Random Walk in Random Poisson Potential

You see a simple symmetric random walk on a lattice. All positions visited by the walker so far are marked black, and the current position in green. The starting point of the walker is chosen randomly too. The walker moves in an environment of independent identically distributed yellow Poisson 'hills', i.e. proportional to 1/r. Yellow regions are of high potential, therefore dangerous for the walker, blue regions are of lower potential and relatively safe. If the walker hits some yellow 'hill' it may be killed (indicated by a red dot), but it has a chance to survive: a random number between 0 and 1 will be generated and compared to the Potential of the current location, if this number is smaller than the Potential the walker dies...

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If you want to see this simulation under periodic boundary condition, please click here: non-periodic boundary condition.