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Thread: Finding the error in area of mandelbrot set.

  1. #1
    Super Member Deadstar's Avatar
    Oct 2007

    Finding the error in area of mandelbrot set.

    I'm not really sure where to post this...

    Basically, I've used Maple to plot the Mandelbrot set.
    The way its done is I have a 10000x10000 array that is filled with values between 0 and 1 where each value represents the colour of a pixel on a grid. 0 stands for a black pixel and is part of the set, 1 is white and all other entries are a shade of grey depending on how many iterations they take to diverge.
    To find the area I simply counted the number of 0's in the array (it was only different to the actual value by 0.002%). How would I go about finding the error in this? As in, I'm restricted by the number of iterations I can use,so some pixels that are black may NOT be black if I had a powerful enough computer so that I could increase the max number of iterations.

    The value calculated by pixel counting (by using a massively more powerful computer than mine) is 1.50659177 $\displaystyle \pm$ 0.00000008.
    The value I calculated was 1.506628382.
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  2. #2
    MHF Contributor
    Opalg's Avatar
    Aug 2007
    Leeds, UK
    The inaccuracies obviously occur near the boundary of the set. Can you modify your program so that it recognises when a black pixel has a non-black neighbour? There will presumably be comparatively few of these, and you could then increase the number of iterations for those pixels.
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