  A Brownian ratchet is a one-dimensional diffusion process that drifts toward
a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian
ratchet is a process that alternates between two regimes, a one-dimensional
Brownian motion and a Brownian ratchet, producing directed motion. These
processes have been of interest to physicists and biologists for nearly 25
years. The flashing Brownian ratchet is the process that motivated Parrondo's
paradox, in which two fair games of chance, when alternated, produce a winning
game. Parrondo's games are relatively simple, being discrete in time and space.
The flashing Brownian ratchet is rather more complicated. We show how one can
study the latter process numerically using a random walk approximation.
