File:Cardioid under log mapping.png
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DescriptionCardioid under log mapping.png |
English: cardioid under log mapping[1] |
Date | |
Source | Own work |
Author | Adam majewski |
Source code
/*
b batch file for maxima CAS
There are 2 complex planes :
* w-plane
* z-plane
z is a pont of z-planes
zz is a list of z points
1. draw curve on z plane
2. draw images of z-curve under f on w plane
3. draw images of z-curve under fc on w plane
Adam Majewski
*/
kill(all);
remvalue(all);
/* definitions of functions */
f(z):= float(rectform(log(z)))$
fc(z):= float(rectform(log(z -c)))$
/* conformal map */
g(w):=w/2-w*w/4;
/*
circle D={w:abs(2w)=1 } where w=l(t)
t is angle in turns ; 1 turn = 360 degree = 2*Pi radians
*/
l(t):=%e^(%i*t*2*%pi);
/* converts complex number into list for draw package */
draw_format(z):= [float(realpart(z)),float(imagpart(z))];
compile(all);
print (" ============== compute =============== ")$
/* ---- const ----*/
t : (-1+sqrt(5))/2$ /* Rotation number ( internal angle) t is an irrational number = the Golden Mean */
c :l(t)$
c:g(c)$
/* c : -0.39054087 -0.58678790*%i$ */
iMax:100; /* number of points to draw */
dt:1/iMax;
/* curve is a list of points joned by lines */
/* point to point method of drawing */
t:0; /* angle in turns */
/* compute first point of curve, create list and save point to this list */
/* point of unit circle w:l(t); */
w:rectform(ev(l(t), numer));
circleList:makelist (w, j, 1, 1);
while (t<=1) do
( t:t+dt,
w:rectform(ev(l(t), numer)),
circleList:cons(w,circleList)
);
zz:[0, 1/4, 1/3, 1/2]$
zz:map(l,zz)$
zz:map(g,zz)$
cardioidList: map (g, circleList)$
/* --------- map from z to w plane using -------------------------------*/
logList: map (f, cardioidList)$
logCList: map (fc, cardioidList)$
ww : map(f,zz)$
wwc: map(fc,zz)$
/*-------------- convert lists of complex points to draw format lists --------*/
cardioidList: points(map(draw_format, cardioidList))$
logList: points(map(draw_format, logList))$
logCList: points(map(draw_format, logCList))$
zz: points(map(draw_format, zz))$
ww: points(map(draw_format, ww))$
wwc: points(map(draw_format, wwc))$
/*------------------ draw ------------------------------------------------------ */
path:"~/Dokumenty/mandelbrot_planes/log/maxima/"$ /* pwd */
FileName:"i3p"$ /* without extension which is the terminal name */
load(draw); /* Mario Rodríguez Riotorto http://www.telefonica.net/web2/biomates/maxima/gpdraw/index.html */
draw(
terminal = 'png,
file_name = concat(path,FileName),
columns = 3,
dimensions=[1500,500], /* x = y*columns */
gr2d(title = " z plane ",
xlabel = "z.re ",
ylabel = "z.im",
points_joined =true,
grid = false,
color = red,
point_size = 0.2,
point_type = filled_circle,
cardioidList,
color=blue,
points_joined =false,
point_size = 0.9,
zz
),
gr2d(
title = " w plane : w =log(z)",
xlabel = "w.re ",
ylabel = "w.im",
grid = false,
xaxis = false,
points_joined =true,
color = red,
point_size = 0.2,
point_type = filled_circle,
logList,
color=blue,
points_joined =false,
point_size = 0.9,
ww
),
gr2d(
title = " w plane : w =log(z-c)",
xlabel = "w.re ",
ylabel = "w.im",
/*
yrange = [-0.5,3.5],
xrange = [-2.5,1.5],
*/
grid = false,
xaxis = false,
points_joined =true,
color = red,
point_size = 0.2,
point_type = filled_circle,
logCList,
color=blue,
points_joined =false,
point_size = 0.9,
wwc
)
);
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 4.0 International license.
- 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.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:04, 1 May 2022 | 1,500 × 500 (38 KB) | Soul windsurfer (talk | contribs) | better quolity | |
11:10, 1 May 2022 | 1,500 × 500 (39 KB) | Soul windsurfer (talk | contribs) | Uploaded own work with UploadWizard |
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