File:Distance.png
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Summary
| Description |
English: Distance between point of orbit of discrete dynamical system.
We have discrete dynamical system:
where
Distance between and is :
From this image one can see that:
|
| Source | self-made with Maxima |
| Author | Adam majewski |
See also
-
Distance between points along orbit for various z-points for fc(z)=z*z -0.390540870218399 -0.586787907346969*i
Long description
Maxima code
Here is batch file for Maxima:
c:-0.71+0.1*%i;
f(z,c):=z*z+c;
iMax:300;
z0:0+0*%i;
dist(z_prev,z_next):=
block(
dr:realpart(z_next)-realpart(z_prev),
di:imagpart(z_next)-imagpart(z_prev),
d:sqrt(dr*dr+di*di),
return(d)
);
/* */
z1:f(z0,c);
d1:dist(z0,z1);
/* save the z values to 2 lists */
xx:makelist (1, i, 1, 1); /* list of numbers of iterations */
yy:makelist (d1, i, 1, 1); /* list of distance(z(n),z(n+1)) */
/* */
z_prev:z1;
for i:2 thru iMax step 1 do
block
(
z_next:f(z_prev,c),
d:dist(z_prev,z_next),
xx:cons(i,xx),
yy:cons(d,yy),
z_prev:z_next
);
load(draw);
draw2d(
file_name = "distance",
terminal = 'png,
yrange = [0,0.8],
xrange = [0,iMax],
pic_width = 1000,
pic_height = 1000,
title= "distance between points zn and z(n+1) where z(n+1)=f(zn)= zn*zn+c and z0=0 is critical point",
key = concat("distance for c = ",string(c)),
xlabel = "number of iteration",
ylabel = "distance",
point_type = filled_circle,
point_size = 0.5,
color = red,
points(xx,yy)
);
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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- Under the following conditions:
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:02, 20 April 2008 | | 1,000 × 1,000 (7 KB) | Soul windsurfer | {{Information |Description=Distance between point of orbit of discrete dynamical system |Source=self-made with Maxima |Date= |Author= Adam majewski |Permission= |other_versions= }} |
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