The nonlinearity of circle inversion causes some problems with the IFS approaches to generating limit sets. |

We illustrate Mandelbrot's method with an example, and begin by constructing some cirlces that belong to the limit set. |

Next we simplify the problem by inverting in another circle. |

Now,
we show that the limit set _{1}, C_{2},
C_{3}, C_{4}, C_{5})_{1}. |

Similar arguments show the
limit set _{1}, C_{2},
C_{3}, C_{4}, C_{5})_{2},
S_{3},
S_{4}, and
S_{5}. |

So the limit set is inside S_{1}, and outside
S_{2},
S_{3},
S_{4}, and
S_{5}. We can say
more. |

Continuing this idea quickly generates the limit set, to any desired accuracy. |

Return to circle inversion fractals.