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

After Benoit B. Mandelbrot (born 1924), Polish-born American mathematician.
(American Heritage® Dictionary of the English Language, Fourth Edition)

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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