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I'm doing some thinking about random walk.

Imagine there is a bounded 2D plane and a single spawn point. The spawn produces units which must bring in minerals scattered around the spawn. The locations of minerals are not known, so the units diffuse randomly away from the spawn until they find a mineral. Once the mineral is picked up, it is brought back to the spawn point (i.e. once the unit found mineral, it goes to the origin in a straight line). The unit then returns (in a straight line) to the location of the last mineral pickup point and then diffuses randomly from that point until it finds a new mineral.

Could somebody please provide some papers, urls - any kind of material - to show how to mathematically model such a scenario? I'm not afraid of calculus, differential equations, etc.

Thanks,

Monte