/*{
  "DESCRIPTION": "Dipole: the field lines of a bar magnet made visible. Glowing loops arc from a red north pole to a blue south pole, pulses of charge race along them, and the whole magnet slowly turns. Field lines are exact dipole curves (L = r^3 / x^2); one full turn per loop for a seamless 16s cycle.",
  "CREDIT": "glslop agent (Claude)",
  "CATEGORIES": ["magnetic", "dipole", "field-lines", "physics", "neon"],
  "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": "density", "TYPE": "float", "DEFAULT": 2.2,  "MIN": 1.0, "MAX": 4.0 },
    { "NAME": "thin",    "TYPE": "float", "DEFAULT": 0.02, "MIN": 0.006,"MAX": 0.06 },
    { "NAME": "zoom",    "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.6, "MAX": 1.8 }
  ]
}*/

#define PI  3.14159265359
#define TAU 6.28318530718

const float PERIOD = 16.0;

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

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

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

  // rotate the magnet (one full turn per loop -> seamless)
  vec2 p = rot(th) * uv;
  float r = length(p) + 1e-3;

  // dipole field-line label: L = r^3 / x^2  (constant along a field line)
  float L = (r * r * r) / (p.x * p.x + 2e-3);
  float lg = log(L);

  // draw glowing lines at evenly spaced log-L levels
  float f = lg * density;
  float lane = abs(fract(f) - 0.5) * 2.0;
  float line = pow(1.0 - lane, 5.0);

  // charge pulses racing outward along the lines
  float pulse = 0.6 + 0.6 * sin(r * 8.0 - th * 3.0 + floor(f) * 1.7);
  line *= pulse;

  // field strength ~ 1/r^3 : brighter near the magnet, fade out
  float strength = exp(-r * 1.3);
  float falloff  = smoothstep(1.3, 0.2, r);

  // colour: red near north (p.y>0), blue near south, white in the arcs
  float poleMix = clamp(p.y / r * 0.5 + 0.5, 0.0, 1.0);
  vec3 nCol = vec3(1.0, 0.25, 0.35);     // north = red
  vec3 sCol = vec3(0.3, 0.5, 1.0);       // south = blue
  vec3 lineCol = mix(sCol, nCol, poleMix);

  vec3 col = vec3(0.0);
  col += lineCol * line * (0.5 + 1.6 * strength) * falloff * 2.0 * glow;
  col += vec3(0.9, 0.95, 1.0) * pow(line, 1.8) * (0.4 + strength) * falloff * 1.2 * glow;

  // the two poles (rotated): bright glowing tips of the bar magnet
  vec2 npole = vec2(0.0, 0.16);
  vec2 spole = vec2(0.0, -0.16);
  col += nCol * exp(-dot(p - npole, p - npole) * 120.0) * 2.2;
  col += sCol * exp(-dot(p - spole, p - spole) * 120.0) * 2.2;
  // the bar magnet body
  float bar = smoothstep(0.03, 0.02, abs(p.x)) * smoothstep(0.17, 0.16, abs(p.y));
  col = mix(col, mix(sCol, nCol, smoothstep(-0.16, 0.16, p.y)) * 0.5, bar);

  col = col / (1.0 + col);
  col = pow(col, vec3(0.84));
  col *= 1.0 - 0.18 * dot(uv * zoom, uv * zoom);
  gl_FragColor = vec4(col, 1.0);
}