Mandelbrot set love

Definitions

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

  • n. 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

  • n. the set of complex numbers c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. The boundary of this set is a fractal.

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

  • n. 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 (born 1924), Polish-born American mathematician.

Examples

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Comments

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  • 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