Benoit Mandelbrot Quotes

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

Bottomless wonders spring from simple rules, which are repeated without end.

A fractal is a way of seeing infinity.

Asking the right questions is as important as answering them

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.

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.

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

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

There is a saying that every nice piece of work needs the right person in the right place at the right time.

Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

Order doesn't come by itself.

I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."

The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.

Unfortunately, the world has not been designed for the convenience of mathematicians.

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.

My fate has been that what I undertook was fully understood only after the fact.

The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.

If you look at coastlines, if you look at that them from far away, from an airplane, well, you don't see details, you see a certain complication. When you come closer, the complication becomes more local, but again continues. And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.

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.

For most of my life, one of the persons most baffled by my own work was myself.

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable

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.

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.