Fractal Geometry: Simple Patterns in a Complex World

Professor Michael Barnsley with a fractally transformed teacup and pot. (Credit: Phil Dooley, ANU)

An ANU mathematician has developed a new way to uncover simple patterns that might underlie apparently complex systems, such as clouds, cracks in materials or the movement of the stockmarket.

“Fractal Geometry is a new branch of mathematics that describes the world as it is, rather than acting as though it’s made of straight lines and spheres. There are very few straight lines and circles in nature. The shapes you find in nature are rough.” said Michael Barnsley, Professor of Mathematics at ANU.

FrangoCamera App developed at ANU. (Credit ANU)

“Fractal Fourier analysis provides a method to break complicated signals up into a set of well understood building blocks, in a similar way to how conventional Fourier analysis breaks signals up into a set of smooth sine waves,” said Professor Michael Barnsley, who who presented his work at the New Directions in Fractal Geometry conference.

“There are terrific advances to be made by breaking loose from the thrall of continuity and differentiability…The body is full of repeating branch structures – the breathing system, the blood supply system, the arrangement of skin cells, even cancer is a fractal.”

via www.anu

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