The Secondary Bulbs Symmetry

Every ( m1 / n1 ) primary bulb has decoration very similar to the main bulb one (in "square" parametrisation). So for the secondary bulbs we have simply to add one more m2 / n2 rotation number ( m1 / n1 m2 / n2 ). Note that period of a secondary bulb is n1 x n2 product. In this way we can map all the M-set decorations.
You can determine n2 by the number of spokes in the largest antenna attached to a secondary decoration and the shortest spoke is located m2 = 1 revolutions in the counterclockwise direction from the main spoke in square limited region! But you see three spokes branching point nearby.
For ( 1/3 1/4 ) secondary bulb we have period 3 x 4 = 12 orbit (the left image). But after factorisation (if we connect only 1, 4, 8 and 12 points) we get f o3: z1 -> z4 -> z8 -> z12 -> z1 second order star (small 4-polygon on the right image).

At last, the Jc-set contains infinitely many "junction points" at which 4 distinct black regions in J are attached. And the smallest black region is located m1 = 1 revolutions in the counterclockwise direction from the largest central region. Again in square limited region.


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updated 12 February 2000