Benford Behavior of a Higher-Dimensional Fragmentation Process

Abstract

Nature and our world have a bias! Roughly $30\%$ of the time the number $1$ occurs as the leading digit in many datasets base $10$. This phenomenon is known as Benford's law and it arrises in diverse fields such as the stock market, optimizing computers, street addresses, Fibonacci numbers, and is often used to detect possible fraud. Based on previous work, we know that different forms of a one-dimensional stick fragmentation result in pieces whose lengths follow Benford's Law. We generalize this result and show that this can be extended to any finite-dimensional ``volume''. We further conjecture that even lower-dimensional volumes, under the unrestricted fragmentation process, follow Benford's Law.