Benoît Mandelbrot - The Fractal Geometry of Nature (1982)

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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...

Benoît Mandelbrot

I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."

Benoît Mandelbrot

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

Benoît Mandelbrot

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.

Benoît Mandelbrot

A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.

Benoît Mandelbrot

I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break:" to create irregular fragments... how appropriate for our needs!

Benoît Mandelbrot