## Definitions

### from The American Heritage® Dictionary of the English Language, 5th Edition.

- noun The set of complex numbers
*C*for which the iteration*z*_{n}_{+1}=*z*_{n}^{2}+*C*produces finite*z*for all_{n}*n*when started at*z*_{0}= 0. The boundary of the Mandelbrot set is a fractal.

### from Wiktionary, Creative Commons Attribution/Share-Alike License.

- noun
*mathematics*theset ofcomplex numbers c for which theorbit of 0 underiteration of thecomplex quadratic polynomial zn+1 = zn2 + c remainsbounded . Theboundary of this set is afractal .

### from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

- noun a set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration

## Etymologies

### from The American Heritage® Dictionary of the English Language, 4th Edition

[After Benoit B.

*Mandelbrot*, (1924–2010), Polish-born American mathematician.]## Support

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## Examples

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PossibleUnderscore commented on the word Mandelbrot set

There is an extrememely amusing song by Jonathan Coulton, called Mandelbrot set. It is also a little helpful if you are not really a mathmetician.

Pathological monsters! cried the terrified mathematician

Every one of them is a splinter in my eye

I hate the Peano Space and the Koch Curve

I fear the Cantor Ternary Set

And the Sierpinski Gasket makes me want to cry

And a million miles away a butterfly flapped its wings

On a cold November day a man named Benoit Mandelbrot was born

His disdain for pure mathematics and his unique geometrical insights

Left him well equipped to face those demons down

He saw that infinite complexity could be described by simple rules

He used his giant brain to turn the game around

And he looked below the storm and saw a vision in his head

A bulbous pointy form

He picked his pencil up and he wrote his secret down

Take a point called Z in the complex plane

Let Z1 be Z squared plus C

And Z2 is Z1 squared plus C

And Z3 is Z2 squared plus C and so on

If the series of Z's should always stay

Close to Z and never trend away

That point is in the Mandelbrot Set

Mandelbrot Set you're a Rorschach Test on fire

You're a day-glo pterodactyl

You're a heart-shaped box of springs and wire

You're one bad*** f******g fractal

And you're just in time to save the day

Sweeping all our fears away

You can change the world in a tiny way.

etc...

January 3, 2010