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

black
grey
blue
red
brown
white

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

Benoit Mandelbrot

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

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

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

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

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
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
I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
BENOIT MANDELBROT

Firsts Littles Mathematician Pure World
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
Unfortunately, the world has not been designed for the convenience of mathematicians.
BENOIT MANDELBROT

Convenience Mathematician World
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
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