One can obtain m/n rotation number for the
largest bulb between the 1/2 and
1/3 bulbs
(note that they are both larger then our new bulb)
by adding the numerators and adding the denominators (Farey addition
rule) [1]
2/5 = 1/2
+ 1/3
click the picture to explore it and test bulbs rotating numbers
m/n
So we get next primary bulbs sequences:
1/2 +
1/3 = 2/5 +
1/2 = 3/7 +
1/2 = 4/9 +... and
1/2 +
1/3 = 2/5 +
1/3 = 3/8 +
1/3 = 4/11 +....
And at last 1/n sequence!
1/2 +
0/1 = 1/3 +
0/1 = 1/4 +
0/1 = ... = 1/n
(but may be the right 0/1 bulb is a trick only :)
"square" parametrisation
"5 Stars" Julia trip animation.
[1] Robert L. Devaney The Fractal Geometry of the Mandelbrot Set II.
How to Count and How to Add:
6 How to Add