# 03 What is a fractal? What are some examples of fractals?

## Description

This article is from the sci.fractals
FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous
contributions by others.

# 03 What is a fractal? What are some examples of fractals?

A fractal is a rough or fragmented geometric shape that can be

subdivided in parts, each of which is (at least approximately) a

reduced-size copy of the whole. Fractals are "generally" self-similar

and independent of scale.

There are many mathematical structures that are fractals; e.g.

Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set, and

Lorenz attractor. Fractals also describe many real-world objects, such

as clouds, mountains, turbulence, coastlines, roots, branches of

trees, blood vesels, and lungs of animals, that do not correspond to

simple geometric shapes.

Benoit B. Mandelbrot gives a mathematical definition of a fractal as a

set of which the Hausdorff Besicovich dimension strictly exceeds the

topological dimension. However, he is not satisfied with this

definition as it excludes sets one would consider fractals.

According to Mandelbrot, who invented the word: "I coined "fractal"

from the Latin adjective "fractus". The corresponding Latin verb

"frangere" means "to break:" to create irregular fragments. It is

therefore sensible - and how appropriate for our needs! - that, in

addition to "fragmented" (as in "fraction" or "refraction"), "fractus"

should also mean "irregular," both meanings being preserved in

"fragment"." (The Fractal Geometry of Nature, page 4.)

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