File:Distance.png
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Summary
[edit]DescriptionDistance.png |
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
[edit]-
Distance between points along orbit for various z-points for fc(z)=z*z -0.390540870218399 -0.586787907346969*i
Long description
[edit]Maxima code
[edit]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
[edit]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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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current | 13:02, 20 April 2008 | 1,000 × 1,000 (7 KB) | Soul windsurfer (talk | contribs) | {{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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