Rat's Nest 1/ratsnest1.iso/prgmming/c/siegel.cpp

C/C++ Source or Header | 1996-02-19 | 5.3 KB | 152 lines

//

//+----------------------------------------------------------------------+

//+ Program SIEGEL.CPP                                                   +

//+ By Fausto A. A. Barbuto, [e-mail]               +

//+ Rio de Janeiro, BRAZIL, on May 13, 1994.                             +

//+                                                                      +

//+ Plots a Julia set of the type z -> z^2 + lambda*z, where lambda =    +

//+ exp(2*Pi*GM*i) and GM = (5^(1/2) - 1)/2 (Golden Mean). Siegel disks  +

//+ (are they in fact Siegel disks? I'm not sure) are shown in the inner +

//+ part of the plot.                                                    +

//+                                                                      +

//+ Case with z -> z^2 + 1.001*z*exp(2*Pi*i/20) added Sunday, May 15.    +

//+ (see Fig. 30, pg. 40)                                                +

//+                                                                      +

//+                                                                      +

//+ REFERENCE: Peitgen, H.-O. & Richter, P.H.: "The Beauty of Fractals", +

//+            Springer-Verlag, 1986, pg. 30-31, pg. 77 (Map 25).        +

//+                                                                      +

//+ Needs SVGA256.BGI and SVGA256.H (from SVGABG50 package by Jordan     +

//+ Hargrave).                                                           +

//+                                                                      +

//+ Authorized version for spanky.triumf.ca site (Vancouver, BC, CANADA).+

//+----------------------------------------------------------------------+

//

#include <stdio.h>

#include <conio.h>

#include <graphics.h>

#include <math.h>

#include <stdlib.h>

#include <complex.h>

#include "Svga256.h"



//void far initgraph(int far *,int far *,char far *);



int Vid;  //* Global variable *//



int huge DetectSVGA256()

{

  printf("\n  Which video mode would you like to use? \n\n");

  printf("  0 - 320x200x256\n");

  printf("  1 - 640x400x256\n");

  printf("  2 - 640x480x256\n");

  printf("  3 - 800x600x256\n");

  printf("  4 - 1024x768x256\n\n  ==> ");

  scanf("%d",&Vid);

  return Vid;

}



void main(void)

{

      complex lambda, i;

      double xmin, xmax, ymin, ymax, r, R1, I1, RL, IL;

      double x,y, x0,y0, GM, deltax,deltay, s1, s2, Pi=3.1415926535897932;

      register int npix, npiy, kcolor=1024, k, np, nq, ipen;

      int graphdriver=DETECT, graphmode, icase;



      clrscr();

      printf("\n  Program SIEGEL.CPP \n");

      printf("\n\n  By Fausto A. A. Barbuto, May 14, 1994");

      printf("\n  Rio de Janeiro, Federal Republic of Brazil");

      printf("\n  E-mail: [e-mail]\n\n");

      printf("\n  Reference: Peitgen, H.-O., and Richter, P.H. :");

      printf("\n  'The Beauty of Fractals', Springer-Verlag, 1986");

      printf("\n  Section 2, pp. 27-32\n\n");

      printf("\n  Enter the case:\n");

      printf("\n  (1) z -> z*z +   lambda*z  [lambda=exp(2*Pi*i*GM)]\n");

      printf("                   [GM = Golden Mean = (5^(1/2) - 1.0)/2]\n");

      printf("\n  (2) z -> z*z + s*lambda*z (lambda=exp(2*Pi*i/20), s=1.001");

      printf("\n\n > ");

      scanf("%d",&icase);

      if ((icase < 1) || (icase > 2)) icase = 1;

      clrscr();



      installuserdriver("Svga256",DetectSVGA256);

      initgraph(&graphdriver, &graphmode, "C:\\Borlandc\\Bgi");



      if (Vid == 0) {npix = 320; npiy = 200;}

      if (Vid == 1) {npix = 640; npiy = 400;}

      if (Vid == 2) {npix = 640; npiy = 480;}

      if (Vid == 3) {npix = 800; npiy = 600;}

      if (Vid == 4) {npix =1024; npiy = 768;}

      if((Vid<0) || (Vid)>4) Vid = 2;



      GM = 0.5*(sqrt(5.0) - 1.0);  //* The Golden Mean *//

      i = complex(0.0,1.0);



      if (icase == 1) {

    lambda = exp(2.0*Pi*GM*i);

    xmin = -1.05; xmax = 1.75;

    ymin = -0.75; ymax = 1.45;

      }

      else {

    lambda = 1.001*exp(0.1*Pi*i);

    xmin = -1.75; xmax = 0.75;

    ymin = -1.40; ymax = 1.15;

      }

      RL = real(lambda);

      IL = imag(lambda);

      deltax = (xmax-xmin)/(npix-1);

      deltay = (ymax-ymin)/(npiy-1);



      cleardevice();

      for (np=0; np<=npix-1; np++) {

    x0 = xmin + (double)np*deltax;

    for (nq=0; nq<=npiy-1; nq++) {

    y0 = ymin + (double)nq*deltay;

    x = x0;

    y = y0;

    k  = 0;



     do {

       s1 = (x+RL);

       s2 = (y+IL);

       R1 = x*s1 - y*s2;

       I1 = x*s2 + y*s1;

       r = sqrt(R1*R1 + I1*I1);

       k++;

//*

//*        If r >= kcolor the point escapes towards infinity.

//*

       if (r >= kcolor) {

         ipen = 29 + k;

         putpixel(np,nq,ipen);

       }

//*

//*        Converging points.

//*

       if (k == kcolor) {

//*

//*          The colour shades of the "Siegel disks" (?) are defined here.

//*          (as function of the  distance between the present point [x,y]

//*          and the "invariant" point [x=0,y=0])

//*

         ipen = 17 + (int)(25.0*sqrt(x*x+y*y));

         putpixel(np,nq,ipen);

       }

//*

//*        Returns if no convergence's achieved on either escape or atraction.

//*

       x = R1;

       y = I1;

     } while (r<=kcolor && k<=kcolor);

       }

       if(kbhit()) break;

     }

//*

//*  Clean-up.

//*

     getch();

     closegraph();

}