1 Courant Institute of Mathematical Sciences [New York]
2 Max-Planck-Institut für Informatik
3 Alfréd Rényi Institute of Mathematics
We analyze the one-dimensional version of Jim Propp's $P$-machine, a simple deterministic process that simulates a random walk on $\mathbb{Z}$. The "output'' of the machine is astonishingly close to the expected behavior of a random walk, even on long intervals of space and time.