The Mandelbrot Set and Julia Sets

Julia Sets - Coloring Schemes

If the iterates of z0 fail to satisfy the escape criterion, we assume z0 belongs to the filled-in Julia set Kc and paint black the pixel containing z0.
If the iterates of z0 do satisfy the escape criterion, we usually paint the pixel containing z0 with a color indicating how many iterations were needed to first get farther than 2 from the origin.
For example,
  paint the pixel containing z0 white if z1 is farther than 2 from the origin.
  Paint the pixel light to dark pink if a few more iterates are needed to get farther than 2 from the origin.
  Paint the pixel orange to yellow if a few more iterates are needed to get farther than 2 from the origin.
  Paint the pixel green to blue if a few more iterates are needed to get farther than 2 from the origin.
and so on. The successive magnifications - left to right, top to bottom - illustrate this coloring.

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