I love Jonathan Coulton. I love fractals. I love this song. I want to get a butterfly tattoo on my wrist (I’m not kidding, by the way) to remind me that infinite complexity can be described by simple rules and that:
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home
Note that Jonathan is rocking the “long curly haired geek with beard and glasses look”. I love that. 
I should also note that the song uses the F-word a couple times, so if you’re likely to be offended, well, I warned you.
Also amusing is the note that the person who posted the video included: “Near the end of the song, JoCo looks to his left and smiles. This is because I was waving a picture of a fractal back and forth, like a lighter, on my iPhone.”
Lyrics follow video, might be fun to follow along.
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 badass f#%*ing 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
Mandelbrot’s in heaven, at least he will be when he’s dead
Right now he’s still alive and teaching math at Yale
He gave us order out of chaos, he gave us hope where there was none
And his geometry succeeds where others fail
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home
Just 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 will 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 badass f#%*ing 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
And you’re just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Go on change the world in a tiny way
Come on change the world in a tiny way
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