Hyperbolic Escher Escher tilings converted to the hyperbolic variety.
Sculptures Ultrafractal and Povray working together.
The shape of Planet Earth Could the Earth have been flat after all?
How about cigar shaped? Or do you prefer pear shaped?
It seems it is all possible.
Just a question of enough spin..
Knots and dynamics A collaboration with Prof. Etienne Ghys of the Ecole Normale Supérieure de Lyon, containing material presented at the International Congress of Mathematicians (Madrid, August 2006)
Knots and dynamics animations. A collection of animations where one can see what a matrix looks like in four dimensions, how to make spaghetti using a 'horocycle', and more.. .
Xantox encouraged and helped me to create a visualisation of a canon by Johann Sebastian Bach. This is one of the many ingenious pieces by Bach: this one sounds just as good played from start to end, played from end to start, or played start to end and end to start simultaneously. Here it is.
The hyperbolic chamber
Posted on 2009-01-05 00:10
This an article about hyperbolic geometry. Even if you don't like math, you might want to look at the pictures. Try this for instance.
I also updated my article on the Droste effect.
Hyperbolic Escher
Posted on 2008-08-15 00:08
M.C. Escher only made four "Circle limit" drawings. These are tilings in hyperbolic geometry.
I now have a small gallery of 20 more of these: plain tilings in Euclidian geometry by M.C.Escher, transformed into the hyperbolic variety.
Dimensions: a math film.
Posted on 2008-06-19 11:13
We finally, after 18 monts of work, were able to release "Dimensions", two hours of mathematical animation. 'We' means myself, Etienne Ghys and Aurélien Alvarez, both from the Ecole Normale Supérieure in Lyon.
Go to the Dimensions website to read all about it. From this website you can either order the DVD (only 10 €!), or download the entire film for free!
The website is available in French, English and Dutch. The film is available in even more languages!
New gallery added
Posted on 2008-03-04 14:30
I have added a new gallery, the first in quite a long time.During the past year I have been working on a two-hour animation film, which will be announced here soon.
This gallery is an experiment in using data generated in Ultrafractal as input to Povray. Calculations in Ultrafactal are exremely fast, but the raytracing possibilities are limited. Povray, on the other hand calculates very slowly, but has unlimited and fast raytracing. Combining the strong points of the two seemed the obvious thing to try out.
Featurecolumn at the American Mathematical Society
Posted on 2006-11-01 20:49
The American Mathematical Society this month publishes an article on their website entitled "Lorenz and modular flows: a visual introduction. A tangled tale linking lattices, knots, templates, and strange attractors . . .".
It was written by Prof. Ghys and myself and reflects the material that was presented during a plenary session at the International Congress of mathematicians in August of this year.
The article is loaded with images and animations. Read it at the AMS website's Featurecolumn page, or here.
Here is the AMS press release.
The shape of Planet Earth
Posted on 2006-10-31 18:46
Prof. Etienne Ghys gave a lecture last week on the historical mathematical approaches to defining the shape of the Earth. There is now a new page here that contains a summary of that lecture.
If you ever wondered what shape the Earth could take if it had more rotational energy, then here are the answers.. The shape could be flat, cigar shaped or even pear shaped!
