Circle Inversion Fractals

Overlapping Circles

If the inverting circles overlap, the limit set can become much messier, often extending outside the circles.
When the angles of intersection of the circles are rational multiple of 180 degrees, some relations are imposed between the inversions. For example, it is not difficult to show if C1 and C2 intersect with an angle of (m/n)180, 0 < m < n, then (I1I2)n = identity.
Here is an example of eight circles, with non-tangential intersections 90 deg.
Here is an example of six circles, with non-tangential intersections 60 deg.
Here is an example of four circles very close to generating a 12 cycle.

Return to circle inversion fractals.