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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

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

Facts Fate Understood
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.
BENOIT MANDELBROT

Lying Mountain Nature Science Tree
I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.
BENOIT MANDELBROT

Different Mathematician Uncles Want
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
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
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
$Benoit Mandelbrot Quote - Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.$

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

Arrogance Claims Firsts
There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROT

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

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

Complexity Formulas Simple
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
Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
BENOIT MANDELBROT

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

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 most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
BENOIT MANDELBROT

Chaos Mankind Mathematics
Bottomless wonders spring from simple rules, which are repeated without end.
BENOIT MANDELBROT

Miracle Simple Spring
There is a saying that every nice piece of work needs the right person in the right place at the right time.
BENOIT MANDELBROT

Needs Nice Pieces
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
$Benoit Mandelbrot Quote - A fractal is a way of seeing infinity.$

A fractal is a way of seeing infinity.
BENOIT MANDELBROT

Fractals Infinity Way
Think not of what you see, but what it took to produce what you see.
BENOIT MANDELBROT

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

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

Complexe Mankind Math

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