Fractal analysis of Pi normality

TL;DR

This paper uses fractal analysis on the first billion digits of pi to provide evidence supporting its normality, suggesting digits are uniformly distributed and independent.

Contribution

It applies fractal analysis to a large digit sequence of pi to empirically support its normality, a property not previously confirmed for pi.

Findings

Digits of pi exhibit properties of a random, uniformly distributed sequence

Fractal analysis reveals increasing clarity of normality as more digits are considered

Supports the hypothesis that pi is a normal number

Abstract

\begin{abstract} $\pi$, the ratio between a circumference and is radius, is an irrational transcendental number. Fractal analysis is used here to show that $\pi$\textquoteright{s} digit sequence corresponds to a uniformly distributed random succession of independent decimal digits, and that these properties get clearer as the number of digits in the series grows towards infinity; $ 10^9 $ digits were tested in this work. This indicates that $ \pi $ is normal.