Quotes About Fractals

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.

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.

While fractal geometry is often used in high-tech science, its patterns are surprisingly common in traditional African designs.

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

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.

From a purely mathematical perspective, a power law signifies nothing in particular—it's just one of many possible kinds of algebraic relationship. But when a physicist sees a power law, his eyes light up. For power laws hint that a system may be organizing itself. They arise at phase transitions, when a system is poised at the brink, teetering between order and chaos. They arise in fractals, when an arbitrarily small piece of a complex shape is a microcosm of the whole.

Hausdorff dimension

First, fractal objects, as we have seen, can be generated with a simple rule applied to itself, which makes them ideal for the automatic activity of a computer (or Mother Nature). Second, in the generation of visual intuitions lies a dialectic between the mathematician and the objects generated.

Luckily, infowar turns out to be more survivable than nuclear war—especially once it is discovered that a simple anti-aliasing filter stops nine out of ten neural-wetware-crashing Langford fractals from causing anything worse than a mild headache.

Later, he was to decide that Andrew's life had been fractally weird. That is, you could take any small piece of it and examine it in detail and it, in and of itself, would turn out to be just as complicated and weird as the whole thing in its entirety.

And then she slept and woke no more, and she dreamed slow dreams of strange planets with strange skies and of spiral fractals that flowered in forgotten spaces. And all was silent, and all was dark.

mandelbrot changed the way ibm's engineers thought about the cause of noise. bursts of errors had always sent the engineers looking for a man sticking a screwdriver somewhere.

THE MANDELBROT SET IS the most complex object in mathematics, its admirers like to say. An eternity could not be enough time to see it all, its disks studded with prickly thorns, its spirals and filaments curling outward and around, bearing bulbous molecules that hang, infinitely variegated, like grapes on God's personal vine.

Mandelbrot saw a seemingly smooth boundary resolve itself into a chain of spirals like the tails of sea horses. The irrational fertilized the rational.

One simple but powerful consequence of the fractal geometry of surfaces is that surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that. Even in rock under enormous pressure, at some sufficiently small scale it becomes clear that gaps remain, allowing fluid to flow.

The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up little space, no more than about five percent of the body.

God Father (the Creator) geometrizes, God Mother (Nature) fractalizes.

Scaling also became part of a movement in physics that led, more directly than Mandelbrot's own work, to the discipline known as chaos.

Mandelbrot moved beyond dimensions 0,1,2,3…to a seeming impossibility: fractional dimensions. The notion is a conceptual high-wire act. For nonmathematicians it requires a willing suspension of disbelief. Yet it proves extraordinarily powerful.

Christopher Scholz, a Columbia University professor specializing in the form and structure of the solid earth, first started thinking about fractals.

The fractal dimension of a metal's surface, for example, often provides information that corresponds to the metal's strength.

In fact, he argued, any coastline is—in a sense—infinitely long. In another sense, the answer depends on the length of your ruler.

In terms of aesthetic values, the new mathematics of fractal geometry brought hard science in tune with the peculiarly modern feeling for untamed, uncivilized, undomesticated nature.