The Mandelbrot Set and Julia Sets

The Mandelbrot Set - Stable Cycles

For discs attached to the main cardioid, the period of the cycle of the disc can be read off from the number of spokes in the antenna from the disc.
3 cycle
4 cycle
7 cycle
9 cycle
16 cycle
For discs attached to other discs, the situation is more complicated.
For example, this picture shows the 12-cycle disc attached to the 3-cycle disc atop the main cardioid.
On this 3-cycle disc, the 12-cycle disc is in the relative position of the 4-cycle disc on the main cardioid.
Note there is no point with 12 spokes, but a point with 3 spokes, attached to which there are points with 4 spokes.

Return to stable cycles.