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=Random Walks in NetLogo=
=Random Walks in NetLogo=
Each tick, generate a random heading from 0-359. Gives an even distribution of headings, and the resulting random walk has lots of backtracing and crossings.
rt random 360
rt random 360
fd 1
fd 1
[[File: random_walk.png|400px]]
=Triangular Random Walk=
=Triangular Random Walk=
Distribution:
Distribution:
[[File: triangular_heading.png]] [[File: triangular_walk.png]]
[[File: triangular_heading.png|400px]] [[File: triangular_walk.png|400px]]
=Some Theory=
=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
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), where D is the diffusion constant 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 (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
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:
A random walk constrained to 2 dimensions, the mean displacement is proportional to sqrt(t).
There are supposed to be interesting properties of random walk on a lattice, which is probably the best model of NetLogo movement.
McCrea, W. H. and Whipple, F. J. W. "Random Paths in Two and Three Dimensions." Proc. Roy. Soc. Edinburgh 60, 281-298, 1940.
McCrea, W. H. and Whipple, F. J. W. "Random Paths in Two and Three Dimensions." Proc. Roy. Soc. Edinburgh 60, 281-298, 1940.