A beautiful superposition of random paths

This week’s image and description is by Jochen Voss: please visit his website http://seehuhn.de 

stocastic paths by Jochen Voss
“Each of the lines is a path of a stochastic process.  They are all
generated by the same rule, but because of the randomness each path
comes out differently in the end and I drew all of them into the
same picture.

The plane is divided into square cells, and the process is constructed
so that it normally just runs in circles inside one cell but, because
of random fluctuations, from time to time is pushed into a
neighbouring cell.  (In technical terms: the picture shows solutions
of a stochastic differential equation.)”


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