The following program uses the five inversion circles from the previous page. But now we use five seed circles rather than just one. The slider n controls the number of reflection levels, and model controls how the reflection circles get rendered: as disks, spheres, or hemispheres. In the sphere model, the seed circle of greatest radius is not rendered so as not to occlude the other seed and reflection circles all of which lie in its interior; in the hemisphere model, it is rendered as a gray disk on which the hemispheres sit.

Circle inversion fractal

In the following figure, the seed circles are outlined in green and the inversion circles are in blue. The seed circles intersect each other tangentially and intersect the inversion circles orthogonally.¹

In our program, the five seed circles appear at level . In fact, the five seed circles appear at every level, that is, for every value of . Reflection of a circle in an inversion circle to which it is orthogonal is unchanged by reflection, and each of the seed circles is orthogonal to at least one inversion circle.