Changing the circles certainly can change the limit set.

A simple example is made from five circles, with four constant and the fifth shrinking. |

These three animations illustrate the idea of *fractal motion*
seen in the first example.

In all three, the fixed circles have radius 1 and centers
at

In the one moving circle animation there is a single moving circle, of constant radius, staying tangent to one or two of the fixed circles. | |

In the two moving circles animation there are two moving circles, of varying radius, staying tangent to one or two of the fixed circles and to one another. | |

In the four moving circles animation there are four moving circles, of varying radius, staying tangent to one or two of the fixed circles and to two of the moving circles. |

Return to circle inversion fractals.