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There are very complex shapes which would be the same from close by and far away.

Benoit Mandelbrot

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

Deny Everywhere Roughness
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
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
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
I was in an industrial laboratory because academia found me unsuitable
BENOIT MANDELBROT

Academia Found Laboratory
$Benoit Mandelbrot Quote - A fractal is a way of seeing infinity.$

A fractal is a way of seeing infinity.
BENOIT MANDELBROT

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

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 rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
BENOIT MANDELBROT

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

Complexe Mankind Math
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
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
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
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
I’ve been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I’m not a mathematician only. I’m a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.
BENOIT MANDELBROT

Lists Long Yale
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 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

There are very complex shapes which would be the same from close by and far away.

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There are very complex shapes which would be the same from close by and far away.

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