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s.c
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s.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/
HSV
* Hue is circular, from red at 0, with increasing values running through the rainbow yellow
green blue violet, and then back through purple and pink to red again at 1, where the cycle repeats.
* Saturation blends colour intensity from greyscale at 0 to full blast at 1,
* value controls brightness: black at 0 and full strength at 1
We use single precision float for the calculations: 24bits is more than enough, given each colour channel has only 8bits.
We need to scale the output values from hsv2rgb() from [0..1] to [0..255], and we clamp them to the output
range to make sure no overflow glitches occur.
colour function uses both sources of information now:
* hue coming from the fractional escape time
float hue = ( f i n a l _ n − l o g 2 f ( f i n a l _ z _ a b s + 1 . 0 f ) ) / 6 4 . 0 f ;
float sat = 0.7 f ;
float val = 1.0 f ;
i f ( f i n a l _ n == 0 ) {
sat = 0.0 f ;
val = 0.0 f ;
}
gcc s.c -lm -Wall -fopenmp
./a.out > s.pgm
*/
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 er = 512;
double er2 = er * er; // escape_radius *escape_radius
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;
// iteration
int n;
for (n = 0; n < nMax; ++n)
{
z = z * z + c;
if (cnorm(z) > er2) // abs(z)>er
break;
}
// colour
double hue = 0, sat = 0, val = 0; // interior
if (n < nMax) // exterior
{
// double et = ((double)n)/nMax;
// double final_angle = c_turn(z);
/* the name final_z_abs is confusing indeed, sorry.
Here is where it is set:
https://code.mathr.co.uk/mandelbrot-book/blob/HEAD:/code/gui/main.c#l392
final_z_abs = logf(cabsf(z)) / logf(sqrtf(mpfr_get_d(G.escape_radius2,
GMP_RNDN))) - 1.0f;
It is the radial component of "exterior tiling" colouring, slightly different from Linas' renormalization.
why denominator = 64.0 ?
arbitrary, chosen to make the colouring look ok. try changing it as you like
*/
double final_z_abs = log(cabs(z)) / log(er) - 1.0;
// double final_z_abs = cabs(z);
int final_n = n;
double continuous_escape_time = final_n - log2(final_z_abs + 1.0);
hue = continuous_escape_time/64.0;
sat = 0.7;
val = 1.0;
}
// 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);
fwrite(img, 3 * w * h, 1, stdout);
free(img);
return 0;
}