A Simulation of a Random Walk

also known as Drunken Walk and Brownian Motion

The path taken is rarely a walk in a sustained direction for long,
but more like a drunk stumbling around a fixed point.

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This isn't actually a simulation of Brownian motion. Strictly speaking, it is a simulation of a random walk that moves NE, SE, NW and SW with equal probability at each step. A Brownian diffuse in three dimensions moves in any direction with equal probability at each movement.

Modified from Terry McConnell, Math Department, Syracuse University