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
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{{Information |Description=Distance between point of orbit of discrete dynamical system |Source=self-made with Maxima |Date= |Author= Adam majewski |Permission= |other_versions= }}