/*{
  "DESCRIPTION": "Circle-limit neon: a hyperbolic tiling of the Poincare disk built by dihedral angular folds + a geodesic circle inversion, drawn as glowing geodesic arcs that shrink forever toward the rim. Rotates and colour-cycles. Real-time, seamless 16s loop.",
  "CREDIT": "glslop agent (Claude)",
  "CATEGORIES": ["hyperbolic", "tiling", "neon", "kaleidoscope"],
  "INPUTS": [
    { "NAME": "speed",    "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.0, "MAX": 3.0 },
    { "NAME": "glow",     "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.3, "MAX": 3.0 },
    { "NAME": "hue",      "TYPE": "float", "DEFAULT": 0.0,  "MIN": 0.0, "MAX": 1.0 },
    { "NAME": "circleX",  "TYPE": "float", "DEFAULT": 2.2,  "MIN": 1.1, "MAX": 2.6 },
    { "NAME": "zoom",     "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.5, "MAX": 1.6 },
    { "NAME": "symmetry", "TYPE": "long",  "DEFAULT": 6,    "MIN": 3,   "MAX": 12 }
  ]
}*/

#define PI  3.14159265359
#define TAU 6.28318530718

const float PERIOD = 16.0;
const int   ITER   = 24;

mat2 rot(float a){ float c = cos(a), s = sin(a); return mat2(c, -s, s, c); }

vec3 pal(float t){
  return 0.5 + 0.5 * cos(TAU * (t + vec3(0.55, 0.40, 0.18)));
}

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

  float ph = fract(TIME * speed / PERIOD);
  float th = TAU * ph;

  vec2 z = uv * (1.95 / zoom);
  z = rot(th) * z;                          // spin the whole disk (seamless)
  float r0 = length(z);

  vec3 col = vec3(0.0);
  if (r0 < 1.0){
    float seg = TAU / float(symmetry);
    float cx  = circleX;
    float cr  = sqrt(max(cx * cx - 1.0, 1.0e-3));   // geodesic ⟂ to unit circle
    vec2  cen = vec2(cx, 0.0);

    float parity = 0.0;
    float edge   = 1.0e9;
    for (int i = 0; i < ITER; i++){
      // dihedral angular fold -> one wedge of the p-fold rosette
      float a = mod(atan(z.y, z.x), seg) - 0.5 * seg;
      float rr = length(z);
      z = rr * vec2(cos(a), sin(a));
      z.y = abs(z.y);
      // geodesic circle inversion (the hyperbolic mirror)
      vec2  dd = z - cen;
      float d2 = dot(dd, dd);
      edge = min(edge, abs(sqrt(d2) - cr));         // distance to the arc
      if (d2 < cr * cr){
        z = cen + dd * (cr * cr / d2);
        parity += 1.0;
      } else {
        // already outside the mirror -> in the fundamental domain
        if (i > 1) break;
      }
    }

    // cell colour: hue cycles with fold-depth -> rainbow rings toward the rim
    vec3 c = pal(hue + ph + 0.135 * parity + 0.25 * length(z - cen));
    float tile = 0.55 + 0.45 * sin(parity * 1.6);
    col  = c * (0.28 + 0.7 * tile);
    float arc = 0.02 / (edge + 0.014);
    col += pal(hue + ph + 0.5) * arc * 1.2 * glow;            // electric geodesic arcs
    col += vec3(0.8, 0.95, 1.0) * pow(arc, 2.0) * 0.3 * glow; // white-hot arc cores

    col *= smoothstep(1.0, 0.86, r0);               // fade into the rim
  }

  col = col / (1.0 + col);
  col = pow(col, vec3(0.80));
  col *= 1.0 - 0.16 * dot(uv, uv);

  gl_FragColor = vec4(col, 1.0);
}