Generates Bifurcation Map of x = rx(1 - x)

Right-click the underlined blue exe file links below to save a PC executable version of the relevant program to your local disk.

Note: to scale the display for r to run between 0 and 1, the formula x = 4rx(1 - x) is used in the program.

//bifmap1.c Compiled to bifmap1.exe.
#include <stdio.h>
#include <conio.h>
#include <graph.h>
#define XBIAS  120
#define YBIAS  440
int e = 0;

void scan(float L1, float L2, int L3) {
  int i;
  float l, x;
  for(l = L1; l < L2 && e == 0; l += .001) {
    _settextposition(29, 45); printf("%f",l);
    for(x = .4, i = 0; i < 50; i++) {
      if( kbhit()) {e = 1; break;}
      x = 4 * l * x * (1 - x);
    }
    _settextposition(15, 7); printf("%f",x);
    for(i = 0; i < L3; i++) {
      if( kbhit() ) {e = 1; break;}
      x = 4 * l * x * (1 - x);
      _setpixel(XBIAS + (int)(l * 400), YBIAS - (int)(x * 400));
    }
  }
}

main() {
  int c;
  _setvideomode(_VRES16COLOR);
  _settextposition(1, 26);
  printf("THE BIFURCATION MAP");
  _settextposition(15, 3); printf("X = ");
  _setcolor(7);
  _moveto(XBIAS, YBIAS - 400);
  _lineto(XBIAS, YBIAS);
  _lineto(XBIAS + 400, YBIAS);
  _settextposition(29, 36); printf("LAMBDA = ");
  _setcolor(15);
  scan(0.001, 0.75, 20);
  scan(0.751, 0.85, 600);
  scan(0.851, 1.00, 3000);
  if(e == 0) {_settextposition(29, 36); printf("Finished\07");}
  c = getchar();
  _setvideomode(_DEFAULTMODE);
}

Generates Bifurcation Map of x = x² + c

//bifmap2.c compiled to bifmap2.exe.
#include <stdio.h>
#include <conio.h>
#include <graph.h>
#define XBIAS  370
#define YBIAS  240
int e = 0;
float x, y, cx, cy;

int ComplexIterate() {
  x = x * x + cx;
  if (x > 15 || x < -25) return(1);
  return(0);
}

void scan(void) {
  int i, I = 100;
  for (cx = 1.5, cy = 0; cx > -2.5 && e == 0; cx -= .01) {
    _settextposition(21, 54); printf("%f",cx);
    for (x = 0, y = 0, i = 0; i < 50; i++) {
      if(kbhit()) {e = 1; break;}
      if(ComplexIterate()) break;
    }
    if(cx < -1.25) I = 1000;
    for(i = 0; i < I; i++) {
      if(kbhit()) {e = 1; break;}
      if(ComplexIterate()) break;
      _setpixel(
        XBIAS + (int)(cx * 100),
        YBIAS - (int)(x * 100)
      );
    }
  }
}

yscale(int a) {     //a = -260 or +160
  int y;
  _moveto (XBIAS + a, YBIAS - 200);
  _lineto (XBIAS + a, YBIAS + 200);
  for(y = -200; y < 201; y += 50) {
    _moveto (XBIAS + a - 5, YBIAS + y);
    _lineto (XBIAS + a + 5, YBIAS + y);
  }
}

xscale(int b) {     //b = -210 or +210
  int x;
  _moveto (XBIAS - 250, YBIAS + b);
  _lineto (XBIAS + 150, YBIAS + b);
  for(x = -250; x < 151; x += 50) {
    _moveto (XBIAS + x, YBIAS + b - 5);
    _lineto (XBIAS + x, YBIAS + b + 5);
  }
}

main() {
  int c;
  _setvideomode(_VRES16COLOR);  //640 by 480 16-colour
  _setcolor(7);
  _settextposition(1, 16);
  printf("THE BIFURCATION MAP FOR X = X * X + C.");
  _moveto(XBIAS, YBIAS - 200);
  _lineto(XBIAS, YBIAS + 200);
  _moveto(XBIAS + 150, YBIAS);
  _lineto(XBIAS - 250, YBIAS);
  yscale( -260 ); yscale( 160 );
  xscale( -210 ); xscale( 210 );
  _settextposition(21, 50); printf("C = ");
  _setcolor(15);
  scan();
  if(e == 0) {_settextposition(23, 50); printf("Finished\07");}
  c = getchar();
  _setvideomode(_DEFAULTMODE);
}





/* I, Robert J Morton, author of this program, am a poor 
   but right honourable fellow of the Ancient and Noble 
   Order of the Long-Term Unemployed.

   Please send any gratefully accepted offers of 
   programming work to robmorton@clara.net. */