Everyone is by now familiar with the (2-dimensional) fractal Mandelbrot set... Jennifer Ouellette writes about a 3-dimensional extension of it called a "Mandelbulb" fractal here and the difficulty that was involved in creating a computer generation of it (at left):
(oh, and she ends with another video clip employing Jonathan Coulton's "Mandelbrot Set" song, which I can never hear too many times.)
...Meanwhile, many more folks across the Web have responded to E.O. Wilson's piece which I referenced yesterday. Of course it's a debate full of nuances on both sides, so I won't pursue it further, except to possibly give it a little further context by offering the (16-min.) 2012 TEDTalk where Wilson originally put forth his somewhat rebel view:
pssssst… one word to young people planning their future in 2013… "mathematics"
According to a longish piece from Bloomberg Businessweek, "Math Will Rock Your World." It reports on many of the already well-covered issues (positive and negative) surrounding how mathematics is invading/changing the digital world we now live in:
"The world is moving into a new age of numbers. Partnerships between mathematicians and computer scientists are bulling into whole new domains of business and imposing the efficiencies of math… Says James R. Schatz, chief of the mathematics research group at the National Security Agency: 'There has never been a better time to be a mathematician.' "...companies are hitching mathematics to business in ways that would have seemed fanciful even a few years ago… "Top mathematicians are becoming a new global elite. It's a force of barely 5,000, by some guesstimates, but every bit as powerful as the armies of Harvard University MBAs who shook up corner suites a generation ago... "One significant challenge to the math revolution is to build new businesses from data without sacrificing privacy… The goal now is to create systems that share group information while shielding the individual… Mathematicians are at the heart of the privacy battle -- on both sides...
"As more of the world's information is pooled into mathematics, the realm
of numbers becomes an ever larger meeting ground. It's a percolating
laboratory full of surprising connections, and a birthplace for new
industries. Yes, it's a magnificent time to know math."
But so much for the world of business… At least once a year I find some excuse to link to Jonathan Coulton's rousing "The Mandelbrot Set" song, 'cuz… HEY... it… just… ROCKS… too!! Usually I link to this YouTube version:
…but here is Coulton actually singing the song live (not a great recording, but follow along the marvelous lyrics below. You can also download the tune from Jonathan's website: http://www.jonathancoulton.com/ )
Lyrics:
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 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 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 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 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 -------------------------
(...you'll never get that from Justin Bieber ;-))
ADDENDUM: p.s. for any who don't know, Benoit Mandelbrot passed away a couple of years back. His memoir, "The Fractalist" was published last year.
"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" --Jonathan Coulton
If the life of Benoit Mandelbrot interests you then a new book coming out shortly will be of note, a posthumous autobiography, entitled "The Fractalist." [Mandelbrot died just 2 years ago this month.]
I haven't read it, but from what I can tell, if you're interested primarily in the details of Mandelbrot's mathematical contributions this volume may not be a good choice, but if you're interested in his life this is a definite read:
Video of Mandelbrot Set with Jonathan Coulton's lyrics below:
lyrics:
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**king 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 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**king 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
