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

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

Benoit Mandelbrot

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

Facts Fate Understood
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
I had very, very little training in taking an exam to determine a scientist’s life in France.
BENOIT MANDELBROT

France Littles Training
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
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
$Benoit Mandelbrot Quote - I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.$

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
BENOIT MANDELBROT

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

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
Order doesn’t come by itself.
BENOIT MANDELBROT

Come Itself Order
For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
BENOIT MANDELBROT

Interest Life Thing Wanted
Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
BENOIT MANDELBROT

Branches Color Thinking
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
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’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
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
$Benoit Mandelbrot Quote - I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.$

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
BENOIT MANDELBROT

Nomenclature Numbers Science
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