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Posted (edited)

Fractals

 

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I like fractals. But what are they?

A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.

Yeah, but no. Doesn't cover strange attractors very well. Doesn't even cover all the stuff you can make using procedures similar to the one that produces the Mandelbrot set.

the fractal dimension is greater than the topological dimension

Only covers some fractals.

 

 

I got one which covers all fractals.

Contains nested or chaotic structures

 

 

Lets take a look

 

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Chaotic

 

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Nested & Chaotic

 

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Nested

 

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Chaotic

 

 

Nested in fairly straightforward, it means self recurring. like a tree.

 

Chaotic means like a cloud. Not random, but not entirely ordered ether. Mathematical Chaos allows apparently random numbers to come apparently from nowhere, from just a few repetitions of simple rules.

Edited by alan2here

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