Iterated Function Systems as Human Perceivable Spectral Tests of Randomness

The deterministic generation of pseudorandom sequences is not a trivial task. Quite the contrary; even chaotic functions are often poor pseudorandom sequence generators. Thus, given the range of applications that require random inputs and the cost of actual random number generating equipment, the establishment of reliable tests of randomness becomes necessary. To day, the spectral test seems to be the only reliable test for randomness, as it can examine the correlation between successive symbols in a sequence. The drawback of the spectral test is that its results can only be visualized when comparing for correlation between consecutive pairs or triplets of symbols, while larger groups of symbols can only be examined mechanistically. In this paper, after reviewing the main points of random number and chaotic functions theory, we introduce a 2-dimensional spectral test of randomness that is based on iterated function systems (IFSs) and use it to examine the quality of various chaotic functions as random number generators and to draw conclusions on the randomness of sequences produced by deterministic processes. Key-Words: Spectral test, pseudorandom sequence, Iterated Function System (IFS), chaotic function.