The Optiverse

Yes, this week, again, a hard-to-find video.

The Optiverse is a different sphere eversion, an optimal eversion.

While you look for the video, you may want to have a look here:

http://new.math.uiuc.edu/optiverse/

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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.)”

Nbody

A simulation of the N-body problem for iDevice. It’s free, too. Enjoy! Multiple pendulums next week.

http://itunes.apple.com/us/app/nbody/id347962727?mt=8

As Poincaré himself put it, “One is struck by the complexity of this figure I am not even attempting to draw. Nothing can give us a better idea of the complexity of the three-body problem and of all problems of dynamics where there is no holomorphic integral and Bohlin’s series diverge.”