Wednesday, March 14, 2007

Koch Fractals

Koch Fractals HexagramKoch Fractals look like six-pointed stars.
Picture is coied from Wikipedia (I slightly edited it with Photoshop).
In the Wikipedia entry for Fractal they say
a fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.

1 comment:

Anonymous said...

Do you realize the implications?


"...The simplest way to define a fractal is as a surface or curve that is infinitely wiggly. This means that as you magnify it, you find more and more twists and turns at each level of magnification. Additionally, key images tend to repeat themselves at various levels of magnification.

The concept of a "fractal" originated with the mathematician Benoit Mandelbrot... The central importance of this concept lies in the fact that everything in the universe is really a fractal. The universe is "infinitely wiggly." It possesses infinite detail, and new worlds are revealed with each degree of expansion. Furthemore, in nature one sees basic shapes such as those of spiral galaxies repeating themselves in seashells and at even smaller
levels of magnification.

Based on standard Kabbalistic theory, the Kabbalistic Tree of Life is also a fractal. If we replace each sphere on the tree by a smaller tree and repeat this process ad infinitum, then we create an object of infinite complexity where the image of the tree appears at all levels of magnification. According to Kabbalah, this is the nature of reality. Every aspect of the universe can be represented by the Tree of Life, and there are trees within trees at all levels of magnification. It's a tad mind boggling!.."

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"...Every part of the universe is symbolized by the Tree of Life, and every part of the tree, in a fractal like manner, contains a smaller image of the tree and so on ad infinitum..."

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Tree = Branch