Fractal analysis of Pi normality

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.