Circle Inversion Fractals

Properties of Inversion

Suppose (x,y) lies on the circle C.

Then dist((a,b), (x,y)) = r, the radius of the circle C.

Because dist((a,b), (x,y))*dist((a,b), (x',y')) = r², we see

dist((a,b), (x',y')) = r

and so (x',y') must lie on C.

Because (x,y) and (x',y') lie on the same ray from the center of C, we see

(x'y') = (x,y)

That is, inversion across C takes every point of C to itself.

Return to properties of inversion.