Problem 81. Mandelbrot Numbers

Created by Cody Team

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The <a href="http://en.wikipedia.org/wiki/Mandelbrot_set">Mandelbrot Set</a> is built around a simple iterative equation.<pre> z(1) = c
 z(n+1) = z(n)^2 + c</pre>For any complex c, we can continue this iteration until either
abs(z(n+1)) > 2 or n == lim, then return the iteration count n.<ul><li>If c = 0 and lim = 3, then z = [0 0 0] and n = 3.</li><li>If c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.</li><li>If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.</li></ul>For a matrix of complex numbers C, return a corresponding matrix N such
that each element of N is the iteration count n for each complex number c
in the matrix C, subject to the iteration count limit of lim.If C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]Cleve Moler has a whole chapter on the Mandelbrot set in his book Experiments
with MATLAB: <a href="http://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf">Chapter 10, Mandelbrot Set (PDF)</a>

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Nicholas Howe on 5 Oct 2012

For c==4 and other numbers where abs(c)>2, I think the function should be defined to return 0 rather than 1.

Sam Perry on 13 Dec 2017

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Ratchet_Hamster on 20 Jul 2018

I am really stuck on this one. I know it is likley me not the question but I cannot figure out why in the final validation, -2i should give N=1, I get it to be N=2? any help is appriciated, this is the only situlation where code fails.

rolf harkes on 6 Jan 2019

For people like me that hoped this challenge would end with a pretty picture:
`[X,Y]=meshgrid(-2:0.0025:2,-2:0.0025:2);C=X+i.*Y;N=mandelbrot(C,50);imagesc(N)`

Asif Newaz on 24 Dec 2019

@Ratchet_Hamster
for complex no, u need to take the absolute value to check if it is greater than 2

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Problem 81. Mandelbrot Numbers

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