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/*{
  "DESCRIPTION": "Harmonograph — the looping knot traced by coupled pendulums, glowing and slowly morphing in aurora light.",
  "CREDIT": "claude-opus-4-8",
  "INPUTS": [
    { "NAME": "scale", "TYPE": "float", "DEFAULT": 0.42, "MIN": 0.2, "MAX": 0.7 },
    { "NAME": "width", "TYPE": "float", "DEFAULT": 0.012, "MIN": 0.004, "MAX": 0.04 },
    { "NAME": "glow",  "TYPE": "float", "DEFAULT": 0.7, "MIN": 0.0, "MAX": 1.5 },
    { "NAME": "hue",   "TYPE": "float", "DEFAULT": 0.45, "MIN": 0.0, "MAX": 1.0 }
  ]
}*/

#define TAU 6.28318530718

vec3 palette(float t){ return 0.5 + 0.5 * cos(TAU * (t + vec3(0.0, 0.33, 0.67) + hue)); }

vec2 curve(float s, float ph){
  float p1 = TIME * 0.05 + ph, p2 = TIME * 0.037 + ph;
  float x = sin(3.0 * s + p1) * 0.62 + sin(5.0 * s) * 0.28 + sin(9.0 * s + p1 * 2.0) * 0.12;
  float y = sin(4.0 * s) * 0.62 + sin(2.0 * s + p2) * 0.28 + sin(7.0 * s + p2) * 0.12;
  return vec2(x, y) * scale;
}

float distSeg(vec2 p, vec2 a, vec2 b){
  vec2 pa = p - a, ba = b - a;
  float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);
  return length(pa - ba * h);
}

void main(){
  vec2 uv = (gl_FragCoord.xy - 0.5 * RENDERSIZE) / RENDERSIZE.y;

  const int M = 320;
  float d = 1e9, dGhost = 1e9;
  float bestS = 0.0;
  vec2 prev = curve(0.0, 0.0);
  vec2 prevG = curve(0.0, -0.35);
  for (int i = 1; i <= M; i++){
    float s = float(i) / float(M) * TAU;
    vec2 cur = curve(s, 0.0);
    float dd = distSeg(uv, prev, cur);
    if (dd < d){ d = dd; bestS = s / TAU; }
    prev = cur;
    vec2 curG = curve(s, -0.35);            // earlier-phase echo (motion trail)
    dGhost = min(dGhost, distSeg(uv, prevG, curG));
    prevG = curG;
  }

  float line = smoothstep(width, width * 0.3, d);
  float halo = exp(-d * d / (width * width * 30.0));
  float ghost = exp(-dGhost * dGhost / (width * width * 24.0));

  float pulse = 0.5 + 0.5 * sin(bestS * TAU * 3.0 - TIME * 2.0);
  vec3 c = palette(bestS + 0.05 * TIME);
  vec3 col = c * (line * (0.5 + 0.8 * pulse) + halo * 0.55 * glow);
  col += palette(bestS + 0.05 * TIME + 0.1) * ghost * 0.22 * glow;   // faint trailing echo
  col += line * 0.18;                       // white core

  col *= 1.0 - 0.3 * 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);
}

/*{
  "DESCRIPTION": "Harmonograph — the looping knot traced by coupled pendulums, glowing and slowly morphing in aurora light.",
  "CREDIT": "claude-opus-4-8",
  "INPUTS": [
    { "NAME": "scale", "TYPE": "float", "DEFAULT": 0.42, "MIN": 0.2, "MAX": 0.7 },
    { "NAME": "width", "TYPE": "float", "DEFAULT": 0.012, "MIN": 0.004, "MAX": 0.04 },
    { "NAME": "glow",  "TYPE": "float", "DEFAULT": 0.7, "MIN": 0.0, "MAX": 1.5 },
    { "NAME": "hue",   "TYPE": "float", "DEFAULT": 0.45, "MIN": 0.0, "MAX": 1.0 }
  ]
}*/

#define TAU 6.28318530718

vec3 palette(float t){ return 0.5 + 0.5 * cos(TAU * (t + vec3(0.0, 0.33, 0.67) + hue)); }

vec2 curve(float s, float ph){
  float p1 = TIME * 0.05 + ph, p2 = TIME * 0.037 + ph;
  float x = sin(3.0 * s + p1) * 0.62 + sin(5.0 * s) * 0.28 + sin(9.0 * s + p1 * 2.0) * 0.12;
  float y = sin(4.0 * s) * 0.62 + sin(2.0 * s + p2) * 0.28 + sin(7.0 * s + p2) * 0.12;
  return vec2(x, y) * scale;
}

float distSeg(vec2 p, vec2 a, vec2 b){
  vec2 pa = p - a, ba = b - a;
  float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);
  return length(pa - ba * h);
}

void main(){
  vec2 uv = (gl_FragCoord.xy - 0.5 * RENDERSIZE) / RENDERSIZE.y;

const int M = 320;
  float d = 1e9, dGhost = 1e9;
  float bestS = 0.0;
  vec2 prev = curve(0.0, 0.0);
  vec2 prevG = curve(0.0, -0.35);
  for (int i = 1; i <= M; i++){
    float s = float(i) / float(M) * TAU;
    vec2 cur = curve(s, 0.0);
    float dd = distSeg(uv, prev, cur);
    if (dd < d){ d = dd; bestS = s / TAU; }
    prev = cur;
    vec2 curG = curve(s, -0.35);            // earlier-phase echo (motion trail)
    dGhost = min(dGhost, distSeg(uv, prevG, curG));
    prevG = curG;
  }

float line = smoothstep(width, width * 0.3, d);
  float halo = exp(-d * d / (width * width * 30.0));
  float ghost = exp(-dGhost * dGhost / (width * width * 24.0));

float pulse = 0.5 + 0.5 * sin(bestS * TAU * 3.0 - TIME * 2.0);
  vec3 c = palette(bestS + 0.05 * TIME);
  vec3 col = c * (line * (0.5 + 0.8 * pulse) + halo * 0.55 * glow);
  col += palette(bestS + 0.05 * TIME + 0.1) * ghost * 0.22 * glow;   // faint trailing echo
  col += line * 0.18;                       // white core

col *= 1.0 - 0.3 * 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);
}

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