
#19
Aug711, 08:56 AM

P: 3,015

Also, notice the year when Hausdorff introduced this concept:
http://en.wikipedia.org/wiki/Hausdorff_dimension and compare it to the year stated in the title of your thread. 



#20
Aug711, 09:06 AM

P: 14

As the great Joey Ramone once said: "What is this? What's in it for me?" I've actually defined this concept in my last couple of posts. Nature, being economical, limits herself to a few structures which she repeats at different scales. Look at how the vascular systems of leaves emulate tree branches, and how tree branches emulate trees. Look at how atoms resemble solar systems and galaxies. Fractal geometry is a geometrical framework for understanding nature, the proof of which does not require any slavish emulation on the part of nature, which geometry is ABSTRACTED from nature, which nature, in turn, posesses finite resources with which to implement abstract patterns. WHEW!!! 



#21
Aug711, 09:08 AM

P: 3,015





#22
Aug711, 09:13 AM

P: 14





#23
Aug711, 09:18 AM

P: 3,015





#24
Aug711, 09:30 AM

P: 14

Galaxies and atoms have stuff in the middle and other stuff surrounding it. Galaxies have stuff spinning around their centers, whereas atoms have electrons existing in quantum levels surrounding their nuclei, but the overall similarity is obvious: it's structural repetition which allows for compression of data required to be conserved according to the quantum principle of unitarity. I'm really going to have to take a break from this tedium, seeing as my physical health is extremely poor, and I really haven't the energy for this type of nonsense. 



#25
Aug711, 09:32 AM

P: 3,015




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