The Plastic Brain

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These beautiful drawings provide a powerful visualisation, for me, of the concepts of fields and flux.

Some here.

http://butdoesitfloat.com/

More here

http://www.flickr.com/photos/jellitsch/sets/72157626524733588/with/5631532204/

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Watch spiral galaxies form in your browser.

http://vis.stanford.edu/protovis/ex/nbody-full.html

(Via @ProfessorFunk)

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Salty eigenfunctions of the Laplace operator.

I’ll leave the explanation to the good folks below. I just find it beautiful.

Trblogged from hiremebecauseimsmart:

Proof that differential equations are real.

The shapes the salt is taking at different pitches are combinations of eigenfunctions of the Laplace operator.

(The Laplace operator Delta f = sum_{i=1}^n frac {partial^2 f}{partial x^2_i}. tells you the flux density of the gradient flow of a many-to-one function ƒ. As eigenvectors summarise a matrix operator, so do eigenfunctions summarise this differential operator.)

Remember that sound is compression waves — air vibrating back and forth — so that pressure can push the salt (or is it sand?) around just like wind blows sand in the desert.

Notice the similarity to solutions of Schrödinger PDE’s from the hydrogen atom.

When the universe sings itself, the probability waves of energy hit each other and form material shapes in the same way as the sand/salt in the video is doing. Except in 3-D, not 2-D. Everything is, like, waves, man.

To quote Dave Barry: I am not making this up. Science fact, not science fiction.