10263

Self-Avoiding Random Walks

Trace a path by moving at random from one lattice point to another while avoiding previously visited points.
Such self-avoiding random walks can be used to model the path taken by an object, for example a person walking around and placing land mines at various locations. That person would not want to return to any previously visited site. It can also be a model for an animal moving around marking its territory and not wanting to return to a spot it has already marked, the foraging behavior of animals or birds, and so on. Another kind of example would be a particle moving subject to certain spatial restrictions; technically these are called spatially restricted diffusion processes or Brownian motion with spatial restrictions.

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To describe a long-chain molecule, another algorithm must be used, the pivot algorithm; see Self-avoiding walk.
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