MIKADEMUS's blog: "REFLECTIONS OF A LYCANTHROPE"

I remember back a few years ago spending many days dwelling on the idea that in nature, control could exist within chaos. The idea just popped into my mind one day and like a song you can't seem to get out of in your head the idea played over and over again. I watched a fascinating documentary on "Fractal Geometry" on the weekend and was excited when they described how when you look around in nature with a mind geared to fractal thinking you see them everywhere in patterns of clouds and leaves on trees and such (I love looking for them in nature)describing them as "Islands of Order Within Chaos". Perhaps I had been sensing this connection on a deeper subconscious level and now seeing this documentary had brought it to front and center.
The most famous fractal geometric shape was discovered in 1980 by Benoit Mandlebrot(Born 1924) whose discovery of what is now known as the "Mandlebrot Set" by no coincidence came with the rise of more powerful computing speeds. The shape is now sometimes referred to as the "Thumbprint Of God" and though it is based on a very simple calculation has very far reaching implications. The very frontier of the shape is infinitely complex showing copies of the parent shape growing on it's leading edge even under a billion magnifications in seemingly non stop procession. The Mandlebrot Set (MS) itself is a very simple equation expressed as Capital letter "Z", equals "z" squared plus "c". An important feature of "MS" is the diametrically opposing arrows on the two bars of the equals sign that plot the continuous flow of numbers(coordinates) back and forth which define the image on a two dimensional plane in a process called "Interration" which is characterized much like a dog chasing it's tail.
The simplicity of the (MS) equation means that it could have been discovered centuries ago but wasn't seen until the rise of modern computers because to construct the full set would have involved billions of calculations. Even so the first echos of the (MS) existence showed in Paris at the hands of a French mathematician named Gaston Julia who saw it's shadowy form in his mathematical constructions he did on paper which would become known as "Julia Sets" which is what Benoit Mandlebrot was working with when he came across (MS).
Looking onto the image of (MS) as it evolves on the screen researchers see the forms from nature such as Sea Horses compound insect eyes and leaf patterns like it is speaking to them of the underlying order of chaotic nature, of the very forces that create the world we see from the changing cumulonimbus clouds to the meandering tributaries of a small stream at our feet. The visible universe itself seems to be a fractal of sorts as does the synaptic wiring of our brains..... they seem to express themselves everywhere.
As far as how far outward or inward that (MS) expresses itself in the known universe it has an inward limit known as "The Planck Length. This measures at one million, billion, billionths of an inch under which nothing exists but it has yet to be determined whether there would be an outward limit on the macro scale of the universe.
As far as commercial application of fractal geometry goes it is a long way away from large scale practical application for the average household in electronic devices but I watched with amazement while a soft wear system incorporating fractal geometry took a poor resolution picture which was then expressed as a large pixelated image and after sampling it reconstructed it into a higher resolution picture by restoring data that wasn't there in the first place using fractal theory. Even when the picture was blown up it retained it's resolution.
Many people dealing with hallucinogens have oft times reported seeing fractal type shapes in their expanded state This reinforces the conjecture put forth by Carl Gustav(1875-1961) the cofounder of Modern Psychology who had a patient in 1928 who did a series of pictures that astoundingly show the Mandlebrot Set which supported his idea that the human subconsciousness is a well of primordial universal images. -the man of pech merle.
www.youtube.com/watch