A new kind of fractal? • Hacker News Board

Re: A new kind of fractal?

#51

Post by iazid » Fri, Oct 19, 2012, 5:59 PM UTC

Probably you still can define a fractal by changing slightly the construction.

Anyways, here's my take for a generalization : http://imgur.com/qD0aZ

Re: A new kind of fractal?

#52

Post by knicholes » Mon, Oct 22, 2012, 1:59 PM UTC

To me, it looks VERY similar to the Laue pattern of the enzyme Rubisco. http://www.amazon.com/Photographic-diffraction-Science-Photo...

Re: A new kind of fractal?

#53

Post by chaorder » Wed, Oct 24, 2012, 10:18 PM UTC

madhadron wrote: post #16

It's not a fractal, but it is something familiar. Multiply two complex numbers z and c is equivalent to taking z and applying a rotation and dilation to it, the rotation through arg(c) and the dilation through |c|. Division is the inverse of both, so z/c is z rotated by -arg(c) and dilated by 1/|c|. What you're looking at, then, is taking the operation defined by c (rotate by -arg(c) and dilate by 1/|c|) and asking,…

Thanks Madhadron, this makes a lot of sense. The Gaussian Numbers define a grid in the Complex plane. This calculation highlights complex numbers which represent best the ratios among Gaussian Numbers. It shouldn't be surprising to find such an ordered distribution.