The Leading Digit Law in Nature and Chaos

The distinction between randomness and chaos is subtle but important. Randomness, which governs the fundamental laws of physics, is truly unpredictable; chaos, on the other hand, is a deterministic rule, but one in which a... [ view full abstract ]

The distinction between randomness and chaos is subtle but important. Randomness, which governs the fundamental laws of physics, is truly unpredictable; chaos, on the other hand, is a deterministic rule, but one in which a small change in the initial conditions can reflect wide variability in the outcome. Knowing the difference between the two can be difficult, but the applications in areas such as cybersecurity are immense. We explore a novel new method to distinguish the two using Benford's law, a mathematical theory governing the distribution of leading significant digits.