Benoit Mandelbrot, who discovered mathematical shapes known as fractals, has died of cancer at the age of 85.

Mandelbrot, who had joint French and US nationality, developed fractals as a mathematical way of understanding the infinite complexity of nature.

The concept has been used to measure coastlines, clouds and other natural phenomena and had far-reaching effects in physics, biology and astronomy.

Mandelbrot's family said he had died in a hospice in Cambridge, Massachusetts.

The visionary mathematician was born into a Jewish family in Poland but moved to Paris at the age of 11 to escape the Nazis.

He spent most of his life in the US, working for IBM computers and eventually became a professor of mathematical science at Yale University.

His seminal work, The Fractal Geometry of Nature, was published in 1982. In it, he argued that seemingly random mathematical shapes in fact followed a pattern if broken down into a single repeating shape.

The concept enabled scientists to measure previously immeasurable objects, including the coastline of the British Isles, the geometry of a lung or a cauliflower.

"If you cut one of the florets of a cauliflower, you see the whole cauliflower but smaller," he explained at the influential Technology Entertainment and Design (TED) conference earlier this year.

"Then you cut again, again, again, and you still get small cauliflowers. So there are some shapes which have this peculiar property, where each part is like the whole, but smaller."

Fractal mathematics also led to technological developments in the fields of digital music and image compression.

It has also been influential in pop culture, with the patterns being used to create beautiful and intricate pieces of art. One such design is named in his honour.

Mandelbrot was also highly critical of the world banking system, arguing the economic model it used was unable to cope with its own complexity.

In a statement, French President Nicolas Sarkozy praised Mandelbrot for his "powerful, original mind that never shied away from innovation and battering preconceived ideas".

"His work, which was entirely developed outside the main research channels, led to a modern information theory," he said.

Benoit Mandelbrot, who discovered mathematical shapes known as fractals, has died of cancer at the age of 85.


Fractals are cool.  What made the Mandelbrot set so awesome was that anyone who could do junior-high algebra]http://www.mun.ca/hpc/hpf_pse/manual/hpf0020.htm]junior-high algebra could write the programs (and wait overnight) to produce these images on their own 4.77-megahertz PC.

20 years later, what took all night can be done in real time as a visualization for your MP3 player.  Any time you see something like this in your MP3 player:

http://www.nullsoft.com/free/milkdrop/screenshots/thumb/fractals-01.jpg

You're actually looking at one of these:

http://scienceblogs.com/goodmath/upload/2007/08/julia.png

...which is just another way of looking at the real thing:

http://www.mun.ca/hpc/hpf_pse/manual/mandel_1.gif

Go on.  Look a bit closer.  The closer you think you are to understanding what's going on at the edges of it, the more you realize you're looking at the same thing, just a little differently.

http://www.mun.ca/hpc/hpf_pse/manual/mandel_2.gif

Any similarity between that sort of zoom - where no matter how closely you look, it looks the same, and the sorts of zooms found in nature...

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/romanesque.jpg

...is purely self-statistical.  (And the fact that a 5-minute stock chart that covers a day's trading looks like a monthly stock chart does when it covers 20 years?  Yup, markets are another example of the phenomenon.)

http://www.mun.ca/hpc/hpf_pse/manual/mandel_1.gif

Go on.  Look a bit closer.  The closer you think you are to understanding what's going on at the edges of it, the more you realize you're looking at the same thing, just a little differently.

The mother ship from Spielberg's Close Encounters of the Third Kind was based on this design,