Weierstrassian Levy flights and self‐avoiding random walks

An analogy, involving space–time relationships, is made between a self‐avoiding random walk and a Weierstrass random walk. The self‐avoiding random walk is non‐Markovian while the Weierstrass random walk is Markovian, but with a built‐in self‐similarity characterized by a fractal dimension. It is proposed that the self‐avoiding random walk can be viewed as a Weierstrass random walk whose trajectory is composed of maximally packed self‐similar clusters with the symmetry of the underlying lattice.

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