C code for generating mandelbrot set.

mandelbrot.c

#include <stdio.h>
#include <math.h>

#define PPM_FILE_NAME "mandelbrot.ppm"
#define COMMENT "# This is an image on mandelbrot set"
#define IMAGE_WIDTH 800
#define IMAGE_HEIGHT 800
#define MAX_COLOR_VALUE 255

#define CX_MIN (-2.5 - 0.5) / 1.9
#define CX_MAX (1.5 - 0.5) / 1.9
#define CY_MIN -2.0 / 1.9
#define CY_MAX 2.0 / 1.9

#define PIXEL_WIDTH (CX_MAX - CX_MIN) / IMAGE_WIDTH
#define PIXEL_HEIGHT (CY_MAX - CY_MIN) / IMAGE_HEIGHT

#define ITERATION_TIMES 200
#define ESCAPE_CIRCLE 2 * 2

FILE *file;
static unsigned char pixel[3];

void init_ppm_image() {
        file = fopen(PPM_FILE_NAME, "wb" /* Binary Mode */);
        // Write file headers.
        fprintf(file,
                        "P6\n"
                        " %s\n" /* Comments */
                        " %d\n %d\n" /* File Size */
                        " %d\n" /* 0-255 */,
                        COMMENT, IMAGE_WIDTH, IMAGE_HEIGHT, MAX_COLOR_VALUE);
}

int main() {
        init_ppm_image();

        // Z = Zx + i * Zy
        double Zx, Zy;
        double Cx, Cy;

        // Iterate over every pixel.
        for (int y = 0; y < IMAGE_HEIGHT; ++ y) {
                Cy = CY_MIN + y * PIXEL_HEIGHT;

                if (fabs(Cy) < PIXEL_HEIGHT / 2) {
                        Cy = 0.0;
                }

                for (int x = 0; x < IMAGE_WIDTH; ++ x) {
                        Cx = CX_MIN + x * PIXEL_WIDTH;

                        Zx = 0.0;
                        Zy = 0.0;

                        int iter;

                        for (iter = 0; iter < ITERATION_TIMES &&
                                        Zx * Zx + Zy * Zy < ESCAPE_CIRCLE; ++ iter) {
                                double Zxx = Zx;
                                double Zyy = Zy;
                                // Z(n) = Z(n - 1) ^ 2 + C
                                // Z_x(n) = Z_x(n - 1) ^ 2 - Z_y(n - 1) ^ 2 + C_x
                                Zx = Zxx * Zxx - Zyy * Zyy + Cx;
                                // Z_y(n) = 2 * Z_x(n - 1) * Z_y(n - 1) + C_y
                                Zy = 2 * Zxx * Zyy + Cy;
                        }

                        if (iter == ITERATION_TIMES) {
                                pixel[0] = 0;
                                pixel[1] = 0;
                                pixel[2] = 0;
                        } else {
                                pixel[0] = 255;
                                pixel[1] = 255;
                                pixel[2] = 255;
                        }

                        fwrite(pixel, 1, 3, file);
                }
        }
        fclose(file);
}