Circle Inversion Fractals

Properties of Inversion

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 (x', y') is the inverse of (x, y) across C, then (x, y) is the inverse of (x', y') across C),
(vi)	takes a circle not passing through (a, b) to a circle not passing through (a, b), and
(vii)	takes a circle passing through (a, b) to a line .

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