Benoit Mandelbrot, the father of fractal geometry, has died. He was 85.

"Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently." -Benoit Mandelbrot (1924-2010)"Benoit Mandelbrot the Maverick, 1924-2010"

*(The Atlantic)*

Long Live Mandelbrot *(Imaginary Foundation)*

“Mandelbrot’s in heaven.”

— Jonathan Coulton

Mandelbrot Set

I guess JoCo needs to update his song…

http://www.jonathancoulton.com/songdetails/Mandelbrot Set

Not many people know that Mandelbrot did his best thinking about Fractal Geometry while he was standing at his bathroom sink, staring at himself in the mirror.

RIP

http://www.digitalartform.com/archives/2004/11/benoit_mandelbr.html

I zoomed in on that photo and I’m pretty sure his hair is a fractal.

The man may be gone but his contributions go on forever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever. And ever.

“My fate has been that what I undertook was fully understood only after the fact.”

Benoit Mandelbrot

RIP

Such a shame that he didn’t get more mainstream recognition – his work truly revolutionized the understanding of how the world assembles itself, and without him computer graphics would not be the same. Every CG cloud, every mountain, etc. should be wearing a little black arm band.

While he coined the term “fractal”, expended the concept’s use and understanding, and won the hearts of the masses with his super cool computer representations – it’s good to remember that he stood on the shoulders of great mathematicians who came before him in the field, such as Weierstrass, Koch, Cantor, and Gaston Julia – my 2nd favorite scientist without a nose. I don’t know if “father of fractal geometry” is a fair term here. He certainly cranked a quiet signal up to 11 though.

Rest peacefully in the infinite depths.

Arguably Koch and Julia have more claim to being the ‘father’ of fractal geometry, but Mandelbrot was unquestionably the man who brought it into public use.

Age 17 I spent all of a particularly boring physics lesson coding a crude Mandelbrot generator on my Casio fx-7700. I still have that calculator in a top cupboard; I’ve never had the heart to throw it away since.

Dr. Mandelbrot becomes the Mandelbrot. When we miss him we can visit him there.

Back in the 90s I worked at IBM manufacturing in Poughkeepsie. From time to time we interfaced with R&D in Yorktown Heights. One day we were having lunch there, and I idly looked around the cafeteria- and there’s Mandelbrot, alone at a small table.

“Is that…?”

“Yup.”

It was hard not to stare.

benoit ignited a passion for maths in me that’s still there sixteen years later. jeff buckley once described nusrat fateh ali khan as ‘my elvis’. well, that’s sort of the way i feel about doctor mandelbrot. a sad day.

One of the best math classes I ever took was ‘Chaotic Dynamic Systems’. One of the first java applets I ever wrote (back in the e .8 beta days) was a Mandlebrot set applet.

‘Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.’ – Benoit Mandelbrot.

A friend of mine suggests that JoCo should just replace the lyrics about Mandelbrot still being alive and teaching at Yale with several beats of silence

RIP ~ i wrote my first mandelbrot program for the motorola 6800 cpu in the comodore amiga , around 1986 or so , in forth and assembler language ~ i wrote the inner ” butterfly ” complex arithmetic multiply routine and also implemented a scaled integer square root algorithm myself ~~ so many lovely pictures , and real world physics applications too !!

Rudy Rucker posted a neat remembrance of Mandelbrot on his blog: http://www.rudyrucker.com/blog/2010/10/16/remembering-benoit-mandelbrot/

double MinRe = -2.0;

double MaxRe = 1.0;

double MinIm = -1.2;

double MaxIm = MinIm+(MaxRe-MinRe)*ImageHeight/ImageWidth;

double Re_factor = (MaxRe-MinRe)/(ImageWidth-1);

double Im_factor = (MaxIm-MinIm)/(ImageHeight-1);

unsigned MaxIterations = 30;

for(unsigned y=0; y
{
{

double c_im = MaxIm - y*Im_factor;

for(unsigned x=0; x

double c_re = MinRe + x*Re_factor;

double Z_re = c_re, Z_im = c_im;
{

bool isInside = true;

for(unsigned n=0; n

double Z_re2 = Z_re*Z_re, Z_im2 = Z_im*Z_im;

if(Z_re2 + Z_im2 > 4)

{

isInside = false;

break;

}

Z_im = 2*Z_re*Z_im + c_im;

Z_re = Z_re2 – Z_im2 + c_re;

}

if(isInside) { putpixel(x, y); }

}

}

http://boingboing.net/images/brot.jpg

RIP. For my part, the first Mandelbrot program I wrote from scratch was on my TI-85 (which has a Z80 ÂµP) in high school–I started it around 10 AM, and it had rendered most of the set by 3 PM. Actually, I still have that calculator . . .

Off to measure the coast of Britain in memory.

File under “people I didn’t know were still alive until they died.”

When I was a kid in the mid 1990s, we had a CD-ROM of Encyclopedia Encarta. It had a number of interactive ‘games’, one of which was Fractal Trees, which introduced me to the concept and the name Mandelbrot.

(That Encarta also had some random music videos on it- I remember Changes by David Bowie in particular.)

RIP MANDLEBROT, YOU WILL BE MISSED AND YOUR WORK REMEMBERED.

Thanks for making my video games look awesome! RIP Mandelbrot!

My first exposure to Mandelbrot was Arthur C. Clarke’s “The Colors of Infinity”. To hear Clarke describe it, I remember thinking I was on the verge of unlocking some kind of secret of the universe, with infinite worlds exisitng within each other. But then it ended and I was left thinking, “….”. The a-ha never came. It was just trippy graphics set to a Sci-Fi storyteller.

Looking at his hair next to the fractal image, the mirror story makes perfect sense.

I’d like to think that Dr. Mandelbrot has just zoomed into the macrocosm…or the microcosm. He was a modern day Hermes Trismegistus. RIP mapping that eternal shoreline!

Here’s a Buddhabrot:

http://www.superliminal.com/fractals/bbrot/half_res_rgb.gif

Someone in Bronze Age India has a _lot_ of explaining to do there! C-:

Benoit M. was the winner of a fight between orthodox mathematicians, who claimed that Proofs must come first…

…and programmer-mathematicians, who used computers to explore formulaic spaces BEFORE proving things about the landscapes they discovered.

We who now take computers for granted forget that mathematicians using them were once scorned as “relying on crutches”.

Philip, you’re creating a straw man. How can proofs come first? Any statement that is eventually proved has to start as a conjecture. Mathematical exploration isn’t something that Mandelbrot invented.

Actually I’m citing the Scientific American article on the Mandelbrot, from the early 1980s, IIRC.

Mandelbrot’s eulogies are calling him a “maverick”. I’m pointing out why – because traditionalists did not like programmers leaning on their computer programs.

The issue here is not “strawman” arguments but mythification. Mandelbrot was considered a maverick for a very specific reason.

I was fortunate enough to meet the man many years ago at a fractals in engineering symposium. I am certain that most of the real scientific breakthroughs in the years ahead will come about as a result of studying, in any field, the boundaries. All the action is at the edges! RIP

Rest in peace, sir. Thanks to Benoit Mandelbrot and the really smart guys behind Fractint, I was able to make a little money selling videotapes of color-cycling Mandelbrot tendrils at the Ann Arbor Art Fair in 1992. Fractals got me into computer graphics and computer graphics got me out trouble and into a fascinating and rewarding career.

In my last year of high school, I did a science project where I attempted to calculate the fractal dimension of the edges of tree leaves (maple leaves had the most fractal-like features, and, it so happens, the highest fractal dimension). The math behind my Basic program was a bit over my head, but I did get interesting results.

When presenting the project at a science project expo, I would use a PC with Fractint and would zoom into a Mandelbrot set to demonstrate the internal symmetry of fractals, as an introduction to my project.

Since then, whenever I’ve learned to program graphics on a new platform, I programmed a Mandelbrot set “browser” with zooming capability as one of my first exercises. My most recent attempt is a Mandelbrot set browser for the Nintendo DS. Anyone with a DS flash cart should be able to run this:

http://50wordstories.ca/a/Mandel.nds

The controls are on-screen. Note that selecting a zoom-in area will modify your aspect ratio… I haven’t bothered to correct for that, yet. When not in the mode that lets you select zoom-in coordinates, the L and R buttons cycle the colors.

Also note that if you zoom in too far, you reach the limits of the Double-precision float data type I used, so don’t expect to do any extreme deep-zooming. Anyway, the rendering would take hours at that point, expecially since I didn’t optimize the rendering much.

I got into mathematics because of Mandelbrot, I got into computer science because of Mandelbrot…

Kind of a shock…

When experimenting with hallucinogenic substances it quickly became a frequent thing for me to visit a flatland like plane where all history is laid out as a Mandelbrot fractal. It was so scary while under the influence to think that every sensory experience, from every nervous twitch to every Luftwaffe bomber takeoff was somehow already graphed into that fractal and we are just experiencing the sensory phonograph stylus playing the pattern back to us.

Benoit Mandelbrot, we will miss you, thanks for the dreams and the bad trips.

And let’s not forget that Barbara “Excuse me stewardess, I speak Jive” Billingsley also died today at age 94.

I guess Mandelbrots don’t go on forever.

One way to honor his memory is to serve fractal broccoli for dinner:

http://en.wikipedia.org/wiki/File:Fractal_Broccoli.jpg

One way to honor his memory is to serve fractal broccoli for dinnerThe problem with this is that the infinite surface area of the first piece uses up all the cheese sauce.

Thank god he wasn’t murdered. The police would have taken forever to draw the chalk outline!

…too soon?

“Take a point called Z in a complex plane….”

Joco

RIP

Dr. Steve Brule?!?

I like Julia.

.. but Quaternions, Newton, IFS are cool kind of fractals as well.

I listed some fractal types here:

http://wotasa.com/cpage.php?id=50

of course you’re welcome to view examples and vote your favorite!

RIP Ben, you surely deserve a nice shaped stone.

I hear he originally wanted to call fractals Benoit Balls but then he thought better of it……

What Hokusai saw in his waves Mandelbrot saw in fractals.

Thank you for your hard work and the inspiration you provided to humanity.