# Coasting along the fractal boundaries

I’ve been tootling around the fractal boundaries of the Mandelbrot Set with the XaoS viewer recently.

Here’s a few of the sights i’ve come across:

To think that such ‘organic’ looking complex, infinite, fractal, similar across scale, ‘as above so below’ forms can naturally arise from a simple rule repeated and fed back to itself!

Boundary conditions are strange and counter-intuitive. I continue in the struggle to understand what, if any significance this has. It certainly feels out of this world.

Read on for a brief ‘explanation’ of the Mandelbrot set.

Take a 2 dimensional plane with an x and y axis and 0 at the centre. Any coordinate on that plane would be what mathematicians call a complex number (made up of one of the regular numbers along the x axis, together with a number along the y axis, which mathematicians call ‘imaginary numbers’)

Any of these complex numbers (coordinates) can be put through a simple mathematical rule that starts with a certain value, makes a set amendment to that value and then feeds the result back into itself (The number of times this rule is carried out on a particular set of coordinates is termed its number of iterations)

(z) = z squared + c

Here, c denotes the coordinate on the 2 dimensional plane. A coordinate is deemed part of ‘The Mandelbrot set’ if, starting with z=0, the value of z does not exceed 2 after successive iterations of the rule (repetitions of the feedback)

The z value for coordinates outside the ‘Mandlebrot set’, do not remain bound after successive iterations and tend towards infinity.

It was only with the advent of the computer age that enough coordinates and iterations could be computed to present some sort of image on a 2 dimensional plane.