators of practical usefulness in massive Monte Carlo calcula-