# Do dynamical systems follow Benford's law?

## 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, Henon, and Roessler. 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 Roessler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others. (c) 2000 American Institute of Physics.

- Authors:

- Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho 83415-2208 (United States)

- Publication Date:

- OSTI Identifier:
- 20216515

- Resource Type:
- Journal Article

- Journal Name:
- Chaos (Woodbury, N. Y.)

- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 2; Other Information: PBD: Jun 2000; Journal ID: ISSN 1054-1500

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DYNAMICS; RANDOMNESS; DISTRIBUTION FUNCTIONS; DATA ANALYSIS; COMPUTER CODES; THEORETICAL DATA

### Citation Formats

```
Tolle, Charles R., Budzien, Joanne L., and LaViolette, Randall A.
```*Do dynamical systems follow Benford's law?*. United States: N. p., 2000.
Web. doi:10.1063/1.166498.

```
Tolle, Charles R., Budzien, Joanne L., & LaViolette, Randall A.
```*Do dynamical systems follow Benford's law?*. United States. doi:10.1063/1.166498.

```
Tolle, Charles R., Budzien, Joanne L., and LaViolette, Randall A. Thu .
"Do dynamical systems follow Benford's law?". United States. doi:10.1063/1.166498.
```

```
@article{osti_20216515,
```

title = {Do dynamical systems follow Benford's law?},

author = {Tolle, Charles R. and Budzien, Joanne L. and LaViolette, Randall A.},

abstractNote = {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 Roessler. 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 Roessler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others. (c) 2000 American Institute of Physics.},

doi = {10.1063/1.166498},

journal = {Chaos (Woodbury, N. Y.)},

issn = {1054-1500},

number = 2,

volume = 10,

place = {United States},

year = {2000},

month = {6}

}