Does anyone know how to produce this?

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I would really like to know how this can be implemented:




Does anyone know the math which is required to do this?

[Ref]

I think it's caledl magic (shaders).

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I'm not quite sure it's the same, but it is very pretty.
Thanks for sharing!

[Clouds]

I'm not sure about the first one. Initially it looked like a relatively simple color cycler but then more motion became apparent.

The second and third ones are a pretty simple "dilate" and "erode" image filter being animated over time and by an animated mask (in the second one.) LÖVE could do it with shader, or with a canvas or image pixel data, or maybe with a per-pixel mesh object.

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You seem to be right in both cases! Dilate/Erode it is.
I just tested it with a picture of clouds and a picture of a cat in Gimp

Thank you very much! I had no idea what to look for.
Maybe I'll even find the first one by experimenting with Gimp

Edit:
Just found this video on vimeo as well, with a more thorough description:

The video simulates the phenomenon of texture breathing, a distinctive and beautiful effect where colours and patterns appear to spontaneously dilate, contract and ripple. The effect is produced by computing the vector derivative of a source photo then applying iterative advection along the resulting axes. A secondary scalar field controls and strength and magnitude of advection and allows a range of interesting effects including pulsing, waving and breathing.

Hmm I guess I have to look some things up...