OpenGL Tutorial 009: Exploring the Mandelbrot Set
// GLFW
#include <GLFW/glfw3.h>
// the usual gang of C++ headers
#include <iostream>
#include <complex>
#include <cmath>
#include <cstdlib>
// this function checks if a point (x,y) is a member of the Mandelbrot set
// it returns the number of iterations it takes for this point to escape from the set
// if (x,y) is inside the set, it will not escape even after the maximum number of iterations
// and this function will take a long time to compute this and return the maximum iterations
int Mandelbrot_Member(double x, double y, const int MAX_ITER)
{
typedef std::complex dcmplx; // define a new data type, the double-precision complex number
dcmplx c(x,y);
dcmplx z(0.0,0.0);
int iter = 0;
while(iter 2.0) break; // (x,y) is outside the set, quick exit from this loop
}
return iter;
}
// calculate pixel colors for the current graphics window, defined by the
// minimum and maximum X and Y coordinates
void showMandelbrot(int WIDTH, int HEIGHT, double xmin, double xmax, double ymin, double ymax)
{
//--------------------------------
// OpenGL initialization stuff
//--------------------------------
// select background color to be white
// R = 1, G = 1, B = 1, alpha = 0
glClearColor (1.0, 1.0, 1.0, 0.0);
// initialize viewing values
glMatrixMode(GL_PROJECTION);
// replace current matrix with the identity matrix
glLoadIdentity();
// set clipping planes in the X-Y-Z coordinate system
glOrtho(xmin,xmax,ymin,ymax, -1.0, 1.0);
// clear all pixels
glClear (GL_COLOR_BUFFER_BIT);
// problem parameters
const int MAX_ITER = 200;
// 2D array size is identical to the window size in pixels
const int NX = WIDTH;
const int NY = HEIGHT;
int *iters = new int[WIDTH*HEIGHT];
double dx = (xmax - xmin)/NX; // grid spacing along X
double dy = (ymax - ymin)/NY; // grid spacing along Y
// fill the 2D array with the "iter" parameter, which
// represents the number of iterations it takes for the
// point to escape from the set
for(int i = 0; i < NX; i++) {
for(int j = 0; j < NY; j++) {
double x = xmin + i*dx; // actual x coordinate
double y = ymin + j*dy; // actual y coordinate
// calculate iterations to escape
iters[i*WIDTH + j] = Mandelbrot_Member(x,y,MAX_ITER);
}
}
// assign color based on the number of iterations - Red Green Blue (RGB)
for(int i = 0; i < NX; i++) {
for(int j = 0; j < NY; j++) {
double x = xmin + i*dx; // actual x coordinate
double y = ymin + j*dy; // actual y coordinate
int VAL = iters[i*WIDTH + j];
if(VAL==MAX_ITER)
{
glColor3f(0,0,0); // black
}
else
{
// ratio of iterations required to escape
// the higher this value, the closer the point is to the set
float frac = (float) VAL / MAX_ITER;
if(frac<=0.5)
{
// yellow to blue transition
glColor3f(2*frac,2*frac,1-2*frac);
}
else
{
// red to yellow transition
glColor3f(1,2-2*frac,0);
}
}
glRectf (x, y,x+dx,y+dy);
}
}
// draw the horizontal and vertical centerlines for the window
glColor3f(1,1,1);
glRectf(xmin+(xmax-xmin)/2-1.95*dx,ymin,xmin+(xmax-xmin)/2+1.95*dx,ymax);
glRectf(xmin,ymin+(ymax-ymin)/2-1.95*dy,xmax,ymin+(ymax-ymin)/2+1.95*dy);
}
int main(int argc, char* argv[])
{
//--------------------------------
// Create a WINDOW using GLFW
//--------------------------------
GLFWwindow *window;
// initialize the library
if(!glfwInit())
return -1;
// window size for displaying graphics
int WIDTH = 800;
int HEIGHT = 800;
// set the window's display mode
window = glfwCreateWindow(WIDTH, HEIGHT, "Mandelbrot Set", NULL, NULL);
if(!window)
{
glfwTerminate();
return -1;
}
// make the windows context current
glfwMakeContextCurrent(window);
//---------------------------------------
// Loop until the user closes the window
//---------------------------------------
// user selection of appropriate quadrant for zooming in
int choice;
std::cout << " +------+------+ " << std::endl;
std::cout << " | | | " << std::endl;
std::cout << " | 1 | 2 | " << std::endl;
std::cout << " | | | " << std::endl;
std::cout << " +------+------+ " << std::endl;
std::cout << " | | | " << std::endl;
std::cout << " | 3 | 4 | " << std::endl;
std::cout << " | | | " << std::endl;
std::cout << " +------+------+ " << std::endl;
// specify initial window size in the X-Y plane
double xmin = -2, xmax = 1, ymin = -1.5, ymax = 1.5;
while(!glfwWindowShouldClose(window))
{
// display the Mandelbrot set in (xmin,ymin)-(xmax,ymax)
showMandelbrot(WIDTH, HEIGHT, xmin, xmax, ymin, ymax);
// swap front and back buffers
glfwSwapBuffers(window);
// poll for and processs events
glfwPollEvents();
// ask user for selecting a region for further zoom-in
std::cout << "Zoom in to <1, 2, 3, 4> [0 to quit]:";
std::cin >> choice;
// update display limits based on user choice
switch (choice) {
case 0:
glfwSetWindowShouldClose(window, GL_TRUE);
break;
case 1:
xmax = xmin + (xmax - xmin)/2;
ymin = ymin + (ymax - ymin)/2;
break;
case 2:
xmin = xmin + (xmax - xmin)/2;
ymin = ymin + (ymax - ymin)/2;
break;
case 3:
xmax = xmin + (xmax - xmin)/2;
ymax = ymin + (ymax - ymin)/2;
break;
case 4:
xmin = xmin + (xmax - xmin)/2;
ymax = ymin + (ymax - ymin)/2;
break;
}
}
glfwDestroyWindow(window);
glfwTerminate();
return 0;
}
To compile this code, use the following Makefile:
all:
g++ -I /usr/local/include/ -L /usr/local/lib -o cpu.x -framework OpenGL -framework Cocoa -framework IOKit -framework CoreVideo CPU_Mandelbrot.cpp -lglfw
clean:
rm *.x
