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 × 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 counter-clockwise
direction from the main spoke in the square limited region!
But you see three spokes branching point nearby.
For ( 1/3 1/4 ) secondary
bulb we have period 3 × 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
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
counter-clockwise direction from the largest central region.
Again in the square limited region.
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Next: The Third level Bulbs
updated 8 Sep 2013