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Brownian motion, random walks, and drunkard's walks have the same characteristics: a number of particles move "randomly" each time period.
In the "Manhattan" version, a particle is likely to move ten blocks north, ten blocks south, ten blocks east, or ten blocks west with equal probability.
In the "Unit One Dimensional" version, a particle is likely to move ten blocks east or ten blocks west with equal probability.
In the "Uniform" models, the distance traveled is uniformly distributed between 0 and 10. In the "Uniform 2-Dimensional" model, therefore, in any trial, a particle may have a delta X of between -10 and 10, and simultaneously a delta Y of between -10 and 10.
Finally, in the "Circular" model, the distance traveled by each particle in each round is 10 units, but the direction is randomly selected from all possible (e.g., 47.365 degrees from due east.
Trials may be run individually, or "Autorun" will keep the animation going until "Stop" is depressed.
If a particle begins to drift off the screen, the image is automatically "zoomed out."
In "The Drunkard's Walk: How Randomness Rules Our Lives", Caltech Physicist Leonard Mlodinow addresses these phenomena and their historical context in terms of the work of Einstein, Brown, and others in Chapter 8, "The Order In Chaos."