Do dynamical systems follow Benford’s law?

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Abstract
Data compiled from a variety of sources follow Benford’s law, which gives a monotonically decreasing distribution of the first digit (1 through 9). We examine the frequency of the first digit of the coordinates of the trajectories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is uniform. The molecular dynamics of fluids, on the other hand, provides trajectories that follow Benford’s law. Finally, three chaotic systems are considered: Lorenz, Hénon, and Rössler. The Lorenz system generates trajectories that follow Benford’s law. The Hénon system generates trajectories that resemble neither the uniform distribution nor Benford’s law. Finally, the Rössler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford’s law for others.

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