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gg.c
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gg.c
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#include <complex.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <omp.h> //OpenM
/*
fork of
mandelbrot-book how to write a book about the Mandelbrot set by Claude Heiland-Alle
https://code.mathr.co.uk/mandelbrot-book/blob/HEAD:/book/
generating an improved grid ( in the exterior) and removed noise near boundary
In the book it is : 1.32 Removing distracting colour.
The bold colours are now a distraction: they don’t show us anything we can’t see from the grid
or the distance estimation. Desaturating the image and making the exterior grid a light grey
gives us a clean style that is easy on the eyes.
gcc gg.c -lm -Wall -fopenmp
./a.out > gg.ppm
*/
static double TwoPi=2.0*M_PI;
double c_arg(complex double z)
{
double arg;
arg = carg(z);
if (arg<0.0) arg+= TwoPi ;
return arg;
}
double c_turn(complex double z)
{
double arg;
arg = c_arg(z);
return arg/TwoPi;
}
const double pi = 3.141592653589793;
//
double cnorm(double _Complex z) // https://stackoverflow.com/questions/6363247/what-is-a-complex-data-type-and-an-imaginary-data-type-in-c
{
return creal(z) * creal(z) + cimag(z) * cimag(z);
}
void hsv2rgb(double h, double s, double v, int *red, int *grn, int *blu) {
double i, f, p, q, t, r, g, b;
int ii;
if (s == 0.0) { r = g = b = v; } else {
h = 6 * (h - floor(h));
ii = i = floor(h);
f = h - i;
p = v * (1 - s);
q = v * (1 - (s * f));
t = v * (1 - (s * (1 - f)));
switch(ii) {
case 0: r = v; g = t; b = p; break;
case 1: r = q; g = v; b = p; break;
case 2: r = p; g = v; b = t; break;
case 3: r = p; g = q; b = v; break;
case 4: r = t; g = p; b = v; break;
default:r = v; g = p; b = q; break;
}
}
*red = fmin(fmax(255 * r + 0.5, 0), 255);
*grn = fmin(fmax(255 * g + 0.5, 0), 255);
*blu = fmin(fmax(255 * b + 0.5, 0), 255);
}
int main()
{
int aa = 4; //
int w = 800 * aa;
int h = 800 * aa;
int nMax = 1024;
double r = 2;// radius of the plane
//double px = r / (h/2); // pixel size
double pixel_spacing = r / ( h/2.0); // = radius / ( height / 2.0 ) ;
double er = 512; // R
double er2 = er * er; // escape_radius *escape_radius = R*R = R2
unsigned char *img = malloc(3 * w * h);
#pragma omp parallel for schedule(static, 1)
for (int j = 0; j < h; ++j)
{
double y = (h/2 - (j + 0.5)) / (h/2) * r;
for (int i = 0; i < w; ++i)
{
double x = (i + 0.5 - w/2) / (h/2) * r;
double _Complex c = x + I * y;
double _Complex z = 0;
double _Complex dc = 0; // derivative with the respect to c
// iteration
int n;
for (n = 0; n < nMax; ++n)
{
dc = 2 * z * dc + 1;
z = z * z + c;
if (cnorm(z) > er2) // abs(z)>er
break;
}
// colour
double hue = 0, sat = 0, val = 1.0; // interior
if (n < nMax) // exterior
{
double de = 2.0 * cabs(z) * log( cabs(z) ) / ( cabs( dc ) * pixel_spacing ) ; // distance estimation
double final_z_abs = log(cabs(z)) / log(er) - 1.0; // not only cabs(z)
int final_n = n; //
double final_z_arg = fmod( carg(z)/TwoPi + 1.0, 1.0);
double continuous_escape_time = final_n - log2(final_z_abs + 1.0);
// improved grid
double k = pow ( 0.5 , 0.5 - final_z_abs ) ;
double grid_weight = 0.05 ;
int grid =
grid_weight < final_z_abs &&
final_z_abs < 1.0 - grid_weight &&
grid_weight * k < final_z_arg &&
final_z_arg < 1.0 - grid_weight * k;
//
hue = continuous_escape_time/64.0;
sat = 0.0; // grid * 0.7;
/* The de here in your code is scaled by pixel spacing, so should be less than around 1 for pixels near the boundary. */
val = fmin(tanh ( fmin ( fmax ( de , 0.0 ) , 4.0 ) ), 0.8 + 0.2 * grid) ;
}
// hsv to rgb conversion
int red, grn, blu;
hsv2rgb(hue, sat, val, &red, &grn, &blu);
//
int k = 3*(j * w + i);
img[k+0] = red;
img[k+1] = grn;
img[k+2] = blu;
}
}
printf("P6\n%d %d\n255\n", w, h); // ppm
fwrite(img, 3 * w * h, 1, stdout);
free(img);
return 0;
}