The Mandelbrot Set and Julia Sets

The Mandelbrot Set - Stable Cycles

On the left we see three points selected from a 3-cycle component of the Mandelbrot set; on the right, the corresponding sequences.
Note all three sequences of points - red, green, and blue - converge to (different) 3-cycles.
This illustrates that sequences generated by points c in an n-cycle component converge to nearby n-cycles.

Return to stable cycles.