### fract.al

Fractals - What are Fractals?

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What are Fractals?

By Tom

The natural world around us is defined by irregular surfaces and shapes with uneven edges and rough corners. However, since Euclid classical geometry has only described the smooth ideal shapes - the circle, sphere, square, cube… - rarely, if ever, found in nature.

Fractals are the geometry of the natural world, they describe the texture of reality!

This insight was introduced by the Polish born French/American mathematician, Benoit Mandelbrot.

In 1975 he coined the word ‘fractal’ as a way to describe shapes that are detailed at all levels of scale. What started as an investigation into an obscure area of mathematics culminated in Mandelbrot defining the new field of fractal geometry.

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line…”

as described by Mandelbrot in his introduction to The Fractal Geometry of Nature.

Fractal geometry is an extension to classical geometry, which with the aid of computers, can model and describe structures from sea-shells to galaxies!

- Self-Similarity
- Fractal Dimension
- How Long is a Coastline?
- The First Fractal Explorations
- Complex Numbers
- Julia and Fatou
- Self-Squared Dragons
- A Map of Julia Sets - The Mandelbrot Map!
- Dressing the Fractal
- Further Reading

Erstellt: 2015-03