  We study chemotaxis in a porous medium using as a model a biased ("hungry")
random walk on a percolating cluster. In close resemblance to the 1980s arcade
game Pac-Man, the hungry random walker consumes food, which is initially
distributed in the maze, and biases its movement towards food-filled sites. We
observe that, on the percolating cluster, the mean-squared displacement of the
pacman process shows anomalous dynamics, which follow a power law with a
dynamical exponent different from both that of a self avoiding random walk as
well as that of an unbiased random walk. The change in dynamics with the
propensity to move towards food is well described by a dynamical exponent that
depends continuously on this propensity, and results in slower differential
growth when compared to the unbiased random walk.
