Dynamics of Eulerian walkers

We investigate the dynamics of Eulerian walkers as a model of self-organized criticality. The evolution of the system is divided into characteristic periods which can be seen as avalanches. The structure of avalanches is described and the critical exponent in the distribution of first avalanches $\tau =2\mathrm{}$ is determined. We also study a mean square displacement of Eulerian walkers and obtain a simple diffusion law in the critical state. The evolution of an underlying medium from a random state to the critical one is described.