Benoit Mandelbrot Quotes

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

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.

I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on - why they had made it that way.

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.

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

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.

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.

Geometry is the archetype of the beauty of the world.

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

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.

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

Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.

I ran into Isosceles. He had a great idea for a new triangle!

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.

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.

I make fractals. They're like mathematical pictures. My stepdad is actually a rocket scientist, so in his free time, he gave me a fractal program for fun. He showed me how to use it when I was about nine or 10, and I made thousands of fractals.

Mathematics is the true language that the universe is written in. They key to understanding the world around us.

My dad is a mathematician; I think we both have that problem-solving, looking-for-patterns way of thinking.

I like science and mathematics. When I say mathematics, I don't mean algebra or math in that sense, but the mathematics of things.

Anybody can find infinite Mandelbrot figures in his navel.

Geometry draws the soul towards truth.

The right angle is one of the world's basic shapes.

How are you going to change the world? The answer is easy. By changing the world that exists in your head.

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.