
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."

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.

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.

I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure  I wanted to do something different.

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.

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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.

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

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

Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

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.

Asking the right questions is as important as answering them

I spent my time very nicely in many ways, but not fully satisfactory.
Then I became Professor in France, but realized that I was not  for the job that I should spend my life in.

About Benoit Mandelbrot

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.

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.

It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.

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.

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

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

For much of my life there was no place where the things I wanted to investigate were of interest to anyone.

In fact, I barely missed being number one in France in both schools.
In particular I did very well in mathematical problems.

Many painters had a clear idea of what fractals are.
Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes. And how did he choose them? Well, he had the balance of trees, of lawns, of houses in the distance. He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling.

The most important thing I have done is to combine something esoteric with a practical issue that affects many people.

There are very complex shapes which would be the same from close by and far away.

The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may not be true. And that idea is still unproven. It is the foundation, what started me and what everybody failed to **** prove has so far defeated the greatest efforts by experts to be proven.

Pictures were completely eliminated from mathematics;
in particular when I was young this happened in a very strong fashion.

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.

Until a few years ago, the topics in my Ph.D. were unfashionable, but they are very popular today.

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

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.

The techniques I developed for studying turbulence, like weather, also apply to the stock market.

Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomadsbychoice are essential to the intellectual welfare of the settled disciplines.

When people ask me what's my field? I say, on one hand, a fractalist.
Perhaps the only one, the only fulltime one.

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.

The rare scholars who are nomadsbychoice are essential to the intellectual welfare of the settled disciplines.

The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn't expect that it was possible. I just moved from step to step to step.

The straight line has a property of selfsimilarity.
Each piece of the straight line is the same as the whole line when used to a big or small extent.

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.

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.

If you assume continuity, you can open the wellstocked 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).

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.

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to fullfledged theories, by identifying a family of shapes I call fractals.

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

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

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.

I don't seek power and do not run around.

It was a very big gamble. I lost my job in France, I received a job in which was extremely uncertain, how long would IBM be interested in research, but the gamble was taken and very shortly afterwards, I had this extraordinary fortune of stopping at Harvard to do a lecture and learning about the price variation in just the right way.

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, from far away, it is the same; it is a straight line.

When the weather changes, nobody believes the laws of physics have changed.
Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed.

A fractal is a way of seeing infinity.

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