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From my understanding of the Mandelbrot Set, it represents the set of complex numbers 'c' for which the function: f(z) = z^2 + c that doesn't diverge. The set of these numbers is coloured black while everything else is white. I believe it is also contained within a circle of radius 2.

If a number can either be in the set or out of the set, what do the various other colours, such as green and red, represent? Mandelbrot Set image I am referring to

Apologies for posting an image link, I don't have enough reputation to embed an image.

Atiksh
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1 Answers1

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The colors are usually chosen from how fast the sequence diverges, measured by how many iterations it takes until $|z_k|$ has become larger that some certain value that guarantees divergence.

From https://en.wikipedia.org/wiki/Mandelbrot_set#Computer_drawings:

The color of each point represents how quickly the values reached the escape point. Often black is used to show values that fail to escape before the iteration limit, and gradually brighter colors are used for points that escape. This gives a visual representation of how many cycles were required before reaching the escape condition.

md2perpe
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