File:Cr orbit 3.png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Cr_orbit_3.png (640 × 480 pixels, file size: 4 KB, MIME type: image/png)
File information
Structured data
Captions
Summary
[edit]DescriptionCr orbit 3.png | critical orbit. Here one can see that point z=0 tends to 3 point attracting cycle. |
Source |
self-made with Maxima program ( code below) This plot was created with Gnuplot by n. |
Author | Adam majewski |
See also
[edit]-
Critical orbit in Siegel disc case : Golden mean
-
3D view of critical orbit tending to parabolic fixed point
-
distance between points of critical orbit in case of attracting fixed point
Maxima source code
[edit]/* this is batch file for Maxima. Save it with mac extension. It computes orbit of Z0 under f(z,c), finds period and draws orbit */ c:-0.2-0.7*%i; f(z,c):=z*z+c; z0:0; iMax:100; eps:0.01; /* first point */ z:z0; orbit:[z]; /* ------------------- compute forward orbit -----------------------------*/ for i:1 thru iMax step 1 do block ( z:f(z,c), orbit:endcons(z,orbit) /* disp(rectform(orbit[i])) */ ); /* ----------- find period of orbit --------------------------------------*/ IsEqual(c1,c2,eps):= if abs(realpart(c1)-realpart(c2))<=eps and abs(imagpart(c1)-imagpart(c2))<=eps then true else false; GivePeriod(orbit,eps):= block ( period:0, iLast:length(orbit), i:iLast, block ( loop, i:i-1, if not IsEqual(orbit[iLast],orbit[i],eps) then go(loop), period:iLast-i ) ); period:GivePeriod(orbit,eps); print(period); /*-------------- draw orbit on the screen ----------------------------- */ /* save the z values to 2 lists */ xx:makelist (realpart(z0), i, 1, 1); /* list of re(z) */ yy:makelist (imagpart(z0), i, 1, 1); /* list of im(z) */ for i:2 thru length(orbit) step 1 do block ( xx:cons(realpart(orbit[i]),xx), yy:cons(imagpart(orbit[i]),yy) ); load(draw); draw2d( file_name = "orbit", terminal = 'png, yrange = [-1,1], xrange = [-1,1], title= concat("Period ",string(period)," orbit of z0=",string(z0)," for c=",string(c)," f(z,c):=z*z+c "), key = "point of orbit", xlabel = "Z.re ", ylabel = "Z.im", point_type = filled_circle, point_size = 0.5, color = red, points(xx,yy) );
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:50, 2 March 2008 | 640 × 480 (4 KB) | Soul windsurfer (talk | contribs) | {{Information |Description=critical orbit |Source=self-made |Date= |Author= Adam majewski |Permission= |other_versions= }} |
You cannot overwrite this file.
File usage on Commons
The following 4 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on el.wikipedia.org
- Usage on en.wikipedia.org
- Usage on en.wikibooks.org