/*{
  "DESCRIPTION": "Potential-flow visualizer — curl-noise background superposed with moving point vortices and sources, traced as line-integral-convolution streaks colored by flow speed.",
  "CREDIT": "claude-opus-4-8",
  "INPUTS": [
    { "NAME": "scale",     "TYPE": "float", "DEFAULT": 2.6, "MIN": 1.0, "MAX": 6.0 },
    { "NAME": "vortexStr", "TYPE": "float", "DEFAULT": 0.5, "MIN": 0.0, "MAX": 1.5 },
    { "NAME": "contrast",  "TYPE": "float", "DEFAULT": 1.5, "MIN": 0.5, "MAX": 3.0 },
    { "NAME": "hue",       "TYPE": "float", "DEFAULT": 0.58, "MIN": 0.0, "MAX": 1.0 }
  ]
}*/

float hash(vec2 p){ p = fract(p * vec2(123.34, 456.21)); p += dot(p, p + 45.32); return fract(p.x * p.y); }
float noise(vec2 p){
  vec2 i = floor(p), f = fract(p); f = f * f * (3.0 - 2.0 * f);
  float a = hash(i), b = hash(i + vec2(1.0, 0.0)), c = hash(i + vec2(0.0, 1.0)), d = hash(i + vec2(1.0, 1.0));
  return mix(mix(a, b, f.x), mix(c, d, f.x), f.y);
}
float fbm(vec2 p){ float s = 0.0, a = 0.5; for (int i = 0; i < 3; i++){ s += a * noise(p); p = p * 2.0 + 3.0; a *= 0.5; } return s; }
vec3 palette(float t){ return 0.5 + 0.5 * cos(6.28318 * (t + vec3(0.0, 0.33, 0.67) + hue)); }

// i-th singularity centre (drifts over time)
vec2 centre(int i, float t){
  float fi = float(i);
  return scale * 0.6 * vec2(sin(t * 0.3 + fi * 1.7), cos(t * 0.27 + fi * 2.3));
}

// superposed velocity field: curl-noise turbulence + point vortices/sources
vec2 field(vec2 q, float t){
  float a = fbm(q * 0.6 + vec2(0.0, t * 0.1)) * 6.28318 * 1.5;   // rotational background
  vec2 v = vec2(cos(a), sin(a));
  for (int i = 0; i < 4; i++){
    vec2 d = q - centre(i, t);
    float r2 = dot(d, d) + 0.12;
    float fi = float(i);
    v += vortexStr * (fi - 1.5) * vec2(-d.y, d.x) / r2;   // vortices (mixed signs)
    v += 0.25 * (mod(fi, 2.0) - 0.5) * d / r2;            // sources / sinks
  }
  return v;
}

void main(){
  vec2 uv = (gl_FragCoord.xy - 0.5 * RENDERSIZE) / RENDERSIZE.y;
  vec2 q = uv * scale;
  float t = TIME;

  // line-integral convolution: smear high-freq noise along streamlines (both directions)
  float acc = 0.0, wsum = 0.0;
  vec2 pf = q, pb = q;
  for (int i = 0; i < 18; i++){
    float wi = 1.0 - float(i) / 18.0;
    vec2 ff = field(pf, t), fb = field(pb, t);
    pf += ff / (length(ff) + 1e-4) * 0.03;
    pb -= fb / (length(fb) + 1e-4) * 0.03;
    acc += wi * noise(pf * 9.0 + t * 1.5);
    acc += wi * noise(pb * 9.0 + t * 1.5);
    wsum += 2.0 * wi;
  }
  acc /= wsum;
  acc = pow(clamp((acc - 0.5) * contrast + 0.5, 0.0, 1.0), 1.3);

  // colour by local flow speed (magnitude) -> "wind speed" map
  vec2 fv = field(q, t);
  float speed = length(fv);
  vec3 col = palette(0.5 + 0.18 * log(1.0 + speed) + 0.1 * acc) * (0.14 + acc);
  col += acc * acc * 0.22;

  // glowing vortex cores
  for (int i = 0; i < 4; i++){
    float od = length(q - centre(i, t));
    col += palette(0.1 + 0.2 * float(i)) * 0.09 / (0.04 + od * od);
  }

  col *= 1.0 - 0.22 * dot(uv, uv);
  col = col / (1.0 + 0.5 * col);
  col = pow(max(col, 0.0), vec3(0.9));
  gl_FragColor = vec4(col, 1.0);
}