File:Amoeba2.png

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Summary[edit]

Description The amoeba of P(z, w)=3z2+5zw+w3+1
Date 28 February 2007 (original upload date)
Source Own work
Author Oleg Alexandrov
File:Amoeba2.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
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Licensing[edit]

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

C++ code[edit]

#include <iostream>
#include <fstream>
#include <cmath>
#include <complex>
using namespace std;

double small = 1e-14;
double mylog (double);
int main(){

  double A=-5, B=5;
  int N=1000;

  double h= (B-A)/(N-1);
  double theta0 = 2*M_PI/(N-1.0);

  ofstream mfile ("data.txt");

  for (int i=0 ; i < N ; i++){
    double r = exp(A+i*h);

    for (int j=0 ; j < N ; j++){
      double theta = j*theta0;

      complex<double> z2 = polar(r, theta);
      complex<double> root = sqrt(25.0*z2*z2-12.0*(z2*z2*z2+1.0));
      complex<double> z11 = (-5.0*z2+root)/6.0;
      complex<double> z12 = (-5.0*z2-root)/6.0;

      double a1 = mylog(abs(z11));
      double a2 = mylog(abs(z12));
      double b  = mylog(abs(z2));

      mfile << a1  << ' ' << b << endl;
      mfile << a2  << ' ' << b << endl;
    }
  }
  mfile.close();

  return 0;
}
double mylog (double x){

  if (x< 0){
    cerr << "Error in log, negative x!" << endl;
    exit(0);
  }

  if (x < small){
    return log (small);
  }

  return log (x);

}

Matlab code which reads the data output by the C++ code and graphs it[edit]

A=load('data.txt');

plot(A(:, 1), A(:, 2), '.');
axis equal; axis off;

axis([-4 6 -5 5])
saveas(gcf, 'amoeba2.eps', 'psc2');

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current04:22, 9 March 2007Thumbnail for version as of 04:22, 9 March 20071,504 × 1,446 (13 KB)Oleg Alexandrov (talk | contribs)
04:42, 28 February 2007Thumbnail for version as of 04:42, 28 February 20071,078 × 1,092 (28 KB)Oleg Alexandrov (talk | contribs)
04:17, 28 February 2007Thumbnail for version as of 04:17, 28 February 20071,078 × 1,081 (40 KB)Oleg Alexandrov (talk | contribs)Made by myself with matlab.

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