Quotes About Fractals

To find the new x, the rule was to take the old y, add 1 and subtract 1.4 times the old x squared. To find the new y, multiply 0.3 by the old x. That is: xnew = y +1 – 1.4x2 and ynew = 0.3x. Hénon picked a starting point more or less at random, took his calculator and started plotting new points, one after another, until he had plotted thousands.

John Hubbard, exploring iterated functions and the infinite fractal wildness of the Mandelbrot set, considered chaos a poor name for his work, because it implied randomness. To him, the overriding message was that simple processes in nature could produce magnificent edifices of complexity without randomness. In nonlinearity and feedback lay all the necessary tools for encoding and then unfolding structures as rich as the human brain.

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

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

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.

What are you thinking, Evan? So I told him. Every you, every me. Fractals. Fracturs. I wonder who she is now, I said. So do I, Jack admitted. All the time.

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.

Any detail can be magnified to reveal even more detail ad infinitum. The technical term is "infinite complexity." Fractals are the theological equivalent of what theologians call the incomprehensibility of God. Just when we think we have God figured out, we discover a new dimension of His kaleidoscopic personality.

The abstract, curvilinear motifs of ancient Islamic decorative art found in mosaics and carpet design appear again and again at all scales of magnification on the boundary of the Mandelbrot set.

Arthur C. Clarke thinks that it may be just a coincidence, "but", he writes, "the Mandelbrot set does indeed seem to contain an enormous number of mandalas or religious symbols, which are found in ecclesiastical designs-such as stained glass windows, and particularly in Islamic art. We find many forms like the Paisley pattern echoing the Mandelbrot set centuries before it was discovered!

Fractal Beats The body structures of all of nature's animals are fractal, and so too is their behaviour (see Orchid Fractals) and even their timing. Our heart beats seem regular and rhythmic, but when the structure of the timing is examined in fine detail, it is revealed to be very slightly fractal. And this is very important.

Research employing fractal rules has revealed a three-quarter power law even in the circulatory system.

Self-similarity on all scales is a key factor in understanding and describing nature's phenomena.

Zooming into the boundary of the M-set, we find smaller and smaller island molecules, surrounded by increasingly intricate circular patterns, evocative of Oriental art, particularly in the meditative designs of Buddhism known as mandalas.

In Mahayana Buddhism, the fractal nature of reality is illustrated in the Avatamsaka Sutra by the metaphor of Indra's net, a vast network of precious gems hanging over the palace of the god Indra, so arranged that if you look at one you see all the others reflected in it.

Nature finds the same solution to many different problems, like how to drain water from the land into the oceans, and how to get blood from our hearts to our fingertips and back again. And the templates that nature uses are fractals. Clouds look the same at all scales. It is impossible to determine the size of a cloud from a photograph of it.

Art is about those things which we do not always immediately recognize or understand. The artist helps us to see things more clearly, revealing previously hidden patterns to us. Art is fractal. Art reflects and expresses the fractal nature of our conscious perceptions of the world, as interpreted by our fractal brains.

The signature of chaos is the fractal attractor-fractals are the patterns of chaos

Period-doubling is a general principle of nature.