Simple fractal definition

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

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 October 6, 200817 yr by alan2here