Some points jump into infinity very fast, some take more cycles, and some go to "0".

A palette is assigned to the number of jumps. To speed up calculations a boundary is set, i.e. "64 iterations = infinity." You then can use a palette with 64 colors, nicely shaded. Jumps to "0" is black. Other points are shaded. Outside the set the colors fade into the background color.

Numberphile on Youtube has some very interesting videos. Within the black region there are amazing patterns too. You could plot them in a default Mandelbrot set picture, but it would look like chaos. Every point in this region has a iteration pattern into "0." Some look chaotic, some are symmetric like stars.

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