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

black
grey
blue
red
brown
white

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

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.
BENOIT MANDELBROT

Able Colossal Fashion Kind Rewarded Risk
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 had very, very little training in taking an exam to determine a scientist’s life in France.
BENOIT MANDELBROT

France Littles Training
The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
BENOIT MANDELBROT

Powerful Science Tool
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
Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
BENOIT MANDELBROT

Branches Color Thinking
$Benoit Mandelbrot Quote - A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…$

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROT

Definitions Scales Science
$Benoit Mandelbrot Quote - Beautiful, damn hard, increasingly useful. That’s fractals.$

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

Beautiful Fractals Increasingly
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
It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.
BENOIT MANDELBROT

Clouds Simple Views
One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.
BENOIT MANDELBROT

Luck Persistence Reward
If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
BENOIT MANDELBROT

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

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
I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
BENOIT MANDELBROT

Book Dream Kind
Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.
BENOIT MANDELBROT

Helpful Littles Machines
The Mandelbrot set is the most complex mathematical object known to mankind.
BENOIT MANDELBROT

Complexe Mankind Math
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
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

Circles Clouds Mountain
An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
BENOIT MANDELBROT

Arrogance Claims Firsts
Think not of what you see, but what it took to produce what you see.
BENOIT MANDELBROT

Produce See Thinking Took
My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.
BENOIT MANDELBROT

Choices Complicated People
In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
BENOIT MANDELBROT

Country Numbers Problem School
If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
BENOIT MANDELBROT

Lines Looks Shapes Straight
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
My fate has been that what I undertook was fully understood only after the fact.
BENOIT MANDELBROT

Facts Fate Understood
Unfortunately, the world has not been designed for the convenience of mathematicians.
BENOIT MANDELBROT

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

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

Chaos Shapes Strong