Rescaled range analysis and the fractal dimension of pi

Research output: Other contribution


The purpose of this paper is to determine the so-called 'global fractal dimension' of the digits of pi-3, and to study the variability of the fractal dimension over different ranges. It is seen that the digits of pi have a fractal dimension of nearly 1.5, as could be expected for a random sequence. This result is related to the fractal Brownian movement which has the same fractal dimension. The value of 1.5 is not exactly reached by pi, certainly not at longer ranges. A comparison is made with digits calculated from two popular random number generators. This indicates that over the longer ranges, in the order of thousands of digits, the digits of pi are more random than those obtained with the random number generators.
Original languageEnglish
TypeScientific paper on personal web page
Media of outputPersonal webpage
Number of pages0
Publication statusPublished - 7 Feb 1996


  • Digits of pi-3
  • Rescaled range analysis
  • Fractal dimension
  • Random number generators


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