Rescaled range analysis and the fractal dimension of pi

P. Vanouplines

University Library, Free University Brussels,
Pleinlaan 2, 1050 Brussels, Belgium

New research

Bailey (1988) writes the following about the randomness of pi:

Such a guaranteed property could, for instance, be the basis of a reliable pseudo-random number generator. Unfortunately, this assertion has not been proven in even one instance. Thus, there is a continuing interest in performing statistical analyses on the decimal expansion of these numbers to see if there is any irregularity that would suggest this assertion is false.

Chudnovsky and Chudnovsky (1991) write:

..., the decimal expansion of pi in billion plus range passes with flying colors all classical randomness tests: frequency, chi square, poker, arctan law, ... etc.

With the rescaled range analysis we do not only add another randomness test, but also the feature of calculating the popular fractal dimension.

This chapter contains the following paragraphs:

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Last updated on Sunday 19 November 1995.
©Patrick Vanouplines.