/* Logistic Difference Equation and Bifurcation * * This program draws an inverted parabola for the function * y = k*x*(1-x) * where the initial k and x are determined by mouse input * and the range for k is between 0 and 4 and x ranges from 0 * to 1. The program then plots 500 iterations of the * function as each new x value is determioned from the * previous y. This is demonstrated by reflecting thhrough * the equation of the line, y = x. */ #include #include #include #include #define initial_width 600 #define initial_height 600 #define max_colors 10 int main_window, sub_window1; // The following code permits drawing text on the screen // Bitmap character fonts must be pre-defined float colarry[max_colors][3] = {{1.0, 0.0, 0.0}, {0.0, 0.8, 0.0}, {0.0, 0.0, 0.8}, {0.8, 0.0, 0.8}, {0.9, 0.9, 0.0}, {0.0, 0.8, 0.8}, {1.0, 0.5, 0.5}, {0.3, 1.0, 0.3}, {0.5, 0.5, 1.0}, {0.0, 0.0, 0.0} }; // Routine to plot text void bitmap_output(int x, int y, int z, char *string, void *font) { int len, i; glRasterPos3f(x, y, 0); len = (int) strlen(string); for (i = 0; i < len; i++) { glutBitmapCharacter(font, string[i]); } } // Routine to plot parabola for equation F(x)=k*x*(1-x) void plot_parabola(float k) {float x, y, step; int i; glBegin(GL_LINE_STRIP); for (i=0; i<600; i++) {x= i*(1.0/600); y= k*x - k*x*x; //if (i%20 == 0) {printf ("%d %f %f \n", i, x, y); } glVertex3f(x, y, 0.0); } glEnd(); glFlush(); } // Plot diagonal line, y=x, used in iteration process void plot_line(void) { glBegin(GL_LINE_STRIP); glColor3f(0.8, 0.8, 0.8); glVertex3f(0.0,0.0,0.0); glVertex3f(1.0, 1.0, 0.0); glEnd(); glFlush(); } // The Help routine tells people how to use the module void myhelp(void) { char s[80]; glColor3f(0.0,0.0,0.6); glPushMatrix(); glTranslatef(0.05, 0.95, 0); sprintf(s,"Logistic Difference Equation: F(x)=kx(1-x)"); bitmap_output(0,0,0, s, GLUT_BITMAP_TIMES_ROMAN_24); glPopMatrix(); sprintf(s,"1. Right mouse button and cursor position selects values"); glPushMatrix(); glTranslatef(0.05, 0.85, 0); bitmap_output(0,0,0, s, GLUT_BITMAP_TIMES_ROMAN_24); glPopMatrix(); sprintf(s," Vertical Component: k between 0 and 4"); glPushMatrix(); glTranslatef(0.05, 0.80, 0); bitmap_output(0,0,0, s, GLUT_BITMAP_TIMES_ROMAN_24); glPopMatrix(); sprintf(s," Horozontal Component: x between 0 and 1"); glPushMatrix(); glTranslatef(0.05, 0.75, 0); bitmap_output(0,0,0, s, GLUT_BITMAP_TIMES_ROMAN_24); glPopMatrix(); sprintf(s,"2. Left mouse button draws 500 iterations"); glPushMatrix(); glTranslatef(0.05, 0.65, 0); bitmap_output(0,0,0, s, GLUT_BITMAP_TIMES_ROMAN_24); glPopMatrix(); sprintf(s,"3. Middle mouse button repeats this message"); glPushMatrix(); glTranslatef(0.05, 0.55, 0); bitmap_output(0,0,0, s, GLUT_BITMAP_TIMES_ROMAN_24); glPopMatrix(); } // This routine controls interactive features. void mouse1(int button, int state, int x, int y) { float y0,xn,yn,xtemp; static float k , x0; static char s1[25], s2[25], s3[25], s4[25]; int i; static int num = 0; // Selecting Button Zero will plot 500 iterations of the logistic // difference equation for the parameters chosen. if ( button== 0 && state == GLUT_DOWN) { glClearColor(1.0, 1.0, 0.7, 1.0); glClear(GL_COLOR_BUFFER_BIT); sprintf (s4," X0 = %f \0",x0); sprintf (s2," K = %f \0",k); glPushMatrix(); glColor3f(1.0,1.0,0.7); glTranslatef(0.05, 0.95, 0); bitmap_output(0,0,0, s1, GLUT_BITMAP_TIMES_ROMAN_24); glColor3f(0.0,0.0,0.6); bitmap_output(0,0,0, s2, GLUT_BITMAP_TIMES_ROMAN_24); for(i=0; i<25; i++) {s1[i] = s2[i]; } glPopMatrix(); glPushMatrix(); glColor3f(1.0,1.0,0.7); glTranslatef(0.65, 0.95, 0); bitmap_output(0,0,0, s3, GLUT_BITMAP_TIMES_ROMAN_24); glColor3f(0.0,0.0,0.6); bitmap_output(0,0,0, s4, GLUT_BITMAP_TIMES_ROMAN_24); for(i=0; i<25; i++) {s3[i] = s4[i]; } glPopMatrix(); plot_line(); glColor3f(1.0, 0.0, 0.0); plot_parabola(k); xn= x0; glBegin(GL_LINE_STRIP); glVertex3f(x0, 0.0, 0.0); for (i = 0; i < 500; i++) { glColor3f( colarry[num][0], colarry[num][1], colarry[num][2]); num++; if (num>= max_colors) num=0; yn=k*xn - k*xn*xn; glVertex3f(xn,yn,0.0); glVertex3f(yn, yn, 0.0); //printf("%f %f \n", xn, yn); xn = yn; } glEnd(); glFlush(); } // Button 2 shows the values for K and X as well as the shape of // the parabola. if ( (button== 2 )&& state == GLUT_DOWN) {glColor3f(1.0, 1.0, 0.7); glClearColor(1.0, 1.0, 0.7, 1.0); glClear(GL_COLOR_BUFFER_BIT); plot_parabola(k); k = 4- y/(600.0/4); x0 = x/600.0; sprintf (s4," X0 = %f \0",x0); sprintf (s2," K = %f \0",k); glPushMatrix(); glColor3f(1.0,1.0,0.7); glTranslatef(0.05, 0.95, 0); bitmap_output(0,0,0, s1, GLUT_BITMAP_TIMES_ROMAN_24); glColor3f(0.0,0.0,0.6); bitmap_output(0,0,0, s2, GLUT_BITMAP_TIMES_ROMAN_24); for(i=0; i<25; i++) {s1[i] = s2[i]; } glPopMatrix(); glPushMatrix(); glColor3f(1.0,1.0,0.7); glTranslatef(0.65, 0.95, 0); bitmap_output(0,0,0, s3, GLUT_BITMAP_TIMES_ROMAN_24); glColor3f(0.0,0.0,0.6); bitmap_output(0,0,0, s4, GLUT_BITMAP_TIMES_ROMAN_24); for(i=0; i<25; i++) {s3[i] = s4[i]; } glPopMatrix(); glColor3f(1.0, 0.0, 0.0); glColor3f(1.0, 0.0, 0.0); plot_parabola(k); glFlush(); } // Button 1 will clear the screen if ( button== 1 && state == GLUT_DOWN) {glClearColor(1.0, 1.0, 0.7, 1.0); glClear(GL_COLOR_BUFFER_BIT); myhelp(); } } // Main display window void display(void) { glClearColor(1.0, 1.0, 0.7, 1.0); glClear(GL_COLOR_BUFFER_BIT); myhelp(); glFlush(); } // void reshape(int w, int h) { int width = initial_width; int height = initial_height; glViewport(0, 0, w, h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); glOrtho( 0.0, 1.0, 0.0, 1.0, -1.0, 1.0 ); // The default is 1.0 glMatrixMode(GL_MODELVIEW); } int main(int argc, char **argv) { float r,g,b = 0.0; glutInit(&argc, argv); glutInitDisplayMode(GLUT_RGB); glutInitWindowSize(initial_width, initial_height); main_window = glutCreateWindow("My First Window "); glutDisplayFunc(display); glutReshapeFunc(reshape); glutMouseFunc(mouse1); glutMainLoop(); return 0; /* ANSI C requires main to return int. */ }