Information content in the Nagel-Schreckenberg cellular automaton traffic model

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 67; no. 4 Pt 2; p. 047103
• Main Authors: Blue, M, Bush, B W
• Format: Journal Article
• Language: English
• Published: United States 01.04.2003
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.67.047103

We estimate the set dimension and find bounds for the set entropy of a cellular automaton model for single lane traffic. Set dimension and set entropy, which are measures of the information content per cell, are related to the fractal nature of the automaton [S. Wolfram, Physica D 10, 1 (1989); Theory and Application of Cellular Automata, edited by S. Wolfram (World Scientific, Philadelphia, 1986)] and have practical implications for data compression. For models with maximum speed v(max), the set dimension is approximately log((v(max)+2))2.5, which is close to one bit per cell regardless of the maximum speed. For a typical maximum speed of five cells per time step, the dimension is approximately 0.47.