File:Distance Quadratic Siegel Golden Mean.svg
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[edit]DescriptionDistance Quadratic Siegel Golden Mean.svg |
English: Distance between points of orbit for fc(z)=z*z -0.390540870218399 -0.586787907346969*i |
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.
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- to remix – to adapt the work
- Under the following conditions:
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See also
[edit]-
distance between points of critical orbit in case of attracting fixed point
Maxima CAS src code
[edit]/* gives distance between 2 complex points on plane interior points of unit circle under iteration of f(z)=z*z alfa fixed point za : -0.368684439039160 -0.337745147130762*%i interior zi : 1.331250000000000 +0.375000000000000*%i exterior ze : 0.055303418766281 -0.066996098099950 *%i siegel zcr : 0 inside siegel zs1 : -0.162500000000000 -0.143750000000000 *%i inside siege zs2 : -0.256250000000000 -0.187500000000000*% i */ kill(all); GivePlaneDistance(c1,c2):=float(abs(c2-c1))$ f(z):=rectform(z*z+c); GiveList(z0, iMax):= block ( [zprev,znext,dist,d_list], zprev:z0, znext:f(zprev), dist:GivePlaneDistance(zprev,znext), d_list:[[1,dist]], zprev : znext, for i:2 step 1 thru iMax while (abs(znext)<10 ) do ( znext:f(zprev), dist:GivePlaneDistance(zprev,znext), d_list:endcons([i,dist],d_list), zprev : znext ), return(d_list) )$ /* ------------- main -----------------------*/ /* rotation number or internal angle */ t : (-1+sqrt(5))/2; /* golden Mean Siegel disc */ angle : 2*%pi*t; /* from turns to radians */ d : exp(angle*%i); /* point on unit circle */ c : float(rectform(d/2-d*d/4)); /* point on boundary of main cardioid */ i_max:100; zi : 1.331250000000000 +0.375000000000000*%i; i_list:GiveList(zi,i_max); zs1 : -0.162500000000000 -0.143750000000000 *%i; s1_list:GiveList(zs1,i_max); zs2 : -0.256250000000000 -0.187500000000000*%i; s2_list:GiveList(zs2,i_max); ze : 0.055303418766281 -0.066996098099950*%i; e_list:GiveList(ze,i_max); za : -0.368684439039160 -0.337745147130762*%i; a_list:GiveList(za,i_max); zcr : 0.0; cr_list:GiveList(zcr,i_max); /* ----------------- draw ------------ */ load(draw); draw2d( terminal = svg, file_name = "distance", title = "Distance between points of orbit for fc(z)=z*z -0.390540870218399 -0.586787907346969*i", yrange = [0,4], points_joined =true, point_size = 0.4, point_type = filled_circle, color = black, key="exterior but near boundary ", points(e_list), color = red, key="critical point ", points(cr_list), color = blue, key="Siegel 2", points(s2_list), color = blue, key="Siegel 1", points(s1_list), color = green, key="interior, not Siegel ", points(i_list) );
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current | 16:33, 2 November 2011 | 600 × 500 (63 KB) | Soul windsurfer (talk | contribs) |
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