File:Parabolic critical orbit for internal angle one fifth.png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this preview: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 1,000 × 1,000 pixels.
Original file (1,000 × 1,000 pixels, file size: 24 KB, MIME type: image/png)
File information
Structured data
Captions
Summary
[edit]DescriptionParabolic critical orbit for internal angle one fifth.png |
English: parabolic critical orbit for internal angle one fifth for fc(z) = z^2 + c |
Date | |
Source | Own work |
Author | Adam majewski |
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.
See also
[edit]-
Critical Orbit, Inner and outer circle for Golden Mean Quadratic Julia set
-
Critical orbit tends to period 3 orbit
-
3D view of critical orbit tending to parabolic fixed point
-
distance between points of critical orbit in case of attracting fixed point
-
Distance to fixed point for various types of dynamics
-
Siegel disc
-
parabolic cases
Maxima CAS src code
[edit]/* this is batch file for Maxima 5.22.1 http://maxima.sourceforge.net/ tested in wxMaxima wxMaxima 0.8.5 using draw package ( interface to gnuplot ) to draw on the screen */ kill(all); /* ---------- functions ---------------------- */ /* conformal map from circle to cardioid ( boundary of period 1 component of Mandelbrot set */ F(w):=w/2-w*w/4; /* circle D={w:abs(w)=1 } where w=l(t,r) t is angle in turns ; 1 turn = 360 degree = 2*Pi radians r is a radius */ l(t,r):=r*%e^(%i*t*2*%pi); /* http://en.wikipedia.org/wiki/Complex_quadratic_polynomial */ f(z,c):=z*z+c $ GiveCriticalOrbit(c,iMax,denominator):= /* computes (without escape test) critical orbit (forward orbit of critical point ) and saves it to the list */ block( [z,orbit], z:0, /* first point = critical point z:0+0*%i */ orbit:[z], for i:1 thru iMax step 1 do ( z:expand(f(z,c)), orbit:endcons(z,orbit)), return(orbit) )$ /* find fixed point alfa */ GiveFixed(c):= float(rectform((1-sqrt(1-4*c))/2))$ /* give angle with respect to alfa */ GiveAngle(z,alfa):= carg(z-alfa) $ compile(all)$ /* ---------- constant ---------------------------*/ Numerator :1; denominator :5; internalAngle: Numerator/denominator; internalRadius:1; iMax:50000000; /* -------------- main ----------------- */ /* point of unit circle w:l(internalAngle,internalRadius); */ w1:l(internalAngle,internalRadius); /* point of circle */ c: float(rectform(F(w1))) ; /* point of period 1 component of Mandelbrot set */ zAlfa:GiveFixed(c); /* ------------------- compute 5 subsets of forward orbit of critical point ----------*/ z:0; /* first point */ orbit1:[z]; for i:1 thru (denominator-1) step 1 do ( z:rectform(f(z,c)), if i=1 then orbit2:[z] elseif i=2 then orbit3:[z] elseif i=3 then orbit4:[z] elseif i=4 then orbit5:[z] ); for i:(denominator) thru iMax step 1 do ( z:rectform(f(z,c)), j:mod(i,denominator), if j=0 then orbit1:endcons(z,orbit1) elseif j=1 then orbit2:endcons(z,orbit2) elseif j=2 then orbit3:endcons(z,orbit3) elseif j=3 then orbit4:endcons(z,orbit4) elseif j=4 then orbit5:endcons(z,orbit5) ); load(draw); /* ( interface to gnuplot ) by Mario Rodriguez Riotorto http://www.telefonica.net/web2/biomates */ draw2d( title= " Critical Orbit in parabolic case for internal angle = 1/5 ", user_preamble = "", terminal = 'png, pic_width = 1000, pic_height = 1000, xlabel = "Z.re ", ylabel = "Z.im", point_type = filled_circle, points_joined = true, point_size = 1.5, /* */ color =red, key = "1", points(map(realpart,orbit1),map(imagpart,orbit1)), /* */ color =green, key = "2", points(map(realpart,orbit2),map(imagpart,orbit2)), /* */ color =blue, key = "3", points(map(realpart,orbit3),map(imagpart,orbit3)), /* */ color =yellow, key = "4", points(map(realpart,orbit4),map(imagpart,orbit4)), /* */ color =magenta, key = "5", points(map(realpart,orbit5),map(imagpart,orbit5)), /* */ color =black, key = "parabolic fixed point", points([realpart(zAlfa)],[imagpart(zAlfa)]), /* */ color =brown, key = "critical point", points([0],[0]) );
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:46, 14 January 2012 | 1,000 × 1,000 (24 KB) | Soul windsurfer (talk | contribs) |
You cannot overwrite this file.
File usage on Commons
The following 3 pages use this file:
File usage on other wikis
The following other wikis use this file: