Using complex numbers, the process iterated to generate the Mandelbrot set and the Julia sets takes a very simple form: |

z → z^{2} + c |

where z and c are complex numbers. |

To iterate the process, pick a
complex number c and a complex number z_{0}. Then generate the sequence of
complex numbers z_{1}, z_{2}, z_{3}, ... by |

z_{1} = z_{0}^{2} + c |

z_{2} = z_{1}^{2} + c |

z_{3} = z_{2}^{2} + c |

and in general |

z_{n+1} = z_{n}^{2} + c |

How this process generates the
Mandelbrot set and Julia sets is the subject of
Julia Sets and
the Mandelbrot Set.
Here we review the mechanics of ^{2} + c. |

First, we reformulate the process without using complex numbers. |

Next we do an example of the iteration. |

Return to the Mandelbrot set and Julia sets.