Quotes About Fractal

Yet despite appearances, the interstate system is in fact a quintessential fractal when viewed through the lens of the actual traffic flowing on it, rather than when viewed simply as a physical road network. The traffic flow is the very essence of the interstate and is the fundamental reason for its existence.

I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe.

My assumption was that all indigenous architecture would be more fractal. My reasoning was that all indigenous architecture tends to be organized from the bottom up. As it turns out, though, my reasoning was wrong.

IN THE MIND'S EYE, a fractal is a way of seeing infinity.

In reality, a river's basic shape... is not a line but a tree. A river is, in its essence, a thing that branches... Although it flows inward toward its trunk, in geological time it grew, and continues to grow, outward, like an organism, from its ocean outlet to its many headwaters. In the vernacular of a new science, it is fractal, its structure echoing itself on all scales, from river to stream to brook to creek to rivulet, branches too small to name and too many to count.

Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern.

Mandelbrot created the word (noun and adjective, English and French) fractal.

His studies of irregular patterns in natural processes and his exploration of infinitely complex shapes had an intellectual intersection: a quality of self-similarity. Above all, fractal meant self-similar.

Most seductive of all was an image that the authors called a strange attractor.

Blood vessels, from aorta to capillaries, form another kind of continuum. They branch and divide and branch again until they become so narrow that blood cells are forced to slide through single file. The nature of their branching is fractal.

Several chaos-minded cardiologists found that the frequency spectrum of heartbeat timing, like earthquakes and economic phenomena, followed fractal laws, and they argued that one key to understanding heartbeat timing was the fractal organization of the His-Purkinje network, a labyrinth of branching pathways organized to be self-similar on smaller and smaller scales.

The thing about all complexes, splinter personalities, and fractal assignments is that they have no imagination. The can only replay the old events, scripts, and moribund outcome of their origin. But we do have an imagination, the power to image something new, or at least alternative.

Redwoods have an enormous surface area that extends upward into space because they have a propensity to do something called reiteration. A redwood is a fractal. And as they put out limbs, the limbs burst into small trees, copies of the redwood.

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

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.

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 decline of violence is a fractal phenomenon. You can see it over millennia, over centuries, over decades and over years.

In short, what Brown, Enquist, and West are saying is that evolution structured our circulatory systems as fractal networks to approximate a "fourth dimension" so as to make our metabolisms more efficient. As West, Brown, and Enquist put it, "Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional … Fractal geometry has literally given life an added dimension.

strange attractor—do

The word "fractal" was coined in 1975 by the Polish/French/American mathematician, Benoît Mandelbrot (b. 1924), to describe shapes which are detailed at all scales.

We know that different regions in the brain process shape, colour, and motion. Benoit Mandelbrot has hypothesized that perhaps there is a specific circuit in the brain to deal with fractal complexity.

Fractal image compression can even guess, by interpolation, what lies outside the frame of a picture.

Forest Fires: the Fractal Boundary Imagine a plantation of evenly spaced trees on a very hot, dry day. As the temperature soars, the odd leaf or twig ignites, sending a whole tree up in flames. This is an essentially random process – the factors involved are beyond our powers of prediction. But once a tree is in flames, the fire easily spreads to neighbouring trees, and this process can now be modelled with iterative techniques.

Dimensional Magic We are fractal. Our lungs, our circulatory system, our brains are like trees. They are fractal structures. Fractal geometry allows bounded curves of infinite length, and closed surfaces with an infinite area. It even allows curves with positive volume, and arbitrarily large groups of shapes with exactly the same boundary. This is exactly how our lungs manage to maximize their surface area.