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 C4 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 obvious divisions, 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.


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