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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

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Definitions Simple Years

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Marilyn Monroe Paulo Coelho Abraham Lincoln C. S. Lewis Khalil Gibran Charlie Chaplin Gautama Buddha Isaac Newton

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

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

Definitions Scales 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
$Benoit Mandelbrot Quote - Beautiful, damn hard, increasingly useful. That’s fractals.$

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

Beautiful Fractals Increasingly
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
Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
BENOIT MANDELBROT

Facts Observation Order Science
Bottomless wonders spring from simple rules, which are repeated without end.
BENOIT MANDELBROT

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

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

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

Complexity Formulas Simple
Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
BENOIT MANDELBROT

Engineering May Science
$Benoit Mandelbrot Quote - A fractal is a way of seeing infinity.$

A fractal is a way of seeing infinity.
BENOIT MANDELBROT

Fractals Infinity Way
I had very, very little training in taking an exam to determine a scientist’s life in France.
BENOIT MANDELBROT

France Littles Training

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