If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from… — Benoit Mandelbrot Copy Share Image
Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes… — Benoit Mandelbrot Copy Share Image
The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory… — Benoit Mandelbrot Copy Share Image
Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which… — Benoit Mandelbrot Copy Share Image
I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many… — Benoit Mandelbrot Copy Share Image
I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely… — Benoit Mandelbrot Copy Share Image
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It… — Benoit Mandelbrot Copy Share Image
Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory — Benoit Mandelbrot Copy Share Image
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud,… — Benoit Mandelbrot Copy Share Image
There are very complex shapes which would be the same from close by and far away. — Benoit Mandelbrot Copy Share Image
Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes… — Benoit Mandelbrot Copy Share Image
Why is geometry often described as 'cold' and 'dry?' One reason lies in its inability to describe the shape of a cloud,… — Benoit Mandelbrot Copy Share Image
Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities,… — Benoit Mandelbrot Copy Share Image
It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made… — Benoit Mandelbrot Copy Share Image
Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion. — Benoit Mandelbrot Copy Share Image
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… — Benoit Mandelbrot Copy Share Image
One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining… — Benoit Mandelbrot Copy Share Image
My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and… — Benoit Mandelbrot Copy Share Image
The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may… — Benoit Mandelbrot Copy Share Image
Most economists, when modeling market behavior, tend to sweep major fluctuations under the rug and assume they are anomalies. What I have found is… — Benoit Mandelbrot Copy Share Image
I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the… — Benoit Mandelbrot Copy Share Image
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,… — Benoit Mandelbrot Copy Share Image
When I first began studying prices, it wasn't a topic that mathematicians were working on. Purely by accident, I saw a set of data… — Benoit Mandelbrot Copy Share Image
