"The Universe is worked and guided from within outwards . . . and man - the microcosm
and miniature copy of the macrocosm - is the living witness to this Universal Law and
to the mode of its action." [H.P. Blavatsky, Secret Doctrine Vol 1, 274.]

Fractals exist within a hierarchy of self-similar objects or images that display ever increasing complexity and detail. All fractals, whether generated by computers or natural processes, appear as irregular patterns that repeat at smaller or larger scales. The number of iterations [inward looping] determines how much detail is unveiled. Fractals are self-similar and resemble the whole - for example - a head of broccoli. From a distance, we see the round shape of something darkish green in color. As we move closer, we observe that the object's outline is starting to look less smooth and a bit edgy and bumpy. Closer still, we can now identify the object as a head of broccoli topped with millions of tiny florets bufricating from a single branch. We move in and notice smaller clusters of the same form [self-similar] including stems each with their own cluster of florets, smaller stems still growing out of that stem, even smaller stems, all complete with tiny florets that are, of themselves, also tiny fractals. Other examples of fractals include galaxy clusters, foliage, coastlines, piles of dead leaves, fish scales, cells, molecules, DNA and all things great, small, and infinitely small. Fractal Geometry and high-speed computers have teamed up over the last thirty or so years to examine irregular patterns and structures found in nature that could not be examined by classical Euclidian geometry. Fractal Geometry and sister science, Chaos Theory, have been introduced to high-school students in math/geometry class since the 1980's.
 
The Microcosm
Revealed or concealed, fractalian objects are embedded with a code or "seed" infused with unfolding artistry, diversity of detail, and the mathematical adeptness of Intelligent Design. The iteration process visually ends, in the case of a broccoli head, at the tip of each floret, because the process of growth within the SEED has been genetically "programmed." to stop. In fractal geometry parlance, this stop is known as "Bailout." All seeds are programmed to Bailout including the human seed - the MONAD - the seat and root of consciousness. The whereabouts of the MONAD after Bailout - is a time out of mind question.
 
Fractals can diverge to Infinity using computer modeling.
The famous M-Set fractal formula (Mandelbrot Set) generated mathematically using deep computer processing does not end - but rather iterates to infinity or at least to the star Sirius according to its discover, Benoit Mandelbrot. During the iteration process, the details of M-Set diverge into complex yet similar patterns and shapes. If a computer generated fractal can live on through infinity - yet retain some semblance of individuality - why not the Pilgrim Soul?
 
The word fractal was coined by Benoit Mandelbrot who discovered the most famous of all fractal images - the Mandelbrot Set (M-Set) - using a simple formula Z=z^2+c with complex results that allows a number(s) to the right of a decimal point to iterate into a number(s) to the left of a decimal point ad infinitum. The formula Z=z^2+c has been referred to as the thumbprint of God. This mathematical discovery was made possible by calculating vast numbers beyond human capacity. Currently, with deep computing capabilities, the frontiers of exploration through nanoscience and nanotechnology are making further inroads into the realm of the incredibly small -- invisible quarks and strings -- that seem to exhibit "free will." Nanocosmic worlds whirling, swirling and possibly contemplating their own infinitesimally small navels.
 
Fractal Geometry - The Bridge between Science, Art, and Spirituality
Mathematically generated fractal images using high-speed computers that can perform millions and even billions of calculations in instantaneous succession allow us not only a glimpse into the world of fractal geometry, but grant the computer programmer or operator, the physicist, the microbiologist, the chemical engineer, the artist, and others, the power to see what was unseen before, and provide the tools and capacity to create an image from nothing that has been seen before or known except numbers/formulas. Fractal Artists use number formulas to create visual images that are tweaked into aesthetically pleasing compositions and further rendered through the light spectrum as the fractalian details unfold.
 
All things lie veiled in number.
A small percentage of the world's population understood the thrust of Einstein's Theory of Relativity (E=mc2) and few today can envision the far reaching implications of Fractal Geometry, Chaos Theory and Nanotechnology. Those of us who hold true to the tenants of the Hermetic Tradition with an affinity toward philosophy and metaphysics know for certain that something amazing is upon us through this marriage of number and computer generation. A line in the sky has returned full circle and is more than a circle, more than a parabola, more than a trapezoid, much more than anything previously defined in Euclidian geometry as a plane or a solid.