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=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). [https://www.zbp.univie.ac.at/dokumente/einstein2.pdf "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). [https://einsteinpapers.press.princeton.edu/vol2-trans/137 "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.
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). [https://www.zbp.univie.ac.at/dokumente/einstein2.pdf "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). [https://einsteinpapers.press.princeton.edu/vol2-trans/137 "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.