The Mendelbrot Set

One day this week I watched a documentary about Fractal Geometry in Nature and a mathematician named Benoit Mendelbrot. Although it was quite difficult to understand I felt I was on the verge of understanding it and I find the whole idea fascinating. Since most of my inner fascinations deal with time & space, and the relationship of life on Earth to these two components; I can see how fractals fit in quite nicely, not to mention the image is beautiful…by using math he created an image and called it the Mendlebrot Set. It was a very energetic looking graphic.

Initial image of a Mandelbrot set zoom sequence
with a continuously coloured environment-Wiki Photo

His theory is that anything can be measured—and replicated! Like measuring the jagged coastline of a country it may seem impossible to get an accurate distance measurement using linear methods of measurement. By using the fractal method any object can be measured. Even a mountain can be measured using triangle shapes…overlaying triangles of various sizes over an image of the surface of a mountain and then extrapolating the mass from that and voila you got scale measurement. The rugged peaks of mountain ranges are fractal design. (just imagine a jagged set of peaks against a horizon)

This may seem impossible to measure but its actually done by replicating a shape…is it the way nature creates trees, mountains, clouds—the shapes originating from nature or maybe even a formula for creation?

The body of Man is made up of fractal design! They put up an ECG image and damn if it didn’t look exactly like the jagged peaks of the Alps on the horizon—Nature does not give us the square, the straight line, the perfect circle, the cube, the cylinder, the cone…that is mankind’s attempt at replicating nature—we build our houses one box connected to another we take straight lines and combine them to become what we need…but where in nature do you see a perfect box, a straight line, a complete circle that is perfect? Look at a tree it’s a fractal!

Mendelbrot created a mathematical formula and using a computer he was able to create an image using his formula! By adding the end result back to the beginning of the formula like a LOOP the Mendelbrot Set was the result!
A little help from Wiki-

For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set.On the other hand, c = i (where i is defined as i2 = −1) gives the sequence 0, i, (−1 + i), −i, (−1 + i), −i, ..., which is bounded and so i belongs to the Mandelbrot set.

It’s quite a striking image.
So that means by adding the same shape over and over we get mountains, trees, clouds, every thing that has mass and stuff we cant even see. I mean look at a snowflake under a microscope…all-different - all fractal.
So with this new idea of using fractal mathematics the antenna of the cell phone was created it looks similar to this:

Now if you take these shapes and put them on a grid they actually received better than the one straight-line antenna. By using this fractal shape the cell phone industry was revolutionized… to take the sound wave sending and collection to an all-new level. Due to the discovery of Fractal Geometry our world has shifted away from
atypical shapes to shapes that can explain some of the
mysteries of life itself! Including TIME- I always thought of time as
A web, a matrix and I still do—but now it seems we can measure time by using a fractals that was the topic of the book written by Greg Braden...Fractal Time and 2012.

With my minimal ability of understanding I cannot grasp how time can be fractal I am trying very hard to grasp it, and once I do-- Im certain I will become vastly enlightened about the possibilities of how fractals will change life as we know it on planet Earth!  The following is more help from Wiki-

Self similarity in the Mandelbrot set shown by zooming in on a round feature while panning in the negative-x direction. The display center pans from (−1, 0) to (−1.31, 0) while the view magnifies from 0.5 × 0.5 to 0.12 × 0.12 to approximate the Feigenbaum ratio δ.

One of the double spirals zoomed up--this is spectacular..and this was done with MATH-