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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