About Fractals ...
The fractal field is the coded field of the sacred geometry of nature. It lies beyond the morphic field of energy and actually creates the morphic field. The fractal field holds the geometry of the natural world.
To learn more watch NOVA documentary: Fractals: Hunting the Hidden Dimension
(find on Netflix or watch online at http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html)
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems - the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals - such as the Mandelbrot Set - can be generated by a computer calculating a simple equation over and over.
(excerpted from www.fractalfoundation.org - The Fractal Foundation is located in Albuquerque, NM, home of Fractal Friday at the local planetarium)
From sea shells and spiral galaxies to the structure of human lungs, the patterns of chaos are all around us.
Fractals are patterns formed from chaotic equations and contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical reduced-size copy of the whole.
The mathematical beauty of fractals is that infinite complexity is formed with relatively simple equations.By iterating or repeating fractal-generating equations many times, random outputs create beautiful pattern that are unique, yet recognizable.
Text and photos excerpted from http://www.wired.com/wiredscience/2010/09/fractal-patterns-in-nature
This variant form of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the Fibonacci or golden spiral, a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio.
A Simple Explanation Of Fractal Geometry (from www.fractalenergymandala.com)
While the classical Euclidean geometry works with objects which exist in integer dimensions, fractal geometry deals with objects in non-integer dimensions. Euclidean geometry is a description lines, ellipses, circles, etc. Fractal geometry, however, is described in algorithims — a set of instructions on how to create a fractal.
The world as we know it is made up of objects which exist in integer dimensions, single dimensional points, one dimensional lines and curves, two dimension plane figures like circles and squares, and three dimensional solid objects such as spheres and cubes. However, many things in nature are described better with dimension being part of the way between two whole numbers. While a straight line has a dimension of exactly one, a fractal curve will have a dimension between one and two, depending on how much space it takes up as it curves and twists. The more a fractal fills up a plane, the closer it approaches two dimensions. In the same manner of thinking, a wavy fractal scene will cover a dimension somewhere between two and three. Hence, a fractal landscape which consists of a hill covered with tiny bumps would be closer to two dimensions, while a landscape composed of a rough surface with many average sized hills would be much closer to the third dimension.