Benoit Mandelbrot Quotes

Anybody can find infinite Mandelbrot figures in his navel.

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

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

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.

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

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

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.

The beauty of compounding iterative algorithms - evolution, fractals, organic growth, art - derives from their irreducibility.

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

You've never heard of Chaos theory? Non-linear equations? Strange attractors? Ms. Sattler, I refuse to believe you're not familiar with the concept of attraction.

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.

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...

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.

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 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.

It's a product of the fractal laws that govern the world at an informational level. There is no deeper truth.

There are only patterns. Patterns on top of patterns, patterns that affect other patterns, patterns hidden by patterns, patterns within patterns.

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.

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

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.

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