What's a Fractal?

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, and below is a picture of the "Mandelbrot Set" that he discovered in the late seventies along with some magnifications of its boundary. 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!

Author: Christopher P. Benton, 2003