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I've just learnt of Happy numbers, from Doctor Who and I was wondering if they could be used, if applied to numbers in the complex plane, to make a fractal image, like the Madelbrot set? Or do happy numbers not work that way?

I've tried googling for images, but I only get random fractals, and mentions of people being happy about numbers or fractals....and I don't know enough about maple, matlab or mathematica to make an image.

Has this been done?

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How would you define happiness for non-integers? – Hagen von Eitzen Oct 28 '12 at 19:09
@HagenvonEitzen, ah. I hadn't considered that. – Pureferret Oct 28 '12 at 19:20

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