With four disjoint circles, we have to pick the next circle at random every
time. We see that the
green points in *C*_{1} invert to the green points in
*C*_{2}. Similarly, the blue points in
*C*_{4}
and the red points in *C*_{3} invert to
the blue and red points,
respectively, in *C*_{2}.
Since the part of the limit set in *C*_{1} has three
obvious divisions,
the green part of the limit set in *C*_{2} also has
three divisions. Continuing this process, we see the limit set is a Cantor Set.

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