Benoit Mandelbrot Quotes

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.

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.

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.

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.

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.

The straight line, a respectable optical illusion which ruins many a man.

A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.

If you take your thumb and your index finger and look right where they meet - go ahead and do that now - and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals.

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

I made a photograph of a garden in Kyoto, the Zen garden, which is a rectangle. But a photograph taken from any one point will not show, well it shows a rectangle, but not with ninety degree angles.

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

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

I've always had a great feel for space and how objects occupy it.

The straightest line between a straight distance is two points.

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

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

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

Everything has shape, if you look for it. There is no escape from form.

In the mind's eye, a fractal is a way of seeing infinity.

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.

All objects transmit their image to the eye in pyramids and the nearer to the eye these pyramids are intersected the smaller will the image appear of the objects which cause them.

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.