Circles Packing and Kepler Theorem

By a bored Saturday afternoon I decided to make a little code for my amusment to test the sphere packing theorem. So what I did is to try to pack as many small circles into a big one, by an incremental method which doesn't converge but still gives convincing results. The animation showed here is a vizualisation of this incremental method which tries to minimize overlap one by one.

I also tried with circles of various radius. What strikes me is the waves that propagates from circles that have trouble to insert themselves among other. We can see them propagating from one side to an other of the green circle (sorry for colorblind people, those are default gunplot colors).

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Shear waves, medecine and brain

Yesterday evening, too bored by what TV was proposing to me, I decided to watch a conference of Mathias Fink , a french researcher working on multidisciplinary application of waves. Specially shear waves. Here is a brief summary of his talk. In solids, waves have two principal components: compression waves (P-waves for primary) moving in the direction of propagation, and shear waves (S-waves, for secondary) that make ripples in the plane orthogonal to that direction. Since compression waves propagate in the direction of propagation, they move faster than shear waves. Usually ultrasound equipment in medicine only use compressional waves. But since human tissues have a high bulk modulus, the P-wave speed is relatively constant (around 1580 m/s). Human tissues are very stiff if you apply isotropic constraints on them (like pressure of water). However M. Fink and his colleagues proposed a new way to investigate human tissues by first sending a strong compressional wave in ...

Hypnothic patterns of integrer decomposition

http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/

Networks and Life

As you probably may (or may not!) know, molecular biology often study biological functions from interaction network between molecules rather than studying each component one-by-one. It's the opposite of the universal divide-and-conquer strategy, I would call it the all-inclusive strategy. Those interactions networks involves myriads (10.000) of molecules that interacts by various chemical ways, which is generally represented as an oriented graph between each molecular compound. The transcriptional networks describe the relationship between genes and proteins, the protein-protein network s defines the cascades of interactions between some, ingenuously lumped, proteins, the metabolic networks attempt to mimic the flush of metabolic reactions inside living organisms. So the idea is to understand how the main 'thing' works from all those interactions linked together. Of course, other kind of networks are used in many different domain to study more-or-less linked ...

New Horizons

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