Inversion across a cricle C with center (a,b).
(i)  leaves unchanged every point of the circle C, 
(ii)  interchanges the inside and outside of the circle C, 
(iii)  is a contraction on sets outside the circle C, 
(iv)  preserves circles S orthogonal to the inverting circle C, 
(v)  is an involution
(that is, if 
(vi)  takes a circle not passing through

(vii)  takes a circle passing through

Return to circle inversion fractals.