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

Benoit Mandelbrot

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
BENOIT MANDELBROT

Circles Lines Shapes
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
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
I had very, very little training in taking an exam to determine a scientist’s life in France.
BENOIT MANDELBROT

France Littles Training
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’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
Unfortunately, the world has not been designed for the convenience of mathematicians.
BENOIT MANDELBROT

Convenience Mathematician World
Bottomless wonders spring from simple rules, which are repeated without end.
BENOIT MANDELBROT

Miracle Simple Spring
$Benoit Mandelbrot Quote - A fractal is a way of seeing infinity.$

A fractal is a way of seeing infinity.
BENOIT MANDELBROT

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

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

Complexity Formulas Simple
Asking the right questions is as important as answering them
BENOIT MANDELBROT

Asking Important Questions Right
$Benoit Mandelbrot Quote - Beautiful, damn hard, increasingly useful. That’s fractals.$

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

Beautiful Fractals Increasingly
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

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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