|
Friday, 23 May 2008 02:07 |
|
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.
 |
The Secondary Bulbs Symmetry
Subscribe to this comment's feed