| 1. (a) Here is what we find. |
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| The largest midget on the left branch has cardioid with cycle number 4. Going toward the point
where the antenna spokes meet, we find 7 and 10. |
| The largest midget on the right branch has cardioid with cycle number 5. Going toward the point
where the antenna spokes meet, we find 8 and 11. |
| The largest midget on the bottom branch has cardioid with cycle number 9. Going toward the point
where the antenna spokes meet, we find 12 and 15. |
| Patterns |
Going along each spoke, the cycle numbers go up by 3, the period of the disc to which the antenna
is attached. |
The largest midgets on the spokes (excluding the one attaching the antenna to the body of the
Mandelbrot set) have cycles 4 = 3 + 1 and 5 = 3 + 2. |
The largest midget on the spokes attaching the antenna to the body of the
Mandelbrot set has cycle 9 = 3*3. |
| A reliable way to find the cycles is to first magnify the midget Mandelbrot set sufficiently to be
sure the pointer is in the cardioid, then shift-click or right click. The right window shows the cycle
to which the iterates of 0 converge. |
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