The Theory in a Nutshell

Essentially, a fractal is an image composed of a series of microscopic patterns of the whole. Fractals are images plotted in a moving diagram that continually fold and refold in on itself so that any point within a fractal image represents the whole. The term “fractal” comes from the Latin fractua, meaning irregular, and was discovered and coined by Mathematician Benoit Mandelbrot in 1974 while he was a Fellow at IBM.

Similar to a hologram, viewing any portion of a fractal will give you a smaller-scale version of the entire image. A fractal implies infinite length in a finite area. To illustrate, draw a line on a piece of paper, labeling the point on one side A and the other side B. Imagine having a grasshopper start at point A and hopping halfway between the two points. Next, have the grasshopper hop half the distance again, and then again. The grasshopper would theoretically never reach point B. He would hop forever on this finite line. This line represents the fractal phenomena.

In addition to the discovery of fractals in mathematics, Mandelbrot showed that fractals are found throughout nature, leading to entire new fields of exploration in Chaos Theory. Fractal images can be observed throughout nature in the recurring pattern of tree branches, coastlines, and cloud formations, among others.

If you viewed a segment of a fractal image under a microscope, you’d see a smaller variation of the larger pattern. If you magnified the image further, the same pattern would continue to emerge.

Significance to Consciousness and Spirituality

Lessons from Fractal Geometry parallel the Holographic Paradigm: A single point of an image contains the whole image. A fractal and a hologram are similar metaphors. If you cut up a holographic image, each piece will reveal the whole image. Once again, we’re highlighting the interconnectivity of all things and the hidden patterns of order behind the mind’s perception of randomness and chaos.

Everything is part of everything else. Now one can see a deeper meaning in the lines from William Blake’s famous poem, Auguries of Innocence:

To see a World in a grain of sand,
And a Heaven in a wildflower,
Hold Infinity in the palm of your hand,
And Eternity in an hour.

More on the Scientific Convergence:

References:
Briggs, John. Fractals: The Patterns of Chaos. New York: Simon & Schuster, 1992.
Briggs, John & Peat, F. David. Turbulent Mirror: An Illustrate Guide to Chaos Theory and the Science of Wholeness. New York: Harper & Row, 1990.
Mandelbrot, Benoit B. The Fractal Geometry of Nature. New York: W.H. Freeman & Company, 1983.