The Mandelbrot Set and Julia Sets

Combinatorics in the Mandelbrot Set - Principal Series

We begin by looking for patterns in the n-cycle components (discs) attached around the big cardioid.

Starting from the 2-cycle disc, proceeding around the top of the big cardioid we encounter

a 3-cycle disc,

a 4-cycle disc,

a 5-cycle disc,

... and so on.

This is the upper principal series.

The analogous sequence along the bottom of the cardioid is the lower principal series.