Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
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.
Fractals, the theory of relativity, the genome: these are magnificently beautiful constructs.
Imagine a multidimensiona l spider's web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And, in each reflected dew drop, the reflections of all the other dew drops in that reflection. And so ad infinitum. That is the Buddhist conception of the universe in an image.
The beauty of compounding iterative algorithms - evolution, fractals, organic growth, art - derives from their irreducibility.
Each portion of matter may be conceived of as a garden full of plants, and as a pond full of fishes. But each branch of the plant, each member of the animal, each drop of its humors, is also such a garden or such a pond.
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?
A formula can be very simple, and create a universe of bottomless complexity.
At its heart, music is all higher mathematics.
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.
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.
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.
There is no such thing as a complete lack of order, only a design so vast it appears unrepetitive up close.
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.
Beautiful, damn hard, increasingly useful. That's fractals.
Bottomless wonders spring from simple rules, which are repeated without end.
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.
Yes, fractals are what I want to find in my music.
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.
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.
in the smallest cells are reflections of the largest. And in photography, through an interplay of scales, a whole universe within a universe can be revealed.
When people ask me what's my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
The world is a holographic universe, with every piece containing the whole.
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.
There are only patterns. Patterns on top of patterns, patterns that affect other patterns, patterns hidden by patterns, patterns within patterns.
