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

black
grey
blue
red
brown
white

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

Benoit Mandelbrot

Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
BENOIT MANDELBROT

Pleasure Realizing Years
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
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
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 don’t seek power and do not run around
BENOIT MANDELBROT

Around Power Run Running Seek
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
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
$Benoit Mandelbrot Quote - Beautiful, damn hard, increasingly useful. That’s fractals.$

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

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

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

Facts Fate Understood
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
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
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