Circle Inversion Fractals

Inversion Limit Sets

Here is a different arrangement of five inverting circles.

The circles C₁, C₂, C₃, and C₄ have a common circle, A, orthogonal to all four.

So as we have seen, A is the limit set generated by inversion in these four circles.

Consequently, A belongs to L(C₁, ..., C₅).

Similarly, the circle B is orthogonal to the three circles C₂, C₃, and C₅, and so the limit set of inversion in these three circles is B.

Consequently, L(C₁, ..., C₅) contains A and B, and much else besides.

For example, I₅(A) belongs to the limit set, as do I₁(B) and I₄(B), and so on.

We include this example, to see if the general shape looks familiar.