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I notice that fractals resemble natural shapes such as leaves or rivers. Leaves and rivers are solutions to problems in themselves. A leaf is trying to distribute the water to the leaf while the leaf may become broken and the leaf needs to distribute the water efficiently. So this leads me to think, is a fractal a solution to a problem just as a leaf is a solution to a problem?

Are there solutions to math problems hidden in fractals?

Are there solutions to real world problems in fractals?

If so, do fractals provide any solutions to hard problems which would be difficult to solve otherwise? Any quick ways to solve problems with fractals?

Added comments

I still think there is some potential to find solutions to problems within fractals, although no answer on this issue.

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Rather too soft a question for me, but at least in the case of lungs, the fractal arrangement allows for maximal surface area for absorbing oxygen within a very confined space. – J. M. Aug 5 '11 at 5:57
Some fractals resemble leaves or rivers, some (most!) fractals don't resemble anything anyone but a mathematician has ever seen, or will ever see. – Gerry Myerson Aug 5 '11 at 6:54
I think you should read Mandelbrot's book The Fractal Geometry of Nature. That's his thesis: that everything in the world (practically) is a fractal, and why. – GEdgar Aug 5 '11 at 13:41
The real world rarely covers more than a decade in scale, so self-similar mappings can be done over only a limited range of scales. An exception might be turbulence or phase transitions. @Phil Maybe that's the kind of problem that you are interested in? – Alice Aug 9 '11 at 14:22

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