Fractal Geometry Quotes

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.

There's a theory that says that life is based on a competition and the struggle and the fight for survival, and it's interesting because when you look at the fractal character of evolution, it's totally different. It's based on cooperation among the elements in the geometry and not competition.

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.

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.

Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version.

The Web is now philosophical engineering. Physics and the Web are both about the relationship between the small and the large.

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.

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.

The best thing we can do is give students the tools for constructing their own identities - powerful new tools like African fractals - and then just get out of the way.

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

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.

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

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

History is fractal. The closer you look, the more complicated, yet always repeating patterns.

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

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.

I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes that they use. So Native Americans use a combination of circular symmetry and fourfold symmetry.

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.

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.

I'm kinda tired. I was up all night trying to round off infinity. Then I got bored and went out and painted passing lines on curved roads.

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.

Chaos has come to be associated with the study of anything complex, but, in fact, the mathematical techniques are directly applicable only to simple systems that appear to be complex.

In little localized pockets, the universe is capable of building some beautiful complexity.

The Besicovitch style is architectural. He builds out of simply elements a delicate and complicated architectural structure, usually with a hierarchical plan, and then, when the building is finished, the completed structure leads by simple arguments to an unexpected conclusion. Every Besicovitch proof is a work of art, as carefully constructed as a Bach fugue.

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.