# The Secondary Bulbs Symmetry

Every *( *^{m1} / n_{1} )
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} / n_{2} rotation number
*( *^{m1} / n_{1}
^{m2} / n_{2} ).
Note that period of a secondary bulb is *n*_{1} × n_{2}
product. In this way we can map all the M-set decorations.

You can determine *n*_{2} by the number of spokes in the
largest antenna attached to a secondary decoration and the shortest spoke
is located *m*_{2} = 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}: z_{1} → z_{4} → z_{8} →
z_{12} → z_{1} second order star (small 4-polygon on the
right image).

At last, the J_{c}-set contains infinitely many "junction
points" at which 4 distinct black regions in J are attached. And the
smallest black region is located *m*_{1} = 1 revolutions in the
counter-clockwise direction from the largest central region.
Again in the square limited region.

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*updated* 8 Sep 2013