Fractals Quotes

The first of the request prayers in the daily Amidah is a fractal. It replicates in miniature the structure of the Amidah as a whole.

Every you, every me. Fractals. Fractures.

Maybe relationships could have fractals, too. And maybe the sense of loss was when you're becoming a fractal of what you once were to each other.

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

You're a refraction of the one light. You're a waveform of light. You're a fractal, a pattern that continuously changes.

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

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

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

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

A fractal is a way of seeing infinity.

Nowhere else in history has there ever been a flag that stands for the right to burn itself. This is the fractal of our flag. It stands for the right to destroy itself.

I fell in love with flora of all types, especially ferns. Loved the sparse structure and repetition of shape - almost fractal.

Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.

I find enough mystery in mathematics to satisfy my spiritual needs. I think, for example, that pi is mysterious enough (don't get me started!) without having to worry about God. Or if pi isn't enough, how about fractals? or quantum mechanics?

Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.

I don't believe that it's inconsistent to be suspicious of people and also be totally comfortable with deploying the technology, because you know its fractal potential. It's a vote for politics. It's a vote for the will to politics. There will be people, a one percent of people, that can use this stuff effectively, develop it, implement it. That's why it's necessary. That's why civilization exists, so those few people can exercise incredible techniques.

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

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

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.

The simple equations that generate the convoluted Mandelbrot fractal have been called the wittiest remarks ever made.

Fractals, the theory of relativity, the genome: these are magnificently beautiful constructs.

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

Modern humans became fixated on a collective hallucination of linear time, ignoring the fractal spirals of the surrounding universe.

At the earliest drawings of the fractal curve, few clues to the underlying mathematical structure will be seen.

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.

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

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.

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.

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.

Capitalism is like this fractal thing where anything that contains an element of capitalism anywhere inside it is just something that turns into capitalism. It is an incredibly defeatist attitude. If you choose to look at reality that way, I suppose you can, but you have to do enormous violence to reality to do so consistently.

Fractal litigation, whereby the flapping of a butterfly’s wings on one side of the world resulted in a massive compensation claim on the other.

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.

Any issue and any problem, no matter what height you look at it from, no matter how much you extend past the first fractal, it's still a fractal of something that emanates from within your consciousness - from within the human consciousness. And it'll move on and manifest itself externally, and then those are what we pick up as societal ills. But all these battles we're fighting are internal. For me, it's reconciling hope with dread and trying to cut out some place in my mind where my heart can be protected a little bit.

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

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.

I probably spend more time writing than reading science fiction. I find that science-fiction literature is so reactive to all the literature that's gone before that it's sort of like a fractal. It's gone to a level of detail that the average person could not possibly follow unless you're a fan. It iterates upon many prior generations of iterations.

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.

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.

Cocoa-buttered girls were stretched out on the public beach in apparently random alignments, but maybe if a weather satellite zoomed in on one of those bodies and then zoomed back out, the photos would show the curving beach itself was another woman, a fractal image made up of the particulate sunbathers. All the beaches pressed together might form female landmasses, female continents, female planets and galaxies. No wonder men felt tense.

Enchanting is not the word that would immediately spring to mind when describing a play that deals with fractal geometry, iterated algorithms, chaos theory and the second law of thermodynamics, but it is a perfect fit for Tom Stoppard's astonishing 1993 play, which is as beautiful as it is brilliant. This is one Stoppard drama that you don't have to be Einstein to understand -- you can feel it as well as think it. (...) Breathtaking, exhilarating and deeply satisfying.

It has been said that the three great develpments in twentieth century science are relativity, quantum mechanics, and chaos. That strikes me the same as saying that the three great developments in twentith century engineering are the airplane, the computer, and the pop-top aluminum can. Chaos and fractals are not even twentieth century ideas: chaos was first observed by Poincare and fractals were familiar to Cantor a century ago, although neither man had the computer at his disposal to show the rest of the world the beauty he was seeing.

One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.