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output gif image of Madelbrot Set
#include <stdio.h>
#include <math.h>
const int times = 10;
const double x_max = 0.6;
const double x_min =-1.6 ;
const double y_max = 1.00;
const double y_min = -0.35;
const double dx = 0.002;
const double dy = 0.002;
/* If mandelbrot() function returns non-zero, that inidicates divergence. */
int mandelbrot(double c_x, double c_y, int n)
{
double x_n = 0;
double y_n = 0;
double x_n_1;
double y_n_1;
int i;
for(i = 0; i < n; i++) {
x_n_1 = pow(x_n, 2) - pow(y_n, 2) + c_x;
y_n_1 = 2 * x_n * y_n + c_y;
if ( pow(x_n_1, 2) + pow(y_n_1, 2) > 4.0 ){
return i;
} else {
x_n = x_n_1;
y_n = y_n_1;
}
}
return -1;
}
/* FOR CONSOLE */
/*
int main(void)
{
double x;
double y;
int x_length = (x_max - x_min) / dx;
for(y = y_max; y > y_min; y -= dy) {
for(x = x_min; x < x_max; x += dx) {
putchar(mandelbrot(x, y, 300) == 0 ? '*' : ' ');
}
putchar('\n');
}
return 0;
}
*/
#include "gd.h"
double x_imagepos2gaussianpos(int pos, int pixel_number, double min, double max)
{
return min + (max-min) * pos / pixel_number;
}
double y_imagepos2gaussianpos(int pos, int pixel_number, double min, double max)
{
return max - (max-min) * pos / pixel_number;
}
int x_pos2pixelnum(double pos, double min, double max, int pixel_number)
{
int n = -1;
if (min < pos && pos < max) {
n = (int)( (pos - min) / (max - min) * pixel_number);
}
return n;
}
int y_pos2pixelnum(double pos, double min, double max, int pixel_number)
{
int n = x_pos2pixelnum(pos, min, max, pixel_number);
if (n != -1) {
return pixel_number - n;
} else {
return n;
}
}
int main(void)
{
FILE *out;
int x, y;
int x_width = 1600;
int y_width = 900;
gdImagePtr im = gdImageCreate(x_width, y_width);
int black = gdImageColorAllocate(im, 0, 0, 0);
int axis_color = gdImageColorAllocate(im, 255, 255, 255);
int aqua = gdImageColorAllocate(im, 175, 223, 228);
int blue = gdImageColorAllocate(im, 0x00, 0x00, 0xff);
int turquoise = gdImageColorAllocate(im, 0x40, 0xe0, 0xd0);
int DodgerBlue = gdImageColorAllocate(im, 0x1e, 0x90, 0xff);
int DeepSkyBlue= gdImageColorAllocate(im, 0x00, 0xbf, 0xff);
int LightSkyBlue= gdImageColorAllocate(im, 0x87, 0xce, 0xfa);
int SkyBlue = gdImageColorAllocate(im, 0x87, 0xce, 0xeb);
int x0_pixel;
int y0_pixel;
for(x = 0; x < x_width; x++) {
double cur_x = x_imagepos2gaussianpos(x, x_width, x_min, x_max);
for(y = 0; y < y_width; y++) {
double cur_y = y_imagepos2gaussianpos(y, y_width, y_min, y_max);
int n;
printf("%d, %d, -> %f, %f\n", x, y, cur_x, cur_y);
n = mandelbrot(cur_x, cur_y, 300);
if (n == -1) {
/* Mandelbrot Set */
gdImageSetPixel(im, x, y, blue);
} else if (n < 8) {
/* fastest divergence */
gdImageSetPixel(im, x, y, black);
} else if (n < 10) {
gdImageSetPixel(im, x, y, SkyBlue);
} else if (n < 20) {
gdImageSetPixel(im, x, y, LightSkyBlue);
} else if (n < 30) {
gdImageSetPixel(im, x, y, DeepSkyBlue);
} else {
/* slowest divergence */
gdImageSetPixel(im, x, y, DodgerBlue);
}
}
}
/* draw axis */
x0_pixel = x_pos2pixelnum(0, x_min, x_max, x_width);
y0_pixel = y_pos2pixelnum(0, y_min, y_max, y_width);
/* y_axis */
if (x0_pixel != -1) {
int scale_len = 20;
int half_scale_len = scale_len / 2;
int y_05_pixel = y_pos2pixelnum(0.5, y_min, y_max, y_width);
int y_minus05_pixel = y_pos2pixelnum(-0.5, y_min, y_max, y_width);
gdImageLine(im, x0_pixel, 0, x0_pixel, y_width - 1, axis_color);
/* insert y-scale */
/* y = 0.5 */
gdImageLine(im, x0_pixel - half_scale_len, y_05_pixel, x0_pixel + half_scale_len, y_05_pixel, axis_color);
/* y = -0.5 */
/*
gdImageLine(im, x0_pixel - half_scale_len, y_minus05_pixel, x0_pixel + half_scale_len, y_minus05_pixel, axis_color);
*/
}
/* x_axis */
if (y0_pixel != -1) {
int scale_len = 20;
int half_scale_len = scale_len / 2;
int x_minus1_pixel = x_pos2pixelnum(-1, x_min, x_max, x_width);
int x_minus05_pixel = x_pos2pixelnum(-0.5, x_min, x_max, x_width);
int x_minus15_pixel = x_pos2pixelnum(-1.5, x_min, x_max, x_width);
int x_05_pixel = x_pos2pixelnum(0.5, x_min, x_max, x_width);
gdImageLine(im, 0, y0_pixel, x_width - 1, y0_pixel, axis_color);
/* insert x-scale */
/* x = -1 */
gdImageLine(im, x_minus1_pixel, y0_pixel - half_scale_len, x_minus1_pixel, y0_pixel + half_scale_len, axis_color);
/* x = -0.5 */
gdImageLine(im, x_minus05_pixel, y0_pixel - half_scale_len, x_minus05_pixel, y0_pixel + half_scale_len, axis_color);
/* x = -1.5 */
gdImageLine(im, x_minus15_pixel, y0_pixel - half_scale_len, x_minus15_pixel, y0_pixel + half_scale_len, axis_color);
/* x = 0.5 */
gdImageLine(im, x_05_pixel, y0_pixel - half_scale_len, x_05_pixel, y0_pixel + half_scale_len, axis_color);
}
out = fopen("new_mandelbrot.gif", "w");
gdImageGif(im, out);
return 0;
}
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