Home The primary Bulbs counting
The primary Bulbs counting PDF Print E-mail
Friday, 23 May 2008 02:05
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

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