shader.frag

#ifdef GL_ES
precision mediump float;
#endif

uniform vec2 u_resolution;
uniform float u_time;

#define PI 3.1415926535897932384626433832795
float cosh(float x) {
    return (exp(x) + exp(-x)) * 0.5;
}
float sinh(float x) {
    return (exp(x) - exp(-x)) * 0.5;
}
#define cx_mul(a, b) vec2(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x)
#define cx_div(a, b) vec2(((a.x*b.x + a.y*b.y)/(b.x*b.x + b.y*b.y)),((a.y*b.x - a.x*b.y)/(b.x*b.x + b.y*b.y)))
#define cx_sin(a) vec2(sin(a.x) * cosh(a.y), cos(a.x) * sinh(a.y))
#define cx_cos(a) vec2(cos(a.x) * cosh(a.y), -sin(a.x) * sinh(a.y))

vec2 cx_tan(vec2 a) {return cx_div(cx_sin(a), cx_cos(a)); }
vec2 cx_log(vec2 a) {
    float rpart = sqrt((a.x*a.x)+(a.y*a.y));
    float ipart = atan(a.y,a.x);
    if (ipart > PI) ipart=ipart-(2.0*PI);
    return vec2(log(rpart),ipart);
}

vec2 as_polar(vec2 z) {
  return vec2(
    length(z),
    atan(z.y, z.x)
  );
}
vec2 cx_pow(vec2 v, float p) {
  vec2 z = as_polar(v);
  return pow(z.x, p) * vec2(cos(z.y * p), sin(z.y * p));
}

float im(vec2 z) {
  return ((atan(z.y, z.x) / PI) + 1.0) * 0.5;
}

vec3 pal( in float t, in vec3 a, in vec3 b, in vec3 c, in vec3 d )
{
    return a + b*cos(2.*PI*(c*t+d));
}

// Define our points
vec2 a0 = vec2(0.32, -0.45);
vec2 a1 = vec2(-0.49, -0.32);
vec2 a2 = vec2(-0.31, 0.38);
vec2 a3 = vec2(-0.12, 0.04);

vec2 b0 = vec2(-0.71, 0.53);
vec2 b1 = vec2(0.01, 0.23);
vec2 b2 = vec2(-0.24, 0.31);
vec2 b3 = vec2(-0.01, -0.42);

// Blending colors
void main() {
  // Set up our imaginary plane
  vec2 uv = (gl_FragCoord.xy - 0.5 * u_resolution.xy) / min(u_resolution.y, u_resolution.x);
  vec2 z = uv * 10.;

  vec2 polyA = a0
    + cx_mul(a1, vec2(sin(u_time + z)))
    + cx_mul(a2, vec2(sin(u_time * z)))
    + cx_mul(a3, cx_pow(z, 2.0));

  // Calculate the sum of our second polynomial
  vec2 polyB = b0
      + cx_mul(b1, vec2(sin(u_time * z)))
      + cx_mul(b2, vec2(sin(u_time * z)))
      + cx_mul(b3, cx_pow(z, 2.));

  // Calculate the ratio of our complex polynomials
  vec2 result = cx_div(polyA, polyB);

  float imaginary = cx_log(result).y ;
  // float col = (imaginary / PI);


  // pink and blue
  // vec3 col = pal( 
  //   imaginary * 2., 
  //   vec3(abs(sin(u_time / 1.8)),.59,0.93), 
  //   vec3(0.2,0.12,.115), 
  //   vec3(0.2,0.34,.115), 
  //   vec3(abs(sin(u_time / 1.8)),1.13,.112)
  //   );

  // green / red
  // vec4 col = vec4(
  //   pal(imaginary, 
  //   vec3(.52,.45,.61),
  //   vec3(.40,.42,.31),
  //   vec3(.26,.30,.35),
  //   vec3(.15,.4,.4)),
  //   1.0);

  // red/pink and blue
  // vec4 col = vec4(
  // pal(imaginary, 
  // vec3(.92,.25,.61),
  // vec3(-1.,.42,.31),
  // vec3(.26,.30,.35),
  // vec3(.15,.4,.4)), 
  // 1.0);

  // blue / orange / pink / green
  float a = 1.0;
  vec4 col = vec4(
  pal(imaginary, 
  vec3(a,.25,.61),
  vec3(a,.42,.31),
  vec3(.26,.30,a),
  vec3(.15,.4,a)),
  1.0);


  // green / yellow / red
  // float a = 1.0;
  // vec4 col = vec4(
  // pal(imaginary, 
  // vec3(a,.3,.11),
  // vec3(a,.52,.31),
  // vec3(.26,.30,a),
  // vec3(.15,.4,a)),
  // 1.0);

  // float a = 1.0;
  // vec4 col = vec4(
  // pal(imaginary, 
  // vec3(a,.3,.41),
  // vec3(a,.52,.41),
  // vec3(.26,.30,a),
  // vec3(.15,.4,a)),
  // 1.0);


  // MISC
  //   vec3 col = pal( 
  // imaginary * 2., 
  // vec3(abs(sin(u_time / 1.8)),.99,1.93), 
  // vec3(0.2,0.0,.115), 
  // vec3(0.2,0.1,.115), 
  // vec3(abs(sin(u_time / 1.8)),0.13,1.112)
  // );

  // vec3 col = pal( 
  //   imaginary * 2., 
  //   vec3(abs(sin(u_time / 1.8)),.69,2.93), 
  //   vec3(0.3,0.12,.115), 
  //   vec3(0.3,0.34,.115), 
  //   vec3(abs(sin(u_time / 1.8)),1.13,.112)
  //   );

  // vec3 col = pal( 
  //   imaginary * 2., 
  //   vec3(abs(sin(u_time / 1.8)),.79,0.93), 
  //   vec3(0.4,0.12,.115), 
  //   vec3(0.4,0.34,.115), 
  //   vec3(abs(sin(u_time / 1.8)),0.93,.112)
  //   );

  // vec3 col = pal( 
  //   imaginary * 2., 
  //   vec3(abs(cos(u_time / 1.8)),0.11,0.33), 
  //   vec3(0.3,0.12,0.115), 
  //   vec3(0.3,0.94,0.1115), 
  //   vec3(abs(cos(u_time / 1.8)),0.13,.2)
  //   );

  // old
  // gl_FragColor = vec4(col, 1.0);
  
  gl_FragColor = col;

}