With four disjoint circles, we have to pick the next circle at random every
time. We see that the
green points in C1 invert to the green points in
C2. Similarly, the blue points in
and the red points in C3 invert to
the blue and red points,
respectively, in C2.
Since the part of the limit set in C1 has three
the green part of the limit set in C2 also has
three divisions. Continuing this process, we see the limit set is a Cantor Set.
Return to Limit Sets and Inversion