$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$
$Benoit Mandelbrot Quote - The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.$

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The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.

Benoit Mandelbrot

A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.
BENOIT MANDELBROT

Clouds Looks Smooth
In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.
BENOIT MANDELBROT

Definitions Simple Years
Nobody will deny that there is at least some roughness everywhere
BENOIT MANDELBROT

Deny Everywhere Roughness
I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
BENOIT MANDELBROT

Computer Levels Mathematics
$Benoit Mandelbrot Quote - Beautiful, damn hard, increasingly useful. That’s fractals.$

Beautiful, damn hard, increasingly useful. That’s fractals.
BENOIT MANDELBROT

Beautiful Fractals Increasingly
Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
BENOIT MANDELBROT

Branches Color Thinking
The Mandelbrot set is the most complex mathematical object known to mankind.
BENOIT MANDELBROT

Complexe Mankind Math
My fate has been that what I undertook was fully understood only after the fact.
BENOIT MANDELBROT

Facts Fate Understood
Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
BENOIT MANDELBROT

Fashion Happen Mathematics Strong
$Benoit Mandelbrot Quote - Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.$

Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
BENOIT MANDELBROT

Chaos Impossible Past
Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills
BENOIT MANDELBROT

Memories News Pieces Somewhere
I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
BENOIT MANDELBROT

Firsts Littles Mathematician Pure World
$Benoit Mandelbrot Quote - Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.$

Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
BENOIT MANDELBROT

Fractal Humanity Ideas Long Roots
The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
BENOIT MANDELBROT

Lines Pieces Self
A formula can be very simple, and create a universe of bottomless complexity.
BENOIT MANDELBROT

Complexity Formulas Simple
$Benoit Mandelbrot Quote - When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.$

When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
BENOIT MANDELBROT

Field Hands People