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With multiple bays associated with each attractor the possibilities abound.
Cycles of two and seventeen.
Both cycles are visible in this blow up of a part of the boundary between the two-cycle bays. Is there some dominance of the two-cycle over the 17-cycle in the behavior of f?
Cycles of order 11 and 169. The cycle of 169 is not obvious in this view.
Looking at the detail we see a different story. There are 169 bays around the tan area.
Cycles of order five and 27. The cycle of 27 is broken into three sets of nine in the following graphs.
The nine yellow shades are further broken up into three sets of three.
Cycles of nine and seventeen. The cycle of seventeen is completely within the detail between the nine unbounded bays.
When we look at that detail we see on the left a spiral where the cycles seem to have changed roles from that of the previous graph. On the right is a joint spiral of a different kind clearly showing both cycles.
Cycles of five and 98. Looking closely right in the center you can see a discontinuity. (Two of the lines appear broken.) On the left of the discontinuity the approximation of G(z), fn(z/sn), used a value of n one higher than on the right.
Attracting cycles of order five and six. The five-cycle is clearly visible in the boundary. Only the six-cycle has unbounded bays.
Attracting cycles of order six and eight.
Two attracting cycles of order three. Among the graphs shown above this is unique in that the two cycles both have unbounded bays.
Two attracting cycles of order four. In this image, the previous and the next there are two attracting cycles of the same order. Each of those graphs is centered at the origin and shows unbounded bays for each of the cycles with the colors alternating between cycles around the center.
Two attracting cycles of order six. At this point I have only one example of cycles of equal order where only one of the cycles has unbounded bays.
Two attracting cycles of order 17. One of the cycles has unbounded bays. In the next view of the same function we see both cycles.
The cycle in the upper right is the obvious one in the previous image. The bottom left is a second cycle of 17.
Attracting cycles of order three and nine. This also shows a different interaction between cycles and the screen shot will help with the explanation. The larger bays correspond to the cycle of three. We can see a spiral of pink bays coming out from the center. These are separated by smaller bays corresponding to the third, sixth and ninth color in the cycle of nine. Similarly in the spiral of larger orange bays of the three cycle the separating colors are the second, fifth and eighth colors in the cycle of nine. The spiral of larger green bays are separated by the green hues in the first, fourth and seventh positions in the cycle of nine. This kind of interaction requires the order of one cycle to be a divisor of the order of the other.
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