Tolle Charles R., Budzien Joanne L., LaViolette Randall A.
Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415-2208.
Chaos. 2000 Jun;10(2):331-336. doi: 10.1063/1.166498.
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, Henon, and Rossler. The Lorenz system generates trajectories that follow Benford's law. The Henon system generates trajectories that resemble neither the uniform distribution nor Benford's law. Finally, the Rossler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others. (c) 2000 American Institute of Physics.
从各种来源汇编的数据遵循本福特定律，该定律给出了首位数字（从1到9）单调递减的分布。我们研究了一些常见动力系统生成的轨迹坐标首位数字的频率。一维元胞自动机符合首位数字频率均匀的预期。另一方面，流体的分子动力学提供的轨迹遵循本福特定律。最后，考虑了三个混沌系统：洛伦兹系统、亨农系统和罗斯勒系统。洛伦兹系统生成的轨迹遵循本福特定律。亨农系统生成的轨迹既不像均匀分布也不像本福特定律。最后，罗斯勒系统对于某些参数选择生成遵循均匀分布的轨迹，而对于其他参数选择则遵循本福特定律。（c）2000美国物理研究所。
