La canción del conjunto de Mandelbrot

Si nos ponemos a pensar en un objeto matemático al que se le pueda dedicar una canción, posiblemente a más de uno nos viniera a la mente el conjunto de Mandelbrot, ese maravilloso fractal cuya sencilla descripción, que debemos a Benoit Mandelbrot, y curiosas propiedades (aquí un interesante ejemplo) no dejan de sorprendernos.

Pues Jonathan Coulton debió pensar lo mismo que nosotros cuando compuso para su álbum When tradition meets tomorrow (2004) la canción Mandelbrot Set, dedicada al conjunto de Mandelbrot.

Jonathan Coulton es un cantante estadounidense que al parecer tiene experiencia en canciones de temática geek. La que nos ocupa no está mal, y en el estribillo aparece la definición del propio conjunto de Mandelbrot. Ahí va la canción:

Y aquí os dejo la letra, que he encontrado en esta página dedicada a Jonathan Coulton:

Pathological monsters! cried the terrified mathematician
Every one of them a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
The Sierpinski Gasket makes me wanna 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
Used his giant brain and he turned the game around
And he looked below the storm
Saw a vision in his head
A bulbous pointy form
Picked his pencil up and he wrote his secret down

Just take a point called Z in the complex plane (Alternate: Take a point called C…)
Let Z1 be Z squared plus C (Alternate: Let Z1 be zero squared…)
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Zs 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 fucking 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
His geometry succeeds where others fail
So 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 (Alternate: Take a point called C…)
Let Z1 be Z squared plus C (Alternate: Let Z1 be zero squared…)
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Zs will always stay
Close to Z instead of 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 fucking 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

Después de escuchar cómo suenan algunas constantes matemáticas, del famosísimo I will derive, del magnífico …Banach-Tarski! o del I integrate by parts, creo que ya tenemos otra canción para nuestra lista de canciones friki-matemáticas. Por cierto, ¿conocéis más? Los comentarios son vuestros.