/*{
  "DESCRIPTION": "Pseudo-Kleinian lattice: a box-fold/sphere-inversion Kleinian limit set raymarched as a lattice of thin glowing cells and filaments, electric orbit-trap colour with hot neon rims. Slowly tumbles. Real-time, seamless 16s loop.",
  "CREDIT": "glslop agent (Claude); pseudo-Kleinian DE after Knighty",
  "CATEGORIES": ["fractal", "raymarch", "neon", "kleinian"],
  "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": "fold",      "TYPE": "float", "DEFAULT": 1.5,  "MIN": 1.1, "MAX": 1.9 },
    { "NAME": "zoom",      "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.5, "MAX": 2.0 },
    { "NAME": "iterCount", "TYPE": "long",  "DEFAULT": 5,    "MIN": 4,   "MAX": 12 }
  ]
}*/

#define PI  3.14159265359
#define TAU 6.28318530718

const float PERIOD = 16.0;
const int   MAXI   = 12;
const int   STEPS  = 110;

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(0.0, 0.33, 0.67)));
}

// pseudo-Kleinian DE: box fold + sphere inversion -> thin cell/filament lattice.
float map(vec3 p, float s, mat2 Rt, out float trap){
  p.xz = Rt * p.xz;
  vec3 CSize = vec3(0.98, 0.98, 1.3);
  float DEfactor = 1.0;
  trap = 1.0e9;
  for (int i = 0; i < MAXI; i++){
    if (i >= iterCount) break;
    p = 2.0 * clamp(p, -CSize, CSize) - p;     // box fold
    float r2 = dot(p, p);
    float k = max(s / r2, 1.0);                // sphere inversion
    p *= k; DEfactor *= k;
    trap = min(trap, r2);
  }
  float rxy = length(p.xy);
  return 0.5 * max(rxy - 0.92, abs(rxy * p.z) / length(p)) / DEfactor;
}

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

  float ph = fract(TIME * speed / PERIOD);
  float th = TAU * ph;
  float s = fold + 0.05 * sin(th);
  mat2 Rt = rot(0.4 + 0.4 * sin(th));

  float camDist = 10.0 * zoom;
  float az = th;
  float el = 0.30 + 0.18 * sin(th);
  vec3 ro = camDist * vec3(sin(az) * cos(el), sin(el), cos(az) * cos(el));
  vec3 ta = vec3(0.0);
  vec3 fwd = normalize(ta - ro);
  vec3 rgt = normalize(cross(vec3(0.0, 1.0, 0.0), fwd));
  vec3 upv = cross(fwd, rgt);
  vec3 rd  = normalize(uv.x * rgt + uv.y * upv + 1.6 * fwd);

  // ---- surface raymarch ----
  float t = 0.02;
  float tcap = camDist + 8.0;
  float trapHit = 1.0e9, te = 0.0;
  bool hit = false;
  for (int i = 0; i < STEPS; i++){
    vec3 p = ro + rd * t;
    float tr;
    float d = map(p, s, Rt, tr);
    if (d < 0.0006 * t){ hit = true; trapHit = tr; te = t; break; }
    t += d * 0.6;
    if (t > tcap) break;
  }

  vec3 col = vec3(0.0);

  if (hit){
    vec3 p = ro + rd * te;
    vec2 k = vec2(1.0, -1.0);
    float e = 0.0012, tr;
    vec3 n = normalize(
      k.xyy * map(p + k.xyy * e, s, Rt, tr) +
      k.yyx * map(p + k.yyx * e, s, Rt, tr) +
      k.yxy * map(p + k.yxy * e, s, Rt, tr) +
      k.xxx * map(p + k.xxx * e, s, Rt, tr));

    vec3 base = pal(hue + 0.7 * sqrt(trapHit) + 0.12 * te);
    vec3 lig  = normalize(vec3(0.5, 0.7, 0.5));
    float dif = max(dot(n, lig), 0.0);
    float fres = pow(1.0 - max(dot(n, -rd), 0.0), 2.3);

    col += base * 0.10;
    col += base * dif * 0.22;
    col += base * fres * 4.2 * glow;                 // brighter neon filaments
    col += vec3(1.0) * pow(fres, 5.0) * 0.9 * glow;
    col *= exp(-0.11 * max(te - camDist + 3.0, 0.0));
  }

  col = col / (1.0 + col);
  col = pow(col, vec3(0.78));
  col *= 1.0 - 0.22 * dot(uv, uv);

  gl_FragColor = vec4(col, 1.0);
}