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A beautiful superposition of random paths

This week’s image and description is by Jochen Voss: please visit his website 

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.)”


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

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.”

Outside In – Not Knot

This week we have two videos for you, along with two booklets. Everything sold together as a package.

This is serious math, and visual math at its best. Outside In shows the sphere eversion with the Thurston corrugation method. Not Knot shows that most link complements have a structure of hyperbolic space. You need some math background, at the very least you need to be comfortable with “Dimensions” material level; of course, the more the reader’s math background is solid, the better. But, even with a relatively minimal background, you will be highly rewarded.


This week we pick an activity from a vast website, with material in all sorts of subject, and not only in math and science.

This activity introduces young children to the concept of configuration spaces and to the subtleties of concepts which we sometimes take for granted, such as “dimensionality”, as soon as we are adventurous and play with spaces beyond our familiar and tame differentiable manifolds, with local affine space structure that glues nicely.