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.)”


It was remarked to me that this mathblog is too serious (perhaps it has to do with math being too serious to be left to physicists?) So, off to the start of our new column, Picture of the Week.


"An effective method of dealing with defects is to find a collection site."

Winner of “Bizarre” category of Micrograph 2005

Title: Chisai Benjo (Small Toilet)

Description: An effective method of dealing with defects is to find a collection site.

Magnification: ~15,000X

Instrument: SII NanoTechnology Inc. / SMI2050MS2

Submitted by: Takahashi Kaito (SII Nanotechnology Inc.)