black
grey
blue
red
brown
white

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

Related Topics

Circles Lines Shapes

Bagwalas

Popular Authors

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

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

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

Complexity Formulas Simple
Unfortunately, the world has not been designed for the convenience of mathematicians.
BENOIT MANDELBROT

Convenience Mathematician World
Order doesn’t come by itself.
BENOIT MANDELBROT

Come Itself Order
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
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 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
A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.
BENOIT MANDELBROT

Clouds Looks Smooth
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
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
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
There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROT

Complex Far Away Shapes
$Benoit Mandelbrot Quote - Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.$

Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
BENOIT MANDELBROT

Chaos Impossible Past
$Benoit Mandelbrot Quote - Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.$

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
Think not of what you see, but what it took to produce what you see.
BENOIT MANDELBROT

Produce See Thinking Took

Copyright: 2020 - 2023 | Minimalist Quotes