Do dynamical systems follow Benford's law?

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 traject ories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is u niform. The molecular dynamics of fluids, on the other hand, provides traje ctories that follow Benford's law. Finally, three chaotic systems are consi dered: Lorenz, Henon, and Rossler. The Lorenz system generates trajectories that follow Benford's law. The Henon system generates trajectories that re semble neither the uniform distribution nor Benford's law. Finally, the Ros sler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others. (C) 2000 American I nstitute of Physics. [S1054-1500(00)01402-6].