Circle Inversion Fractals

Circle Inversion Driven IFS

Here is an example: the restricted limit set for inversion in the circls C₁, C₂, C₃, and C₄.

To understand the driven IFS, we note some relations between the C_i and inverses of some of the C_j.

Specifically, C₁ is tangent to I₄(C₃), denoted 43, and to 42.

Consequently, any part of the limit set interior to C₄ that inverts from parts interior to C₃ or C₂ are not interior to C₁.

Then the only forbidden combination is that I₄ cannot immediately follow I₁.

That is, 1->4 is forbidden. This explains why a familiar driven IFS picture is generated.

Return to circle inversion driven IFS.