// Noise Related Functions
float mod289(float x) { return x - floor(x * (1.0 / 289.0)) * 289.0; }
vec4 mod289(vec4 x) { return x - floor(x * (1.0 / 289.0)) * 289.0; }
vec4 perm(vec4 x) { return mod289(((x * 34.0) + 1.0) * x); }
float noise(vec3 p) {
  vec3 a = floor(p);
  vec3 d = p - a;
  d = d * d * (3.0 - 2.0 * d);
  vec4 b = a.xxyy + vec4(0.0, 1.0, 0.0, 1.0);
  vec4 k1 = perm(b.xyxy);
  vec4 k2 = perm(k1.xyxy + b.zzww);
  vec4 c = k2 + a.zzzz;
  vec4 k3 = perm(c);
  vec4 k4 = perm(c + 1.0);
  vec4 o1 = fract(k3 * (1.0 / 41.0));
  vec4 o2 = fract(k4 * (1.0 / 41.0));
  vec4 o3 = o2 * d.z + o1 * (1.0 - d.z);
  vec2 o4 = o3.yw * d.x + o3.xz * (1.0 - d.x);
  return o4.y * d.y + o4.x * (1.0 - d.y);
}
float PHI = 1.61803398874989484820459; // Φ = Golden Ratio
float gold_noise(in vec2 xy, in float seed) {
  return fract(tan(distance(xy * PHI, xy) * seed) * xy.x);
}
float random(vec3 scale, float seed) {
  return fract(sin(dot(gl_GlobalInvocationID.xyz + seed, scale)) * 43758.5453 +
               seed);
}

// Fractal Brownian Noise
float fbm(vec3 x, int octaves) {
  float v = 0.0;
  float a = 0.5;
  vec3 shift = vec3(100);
  for (int i = 0; i < octaves; ++i) {
    v += a * noise(x);
    x = x * 2.0 + shift;
    a *= 0.5;
  }
  return v;
}

float random(vec2 st) {
  return fract(sin(dot(st.xy, vec2(12.9898, 78.233))) * 43758.5453123);
}

float noise(vec2 st) {
  vec2 i = floor(st);
  vec2 f = fract(st);
  float a = random(i);
  float b = random(i + vec2(1.0, 0.0));
  float c = random(i + vec2(0.0, 1.0));
  float d = random(i + vec2(1.0, 1.0));
  vec2 u = f * f * (3.0 - 2.0 * f);
  return mix(a, b, u.x) + (c - a) * u.y * (1.0 - u.x) + (d - b) * u.x * u.y;
}

float fbm(vec2 st) {
  float value = 0.0;
  float amplitude = 0.5;
  for (int i = 0; i < 5; i++) {
    value += amplitude * noise(st);
    st *= 2.0;
    amplitude *= 0.5;
  }
  return value;
}