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I am trying to continuous coloring the inside point for a fractal image,such as $z \to z^2+C$. For those outside point, we can use the escape iteration to determine the color, just as the description in the Wikipedia. However, how to coloring those inside point, which wouldn't escape? I mean use some good color. Has anyone done it before and can give some suggestions?

Best Regards,

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    In the very same article you mention, there is a method described. See the "interior distance estimation".2011-12-22
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    See : http://en.wikibooks.org/wiki/Fractals HTH2012-10-14

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