Someone figured out a use a long time ago: the Doctor Who (British SciFi) opening sequence. And apparently before that for Amahl and the Night Visitors, a drama broadcast in 1951: http://www.bbc.co.uk/dna/h2g2/A907544
You can do something similar, although not quite as intricate, by simply pointing your webcam at a computer screen that is displaying the webcam-feed. You get infinitely repeating patterns that respond in beautiful ways to subtle tilts and nudges of the webcam. It's really pretty impressive and worth 5 minutes of your time if you have an external webcam around.
Doesn't it depend on your precise definition of Fractal. In nature they're not self-similar repetitions at altered scale but approximate the same¹. There is always a limitation in nature of resolution (lumpiness of atoms) just as no true circle can exist in nature (at least in our realm Plato², please correct me if I'm wrong).
So technically most (all I think) fractals do not occur extent in reality but only the mathematical description of them occurs.
_Godel, Escher, Bach_ describes similar phenomena with camera feedback loops. When I read GEB, I wondered if it would be possible to create a Sierpinski triangle using four specially shaped/curved mirrors. I briefly played with povray, but didn't figure it out.
Does real-time video not at the very least involve a micro-controller? So arguably this is one way to make fractals WITH a computer. It looks cool and video feedback does make nice effects.
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[ 3.2 ms ] story [ 41.2 ms ] threadhttp://www.fourmilab.ch/images/Romanesco/
Example feedback patterns: http://www.youtube.com/watch?v=C8Xm3EA3_XE
Triangular pattern doesn't say very much. Is this supposed to mean that the trick will work iff the screens are not collinear?
So technically most (all I think) fractals do not occur extent in reality but only the mathematical description of them occurs.
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¹ note the precise definition of "similar" in geometry, http://en.wikipedia.org/wiki/Similarity_%28geometry%29. ² I can't recall Plato's take on [perfect] forms of biological "shapes" like trees and such.