Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
- noun The set of complex numbers C for which the iteration zn+1 = zn2 + C produces finite zn for all n when started at z0 = 0. The boundary of the Mandelbrot set is a fractal.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun mathematics the
set 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.]
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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