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#version 330 core
out vec4 out_color;
uniform int u_width;
uniform int u_height;
uniform float u_real_start;
uniform float u_real_end;
uniform float u_imag_start;
uniform float u_imag_end;
uniform int u_iterations;
uniform bool u_smooth;
uniform float u_samples;
uniform sampler1D u_texture;
#define ESCAPE_RADIUS 4.0
#define LOG_2 0.69314718056
int mandelbrot_func(vec2 c)
{
vec2 z;
vec2 z_square;
int n;
z = c;
for (n = 0; n < u_iterations; n++)
{
z_square = z * z;
if (z_square.x + z_square.y > ESCAPE_RADIUS)
break;
z.y = 2.0 * z.x * z.y;
z.x = z_square.x - z_square.y;
z += c;
}
return n;
}
float mandelbrot_smooth(vec2 c)
{
vec2 z;
vec2 z_square;
int n;
z = c;
for (n = 0; n < u_iterations; n++)
{
z_square = z * z;
if (z_square.x + z_square.y > ESCAPE_RADIUS)
break;
z.y = 2.0 * z.x * z.y;
z.x = z_square.x - z_square.y;
z += c;
}
if (n == u_iterations)
return float(n);
// http://linas.org/art-gallery/escape/escape.html
z_square = z * z;
z.y = 2.0 * z.x * z.y;
z.x = z_square.x - z_square.y;
z += c;
z_square = z * z;
z.y = 2.0 * z.x * z.y;
z.x = z_square.x - z_square.y;
z += c;
float modulus = sqrt(z.x * z.x + z.y * z.y);
return float(n) - log(log(modulus)) / LOG_2;
}
vec4 mandelbrot_color(vec2 c)
{
float n;
if (u_smooth)
n = mandelbrot_smooth(c);
else
n = float(mandelbrot_func(c));
if (n == float(u_iterations))
return vec4(0.0, 0.0, 0.0, 1.0);
else
return texture(u_texture, n / float(u_iterations));
}
vec4 supersample_grid(vec2 c)
{
vec2 epsilon;
vec2 _sample;
vec2 _step;
vec4 color;
color = vec4(0.0, 0.0, 0.0, 0.0);
_step.x = (u_real_end - u_real_start) / float(u_width);
_step.y = (u_imag_end - u_imag_start) / float(u_height);
epsilon.y = 0.0;
while (epsilon.y < u_samples)
{
epsilon.x = 0.0;
while (epsilon.x < u_samples)
{
_sample = c + _step * (epsilon / u_samples);
color += mandelbrot_color(_sample);
epsilon.x += 1.0;
}
epsilon.y += 1.0;
}
return color / (u_samples * u_samples);
}
void main()
{
vec2 c;
float n;
c.x = u_real_start + float(gl_FragCoord.x) / float(u_width) * (u_real_end - u_real_start);
c.y = u_imag_start + float(gl_FragCoord.y) / float(u_height) * (u_imag_end - u_imag_start);
if (u_samples == 1.0)
out_color = mandelbrot_color(c);
else
out_color = supersample_grid(c);
}
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