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.

Yes, fractals are what I want to find in my music.

All created forms are fractal, as is their purpose, use, and allotted time for existence.

If you learned how to make a cloud, your time is not wasted.

The universe is fractal. The closer you look at it, the more interesting it becomes.

An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.

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.

There is no such thing as a complete lack of order, only a design so vast it appears unrepetitive up close.

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.

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

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.

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

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.

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.

You existed. You existed now as a fractal. Definition: A fractal is generally a rough or fragmented geometric shape that can be broken into parts, each of which is (at least approximately) a reduced-size copy of the whole. Maybe I was a fractal. Maybe the photographer was a fractal. Maybe we were all fractals.

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.

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...

Unfortunately, nature seems unaware of our intellectual need for convenience and unity, and very often takes delight in complication and diversity.

Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, 'This is fabulous! I wonder why?' And of course I had to go to Africa and ask folks why.

If you look at any leaf on any tree branch, it's similar to but not exactly a repetition of the previous branch. So the new science of complexity or showing how an architecture can be produced just as quickly, cheaply and efficiently by using computer production methods to get the slight variation, the self-similarity.

The rain begins with a single drop.

He was afflicted by the thought that where Beauty was, nothing ever ran quite straight, which no doubt, was why so many people looked on it as immoral.

Fractal geometry is everywhere, even in lines drawn in the sand. It's the cycle of life... You see fractals in plants, in flowers. Within the human lung are branches within branches.

People think of waves as going in an orderly crash - whoosh - crash - whoosh, but in fact there are lots of different crashes and whooshes, all at different stages, and all going off at the same time.

Nature doesn't feel compelled to stick to a mathematically precise algorithm; in fact, nature probably can't stick to an algorithm.