Circle Inversion Fractals

Circle Inversion Driven IFS

Now we expand the circle C₁ and note how the driven IFS changes.

As C₁ expands to intersect 43 and 42, we expect some additional combinations of inversions to be forbidden.

To understand this picture, note C₁ is tangent to I₄(I₃(C₄)) and to I₄(I₃(C₂)), with the latter interior to C₁.

Consequently, the combination 2->3->4->1 is forbidden, while 2->3->4->2 is allowed.

Similarly, 3->2->4->1 is forbidden, while 3->2->4->2 is allowed.

In the driven IFS, the forbidden squares 1432 (red) and 1423 (blue) are shaded.

Of course, any address containing these is forbidden.

Return to circle inversion driven IFS.