The following images are the geometric inversion of circles. (for math definition, see: Inversion.) Start with set of circles, then invert them with respect to themselves. Take the result and apply inversion with respect to starting circles again. This process can be repeated. Each small graphics show the configuration of the starting (and inverting) circles. Circles retain their color after inversion.

In the first image for example, it starts with seven circles and let's call it generation 0. Invert generation 0 circles with respect to generation 0 circles, we get generation 1. Invert generation 1 with respect to generation 0 we get generation 2… etc. Note that the inversions are always done with respect to generation 0 circles. The image shows the result after 4 inversions.

Inversion of Parallel Lines

The following are inversion of parallel lines with respect to a circle centered on the origin. Color has no significance.