_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.
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.
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
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.
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.
