Information content in the Nagel-Schreckenberg cellular automaton traffic model

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.