R.I.P Mandelbrot

  Quote

AFP

 

Benoit Mandelbrot, a French-American mathematician who explored a new class of mathematical shapes known as "fractals", has died aged 85.

 

His wife Aliette told the New York Times on Saturday he died of pancreatic cancer at a hospice in Cambridge, Massachusetts, on Thursday.

 

His seminal book, "The Fractal Geometry of Nature," published in 1982, argued that irregular mathematical objects once dismissed as "pathological" were a reflection of nature.

Advertisement: Story continues below

 

The fractal geometry he developed would be used to measure natural phenomena like clouds or coastlines that once were believed to be unmeasurable.

 

He applied the theory to physics, biology, finance and many other fields of study.

 

"Fractals are easy to explain, it's like a romanesco cauliflower, which is to say that each small part of it is exactly the same as the entire cauliflower itself," Catherine Hill, a statistician at the Gustave Roussy Institute, told AFP.

 

"It's a curve that reproduces itself to infinity. Every time you zoom in further, you find the same curve," she said.

 

David Mumford, a professor of mathematics at Brown University, told the Times that Mandelbrot had effectively revolutionised his field.

 

"Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found," the Times quoted him as saying.

 

"He was one of the primary people who realised these were legitimate objects," Mumford added.

 

Mathematicians and economists were among those who reacted swiftly to Mandelbrot's death on the internet.

 

Nassim Nicholas Taleb, the statistician and philosopher best known for the book "The Black Swan," turned over his website to mourn Mandelbrot's passing.

 

The page featured only the words: "Benoit Mandelbrot, 1924-2010, A Greek among Romans."

 

Chris Anderson, the organiser of the TED conferences that feature addresses from prominent thinkers drawn from a variety of fields, offered his condolences on his Twitter page.

 

He described Mandelbrot, who addressed the Technology, Entertainment, Design conference earlier this year, as "an icon who changed how we see the world".

 

A professor emeritus at Yale University, Mandelbrot was born in Poland but as a child moved with his family to France where he was educated.

 

In the United States and around the world, his work attracted the attention of academics, but also pop culture because the fractals he uncovered could be illustrated in stunningly beautiful, multi-coloured representations.

see you on the other side of the border, bro

*pours self-similar forty*

oh shit. i'm fucking saddened by this, the man was like elvis to me

  On 10/16/2010 at 10:29 PM, kaini said:

oh shit. i'm fucking saddened by this, the man was like elvis to me

kaini please don't change your avatar

goodbye

[vimeo]1908224[/vimeo]

Cool story, bro

2+2= 4

*tips cap and nods to kaini*

We need a watmm fractal.

what makes it really sad for me is that he only became aware of the mandelbox/mandelbulb about six months ago, and was apparently very interested.

rudy rucker on mandelbrot: "In the event, it’s not really like meeting Gödel because I’m not so young and starry-eyed that I see Mandelbrot as a mythopoetic guru. Yet it is like meeting Gödel in the sense that for these two special oasis hours midway in the long caravan of my life I’m talking to someone whom I feel to be smarter than me. An ascended master."

http://www.rudyrucker.com/blog/2010/10/16/remembering-benoit-mandelbrot/

  Quote

IN 2004, a few years after the burst of the .com bubble, you asked that a little part of the R&D budget of the big financial companies of Wall Street be devoted to fundamental research. Have you been heard ?

 

Nowadays, most of these companies have fired their researchers. So the question is to know what theory are they relying on ? The wet finger ? I don't know.

oh yeah you know you old dirty pig

  On 10/17/2010 at 3:23 AM, Babar said:

  Quote

IN 2004, a few years after the burst of the .com bubble, you asked that a little part of the R&D budget of the big financial companies of Wall Street be devoted to fundamental research. Have you been heard ?

 

Nowadays, most of these companies have fired their researchers. So the question is to know what theory are they relying on ? The wet finger ? I don't know.

 

oh yeah you know you old dirty pig

http://www.youtube.com/watch?v=-58-36lSqG4

both mandelbrot and ratm saw the infocalypse coming, just approached it from different directions

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<ImageHeight; ++y)
{
   double c_im = MaxIm - y*Im_factor;
   for(unsigned x=0; x<ImageWidth; ++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<MaxIterations; ++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); }
   }
}

RIP

lots of future generations will stand on the shoulders of this giant.

80 video fractal zoom playlist, in case you feel like tripping on honour of the man who provided the illustrations for the poetry of reality.

Seriously, how could anyone base their lives round a sad old medieval cult of ignorance, knowing that the real world is this awesome?

  On 10/17/2010 at 3:42 AM, kaini said:

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<ImageHeight; ++y)
{
   double c_im = MaxIm - y*Im_factor;
   for(unsigned x=0; x<ImageWidth; ++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<MaxIterations; ++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); }
   }
}

could you comment your code especially variables (MinRe, MaxIm etc) and enlighten me ? thanks

  On 10/17/2010 at 12:48 PM, Babar said:

  On 10/17/2010 at 3:42 AM, kaini said:

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<ImageHeight; ++y)
{
   double c_im = MaxIm - y*Im_factor;
   for(unsigned x=0; x<ImageWidth; ++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<MaxIterations; ++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); }
   }
}

 

could you comment your code especially variables (MinRe, MaxIm etc) and enlighten me ? thanks

Those are the parameters with which the coordinates in the complex plane are translated to coordinates of your image (or vice versa, but you get the idea). For more info wiki "mandelbrot". As always, when it comes to mathematics/computer science wikipedia is an excellent resource.

Gutted when I heard this on the news this morning :(

As mentioned, his work will inspire generations of research to come, without doubt.

it's 20/10/2010 (GMT). i would have liked if mandelbrot could have held out until today, and i'm sure he would have got a lol out of it too if he did.

Good riddance.

  On 10/17/2010 at 12:48 PM, Babar said:

  On 10/17/2010 at 3:42 AM, kaini said:

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<ImageHeight; ++y)
{
   double c_im = MaxIm - y*Im_factor;
   for(unsigned x=0; x<ImageWidth; ++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<MaxIterations; ++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); }
   }
}

 

could you comment your code especially variables (MinRe, MaxIm etc) and enlighten me ? thanks

all the double_Re and double_Im stuff is just a very primitive way of establishing a structure for complex numbers

i've tried some pseudocode - i'm a bit wasted

http://en.wikipedia.org/wiki/Mandelbrot_set is also good

apologies if any mistakes, but the algorithm is basically

  Quote

1. establish a type for complex numbers. the rules complex numbers obey are:

1a. complex numbers are basically a 2d array, let's call it z

1b. the first dimension of the array is A - integers; the regular number line

1c. the second dimension of the array is B - i. i = sqrt(-1)

more info at http://en.wikipedia.org/wiki/Complex_number

 

2. map the available screen resolution R onto another array of real numbers M

2b. M starts at (-2, -2) and ends at (2, 2) - in other words the program should be able to plot at a 2d real M between (-2,-2) and (2,2) and the program should map it onto array R and subsequently, a pixel on-screen.

 

3.

initalize n=0

for each R(y) (

..... for each R(x) (

..... z(n) = a complex number (0,0)

..... c = a complex number, current value of M

..... repeat

............z(n+1) = z(n)^2+c (bearing in mind the rules for complex numbers above)

............if sqrt(z(A)^2+z(B)^2) exceeds 2 at any point, colour the pixel white and goto bail (been proven that the radius of the M-set is 2).

............if n exceeds a certain predefined number (called maximum iteration) colour the pixel black

............add 1 to n

bail: next x pixel

....next y pixel