The Mandelbrot Set

I couldn't post an article on the Julia sets without also posting an article on the Mandelbrot set. The first image below shows the overall form of the set; subsequent images show successive magnification of the the regions indicated. 

The Mandelbrot Set - showing zoom area

Zoomed in to the 'Seahorse Valley'
With the Julia sets we kept c constant, in the polynomial z2 + c, and iterated on z. For the Mandelbrot set we keep z(=0) constant and iterate on c (= p + iq). Here I iterated p and q over the range (-2.25 to 0.75) and (-1.5 to 1.5) resp.

Interpretation of the image is exactly as for the Julia set, although I've changed the colour palette (red has changed to black - all prisoner's are coloured black while all other colours represent the escapee's).
Zoomed in to the 'Seahorse Valley'

and the final zoom - although clearly you could go on zooming in forever

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