Posts Tagged ‘benoit mandelbrot’

Sacred Geometry & Fractals in Nature

June 15, 2012

You’ve heard of the Golden Mean Ratio, depicted by Leonardo da Vinci’s Vitruvian Man?  The Golden Mean Ratio is defined by the Fibonacci sequence, a set of numbers found in nature characterised by the spiral found in uncurling fern fronds, a ram’s horns, and sea shells etc…BUT have you heard about the Mandelbrot set?  The Mandelbrot Set or M-set is a mathematical set of complex numbers that define the boundary of a two-dimensional fractal shape.   The set was first visualised by Benoit Mandelbrot and is expressed in the equation zn+1 = zn2 + c.  The letters in the M-set equation represent number coordinates on a plane that define the location of a point.  But the numbers flow in different directions constantly feeding back on themselves like the ouroborus (serpent eating its own tail), the output of one operation is the input of the other.

This constant looping is called an iteration.  When the M-set is given a number representing a point and the number is iterated through the equation, one of two things happen: either the number gets bigger and bigger and shoots off to infinity or it shrinks to zero. Depending of which happens the fractal program that generates the zoom then knows where to draw a boundary line.  It’s kinda like a map dividing a plane into two distinct territories.  For the points that go to zero you assign the colour black and any point that goes off to infinity you assign a range of colours relative to the rate of speed that it goes off.  So the weird Buddha shape in the centre of the zoom are the points that went to zero…you get it?

The patterns that are generated cannot help but remind you of nature… and it’s pure coincidence that the set, named after Mandelbrot bears a striking resemblance to the word mandala, the best term available to describe the patterns produced by the m-set fractal zoom.

Now here is a video of the Mandelbrot Zoom:

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