Euler-lagrange correspondence of cellular automaton for traffic-flow models.

We propose a Euler-Lagrange transformation for cellular automata (CA) by developing new explicit transformation formulas. This transformation is done in the fully discrete level of variables, and corresponds to the well-known continuous version of it which appears in continuous mechanics such as fluid dynamics and plasma physics. Applying this method to the traffic problem, we have obtained the Lagrange representation of a traffic model, and also succeeded in clarifying the relation between different types of traffic models. It is shown that the Burgers CA, which is a corresponding CA of the continuous Burgers equation, plays a central role in considering this relation.