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newton.glsl
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newton.glsl
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vec2 c_mult (vec2 a, vec2 b)
{
return vec2(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
vec2 c_conj (vec2 a)
{
return vec2(a.x, -a.y);
}
vec2 c_inv (vec2 a)
{
return c_conj(a) / dot(a, a);
}
vec2 c_div (vec2 a, vec2 b)
{
return c_mult(a, c_inv(b));
}
vec4 color ( )
{
vec2 z = position;
int count = 70;
int n;
for (n = 0; n < count; ++n)
{
z = z - c_div(c_mult(c_mult(z, z), z) - vec2(1.0, 0.0), 3.0 * c_mult(z, z));
vec2 f = c_mult(c_mult(z, z), z) - vec2(1.0, 0.0);
if (length(f) < 0.000001)
break;
}
float i = 1.0 - float(n) / float(count);
float a = atan(z.y, z.x);
float pi = 3.1415926535;
vec4 red = vec4(1.0, 0.0, 0.0, 0.0);
vec4 green = vec4(0.0, 1.0, 0.0, 0.0);
vec4 blue = vec4(0.0, 0.0, 1.0, 0.0);
vec4 black = vec4(0.0, 0.0, 0.0, 0.0);
vec4 white = vec4(1.0, 1.0, 1.0, 0.0);
vec4 c;
/*
if (a < - pi / 3.0)
c = blue;
if (a < pi / 3.0)
c = red;
c = green;
*/
if (a < - 2.0 * pi / 3.0)
c = mix(green, blue, 3.0 * a / 2.0 / pi + 2.0);
else if (a < 0.0)
c = mix(blue, red, 3.0 * a / 2.0 / pi + 1.0);
else if (a < 2.0 * pi / 3.0)
c = mix(red, green, 3.0 * a / 2.0 / pi);
else
c = mix(green, blue, 3.0 * a / 2.0 / pi - 1.0);
if (i < 0.5)
return mix(black, c, 2.0 * i);
else
return mix(c, white, 2.0 * i - 1.3);
}