File:Color complex plot2.jpg
Summary
| Description |
English: Colour plot of complex function (x² - 1) * (x-2-I)² / (x² + 2 + 2I), hue represents the argument, sat and value represents the modulo. Contours distinguish intervals [e^i, e^(i+1)] where i=0,1,2... Shadow is on the higher modulus side.
Zeros have pin-wheel of colours, one cycle of the colour wheel for simple zero, two cycles for double zero etc. Contours are approaching poles with the shadowed side, and the colours cycle in reverse order around a pole. |
| Date | |
| Source | Own work |
| Author | Jan Winnicki |
| Other versions |
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Source code
This is the source code used for image generation. It is a slightly modified version of File:Color complex plot.jpg. In this version the real axis is directing right. And contours bring more information.
#include <complex>
#include <fstream>
using namespace std;
void SetHSV(double h, double s, double v, unsigned char color[3]) {
double r=0, g=0, b=0;
if(s==0)
r = g = b = v;
else {
h /= 60;
int i = floor(h);
double f = h - i;
double p = v*(1-s);
double q = v*(1-s*f);
double t = v*(1-s*(1-f));
switch(i){
case 0: r=v; g=t; b=p; break;
case 1: r=q; g=v; b=p; break;
case 2: r=p; g=v; b=t; break;
case 3: r=p; g=q; b=v; break;
case 4: r=t; g=p; b=v; break;
case 5: r=v; g=p; b=q; break;
}
}
int c;
c = int(256*r); if(c>255) c = 255; color[0] = c;
c = int(256*g); if(c>255) c = 255; color[1] = c;
c = int(256*b); if(c>255) c = 255; color[2] = c;
}
complex<double> fun(complex<double>& c ){
const complex<double> i(0., 1.);
return (pow(c,2) - 1.) * pow(c -2. -i, 2) / (pow(c, 2) + 2. + 2. * i);
}
int main(){
const int dimx = 800; const int dimy = 800;
const double rmi = -3; const double rma = 3;
const double imi = -3; const double ima = 3;
ofstream f("complex.ppm", ios::binary);
f << "P6" << endl
<< dimx << " " << dimy << endl
<< "255" << endl;
for(int j=0; j < dimy; ++j){
double im = ima - (ima -imi) *j /(dimy -1);
for(int i=0; i < dimx; ++i){
double re = rmi +(rma -rmi) *i /(dimx -1);
complex<double> c(re, im);
complex<double> v = fun(c);
double a = arg(v)*180/M_PI;
if(a < 0) a += 360;
double m = abs(v);
double ranges;
double rangee = 1;
while(m>rangee){
ranges = rangee;
rangee *= M_E;
}
double k = (m-ranges)/(rangee-ranges);
double sat = k < 0.5 ? 1-2.8*k : 2.8*k-1.1;
if(sat < 0.3) sat = 0.3;
else if(sat > 1) sat = 1;
double val = k < 0.5 ? 1.4-1.6*k : 1.6*k-0.6;
if(val < 0.6) val = 0.6;
else if(val > 1) val = 1;
unsigned char color[3];
SetHSV(a,sat,val,color);
f.write(color,3);
}
}
return 0;
}
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported 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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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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| Annotations | This image is annotated: View the annotations at Commons |
