File:Periodic cycles.png

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Description Periodic cycles in Mandelbrot set
Date
Source Own work
Author António Miguel de Campos - en:User:Tó campos
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Public domain

Notice that in 2/5 bulb there is a cycle of period 5 and the trajectory of the periodic cycle jumps always 2 components counterclockwise, in each iteration (i.e. the cycle rotates by 2/5 of a revolution, in each iteration). The p in p/q works as a rotation parameter. In the bottom part of the Mandelbrot set, the cycles rotate clockwise.

The bulbs are ordered as a sequence of decreasing rational numbers p/q=1/2, 3/7, 2/5, 3/8, 1/3, 2/7, 1/4, 1/5, 1/6, 1/7, etc. Notice that the bulb between the 2/5-bulb and the 1/2-bulb is the 3/7-bulb (2/5+1/2=3/7); and in the middle of the 3/7-bulb and 1/2-bulb, there is also a 4/9-bulb (3/7+1/2=4/9); etc...


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Date/TimeThumbnailDimensionsUserComment
current15:02, 20 March 2006Thumbnail for version as of 15:02, 20 March 2006460 × 400 (87 KB)Tó campos1 (talk | contribs)new version - with more bulb numbers
12:17, 20 March 2006Thumbnail for version as of 12:17, 20 March 2006460 × 400 (85 KB)Tó campos1 (talk | contribs)better version
11:37, 20 March 2006Thumbnail for version as of 11:37, 20 March 2006425 × 380 (103 KB)Tó campos1 (talk | contribs)Periodic cycles in Mandelbrot set (made by António Miguel de Campos)
11:35, 20 March 2006Thumbnail for version as of 11:35, 20 March 2006425 × 380 (103 KB)Tó campos1 (talk | contribs)Periodic cycles in Mandelbrot set (made by António Miguel de Campos)

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