File:DistanceToFixed.png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this preview: 800 × 400 pixels. Other resolutions: 320 × 160 pixels | 640 × 320 pixels | 1,000 × 500 pixels.
Original file (1,000 × 500 pixels, file size: 21 KB, MIME type: image/png)
File information
Structured data
Captions
Summary
[edit]DescriptionDistanceToFixed.png |
English: Distance to fixed point for various types of local discrete dynamics near fixed point . Polski: Typy lokalnej dynamiki w otoczeniu punktu stałego |
Date | |
Source | Own work |
Author | Adam majewski |
File:DistanceToFixed.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:DistanceToFixed.png → File:DistanceToFixed.svg
For more information, see Help:SVG.
|
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.
Maxima CAS src code
[edit]/* gives distance between 2 complex points on plane */ kill(all); /* ---------- functions ---------------------- */ /* http://en.wikipedia.org/wiki/Complex_quadratic_polynomial */ f(z,c):=rectform(z*z+c); /* find fixed point alfa of function f(z,c) */ GiveFixed(c):= float(rectform((1-sqrt(1-4*c))/2))$ GivePlaneDistance(z1,z2):=float(abs(z2-z1))$ GiveList(z0,c, iMax):= block ( [i,zAlfa,zprev,znext,dist,d_list], zAlfa:GiveFixed(c), zprev:z0, znext:f(zprev,c), dist:GivePlaneDistance(zAlfa,znext), d_list:[[1,dist]], zprev : znext, i:1, while abs(znext)<2 and i<iMax do ( znext:f(zprev,c), dist:GivePlaneDistance(zAlfa,znext), d_list:endcons([i,dist],d_list), zprev : znext, i:i+1 ), return(d_list) )$ /* 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 */ ToCircle(t,r):=r*%e^(%i*t*2*%pi); compile(all)$ /* ---------- constant ---------------------------*/ Numerator :1; denominator :2; internalAngle: Numerator/denominator; internalRadius:1; iMax:500; zcr : 0.0; /* ------------- main -----------------------*/ /* parabolic */ w1:ToCircle(internalAngle,internalRadius); /* point of circle */ cp: float(rectform(F(w1))) ; /* point of period 1 component of Mandelbrot set */ ParabolicList:GiveList(zcr,cp,iMax); /* siegel*/ cs:-.5867879078859505*%i-.3905408691260131; z0s: 1.006250000000000 +0.543750000000000*%i; SiegelList:GiveList(z0s,cs,iMax); /* hyperbolic */ ch:0; z0h:0.843750000000000 +0.437500000000000*%i; HyperbolicList:GiveList(z0h,ch,iMax); /* escaping */ ce:-0.189093266739737 +0.677638784067832*%i; z0e:-0.289258118270603 +0.429086915059359*%i; EscapingList:GiveList(z0e,ce,iMax); /* ----------------- draw ------------ */ load(draw); draw2d( terminal = png, file_name = "distance", pic_width = 1000, /* Since Maxima 5.23, pic_width and pic_height are deprecated. */ pic_height = 500, /* See option dimensions. To get the same effect, write dimensions=[800,600] */ title = "Distance between point of orbit and fixed point ", yrange = [-0.1,1.0], points_joined =false, point_size = 0.6, point_type = filled_circle, /* */ key ="parabolic", color = red, points(ParabolicList), /* */ key ="elliptic", color = blue, points(SiegelList), /* */ key ="escaping", points_joined =true, color = black, points(EscapingList), /* */ key ="attracting", points_joined =true, color = green, points(HyperbolicList) );
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 11:40, 22 January 2012 | 1,000 × 500 (21 KB) | Soul windsurfer (talk | contribs) |
You cannot overwrite this file.
File usage on Commons
The following page uses this file: