File:Periodic cycles.png
Periodic_cycles.png (460 × 400 pixels, file size: 87 KB, MIME type: image/png)
Captions
Summary edit
DescriptionPeriodic cycles.png | Periodic cycles in Mandelbrot set |
Date | |
Source | Own work |
Author | António Miguel de Campos - en:User:Tó campos |
Permission (Reusing this file) |
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...
Licensing edit
Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 15:02, 20 March 2006 | 460 × 400 (87 KB) | Tó campos1 (talk | contribs) | new version - with more bulb numbers | |
12:17, 20 March 2006 | 460 × 400 (85 KB) | Tó campos1 (talk | contribs) | better version | ||
11:37, 20 March 2006 | 425 × 380 (103 KB) | Tó campos1 (talk | contribs) | Periodic cycles in Mandelbrot set (made by António Miguel de Campos) | ||
11:35, 20 March 2006 | 425 × 380 (103 KB) | Tó campos1 (talk | contribs) | Periodic cycles in Mandelbrot set (made by António Miguel de Campos) |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.