Random Walk

Random Walks in NetLogo

   rt random 360
   fd 1

Triangular Random Walk

Advance +/- 50 degrees from straight ahead, gives a triangular distribution around 0

   rt random 50
   lt random 50

Distribution:

Some Theory

In a true random walk (ie Brownian motion) the mean displacement along the x-axis is proportional to the square root of time dx=sqrt (2Dt), which gives mean radius of a circle covered by the random walk

Einstein, Albert (May 1905). "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen" (PDF). Annalen der Physik (in German). 322 (8): 549–560. Bibcode:1905AnP...322..549E. doi:10.1002/andp.19053220806. Retrieved 2008-04-10.

Einstein, Albert (1989). "On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat" (PDF). Princeton University Press

A random walk constrained on a lattice:

McCrea, W. H. and Whipple, F. J. W. "Random Paths in Two and Three Dimensions." Proc. Roy. Soc. Edinburgh 60, 281-298, 1940.