| 7. Here are the correspondences: |
| (i) → (a) |
| (ii) → (b) |
| (iii) → (c) |
| (iv) → (d) |
| For Julia sets the cycle corresponds to the number of spokes meeting at a center. Consequently for (i) we have a 5-cycle, for (ii) a 6-cycle, for (iii) an 8-cycle; (iv) is trickier: 2 spokes meet at some centers, 3 spokes at others. |
| For discs attached to the main cardioid of the Mandelbrot set, the number of spokes gives the cycle number. So we see 5 for (a), 6 for (b), 8 for (c), and 3 for (d). |
| But none of the Julia sets has 3 branches meeting at every center, so the disc in (d) must be the disc attached to the 3-cycle disc. Consequently, it is a a 6-cycle disc, the 2-cycle off the 3-cycle disc. |
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