Deep Fractal Zoom - Input Junkie
Deep Fractal Zoom|Almost 10 minutes of garish and beautiful Mandelbrot, going to e 218
Anyone know whether the Mandelbrot set ever repeats? I'm betting not. Whether the patterns are at all predictable without fully computing them?
Link thanks to Geek Press
I've been reading Penrose's The Emperor's New Mind, which discusses the Mandelbrot set among other things; it's a fascinating and very difficult book. From what he says there, it wasn't known to repeat when he wrote it, though I don't know if it's been proven not to repeat.
|Date:||February 18th, 2010 04:28 am (UTC)|| |
Nope! It will be mirrored vertically but as each point on the Mandel corresponds to a discrete Julia set it can't be the same. As to the domain of the function, transfinite cardinals are um... funny kinda things. I'd bet on it being Aleph-1 though (hell, lots of my rants depend on it being so!)
I slogged my way through that book about 20 years ago and congrats on tackling it. It's like Penrose says, it's heavy shit so, gnaw on it, get what you can, and just skip over the parts that make your ears bleed. :D By the way, it took me almost a year of gnawing once in a while, but it was a very tasty bone.
|Date:||February 18th, 2010 05:53 am (UTC)|| |
The Mandelbrot set will never repeat...but you can get things that are so similar, it will be almost identical. That's the joy of self-similarity.
|Date:||February 18th, 2010 10:20 am (UTC)|| |
Thanks, that was relaxing. I bought a cassette of Mandelbrot & Julia sets back in the 90s which moves a lot more slowly than that with electronic music in the background.