How can we tell if a certain cycle belongs to a disc or a cadrioid? Is there any way to analyze this pattern? There is, an algorithm developed by Lavaurs.

The doubling map identifies cycles on the unit circle. |

Here is the algorithm developed by Lavaurs. |

The period of the points under the doubling map correspond to the periods of the components of the abstract Mandelbrot set. |

Return to Combinatorics in the Mandelbrot Set.