File:Distance Quadratic Siegel Golden Mean.svg
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Size of this PNG preview of this SVG file: 600 × 500 pixels. Other resolutions: 288 × 240 pixels | 576 × 480 pixels | 922 × 768 pixels | 1,229 × 1,024 pixels | 2,458 × 2,048 pixels.
Original file (SVG file, nominally 600 × 500 pixels, file size: 63 KB)
Summary
| Description |
English: Distance between points of orbit for fc(z)=z*z -0.390540870218399 -0.586787907346969*i |
| Date | |
| Source | Own work |
| Author | Adam majewski |
| Other versions |
|
| SVG development |  This plot was created with gnuplot. |
Licensing
Adam majewski, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution:
- 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.
Source code
This media was created with Maxima (computer algebra system)
Here is a listing of the source used to create this file.
Here is a listing of the source used to create this file.
/*
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)
);
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:33, 2 November 2011 | | 600 × 500 (63 KB) | wikimediacommons>Soul windsurfer |
File usage
The following page uses this file:
