Benoit Mandelbrot Quotes

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.

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

Reality is made up of circles but we see straight lines.

Today we live in a chaos of straight lines, in a jungle of straight lines. If you do not believe this, take the trouble to count the straight lines which surround you. Then you will understand, for you will never finish counting.

Circles and right lines limit and close all bodies, and the mortal right-lined circle must conclude and shut up all.

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.

The human heart likes a little disorder in its geometry.

Geometry was the first exciting course I remember.

Nobody will deny that there is at least some roughness everywhere.

I see lines of space. I break things down into lines and space, and I balance.

Right angles don't attract me. Nor straight, hard and inflexible lines created by man.

I didn't discover curves; I only uncovered them.

Approach nature in terms of the cylinder, the sphere, and the cone ...

His way had therefore come full circle, or rather had taken the form of an ellipse or a spiral, following as ever no straight unbroken line, for the rectilinear belongs only to Geometry and not to Nature and Life.

Nature eschews regular lines; she does not shape her lines by a common model. Not one of Eve's numerous progeny in all respects resembles her who first culled the flowers of Eden. To the infinite variety and picturesque inequality of nature we owe the great charm of her uncloying beauty.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

All the work of the crystallographers serves only to demonstrate that there is only variety everywhere where they suppose uniformity ... that in nature there is nothing absolute, nothing perfectly regular.

As a child it was clear to me that in some sense math was in the world around us. I became fascinated by what this means. When you look at the shape of the sun and the moon, they're circles, so every time you see a circular thing, there's pi embedded in it.

Nature will not be Buddhist: she resents generalizing, and insults the philosopher in every moment with a million fresh particulars.

It turns out that hyperbolic structures are very common in nature, and the place where lots of people encounter them is coral reefs. Sea slugs, and a lot of other organisms with frilly forms, are biological manifestations of hyperbolic geometry, which is also found in the structure of lettuce leaves and kales, and some species of cactus.

There is no motion in a straight line. A straight line infinitely projected becomes a circle.

A circle is a round straight line with a hole in the middle.

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

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.