A collection of circles, *C*_{1}*C*_{N}*C*_{1}*C*_{N}*D*_{1}*D*_{N}

Starting with a point *z*_{0}*z*_{1}*z*_{1}*z*_{2}*z*_{i}__ limit set__ of inversion across
*C*_{1}*C*_{N}*z*_{i}

If we have two circles, the limit set is just two points.

In the case of four disjoint circles, the limit set is a Cantor set wrapped around a circle.

On this page, we see a group of five circles. Now the limit set consists of a much richer set of points, and the image is more complex. The fractal nature of this limit set is evident, although to be sure it is a more complicated fractal than the familiar Sierpinski gasket. Here the self-similarity is nonlinear: the shape is made of distorted smaller copies of itself.

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