Self-Similarity in Random Walk

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.