Self-Similarity in Random Walk

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A random walk is a simple stochastic process in which a position of an object is translated by some random value, e.g., , at every time step. Despite its mathematical simplicity, the long-term trajectory of a random walk demonstrates stochastic self-similarity, a.k.a. fractal property. One can slide the "scale" controller to observe that the macroscopic shape of the trajectory doesn't change very much at different scales.

Contributed by: Hiroki Sayama (March 2011)
Open content licensed under CC BY-NC-SA


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