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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 arcadegame Pac-Man, the hungry random walker consumes food, which is initiallydistributed in the maze, and biases its movement towards food-filled sites. Weobserve that, on the percolating cluster, the mean-squared displacement of thepacman process shows anomalous dynamics, which follow a power law with adynamical exponent different from both that of a self avoiding random walk aswell as that of an unbiased random walk. The change in dynamics with thepropensity to move towards food is well described by a dynamical exponent thatdepends continuously on this propensity, and results in slower differentialgrowth when compared to the unbiased random walk.

Clearing out a maze: The hungry random walker and its anomalous diffusion