/* The fractal_noise functions are all exactly the same except for the input type. */
float fractal_noise(float p, float octaves, float roughness)
{
  float fscale = 1.0;
  float amp = 1.0;
  float maxamp = 0.0;
  float sum = 0.0;
  octaves = clamp(octaves, 0.0, 16.0);
  int n = int(octaves);
  for (int i = 0; i <= n; i++) {
    float t = noise(fscale * p);
    sum += t * amp;
    maxamp += amp;
    amp *= clamp(roughness, 0.0, 1.0);
    fscale *= 2.0;
  }
  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float t = noise(fscale * p);
    float sum2 = sum + t * amp;
    sum /= maxamp;
    sum2 /= maxamp + amp;
    return (1.0 - rmd) * sum + rmd * sum2;
  }
  else {
    return sum / maxamp;
  }
}

/* The fractal_noise functions are all exactly the same except for the input type. */
float fractal_noise(vec2 p, float octaves, float roughness)
{
  float fscale = 1.0;
  float amp = 1.0;
  float maxamp = 0.0;
  float sum = 0.0;
  octaves = clamp(octaves, 0.0, 16.0);
  int n = int(octaves);
  for (int i = 0; i <= n; i++) {
    float t = noise(fscale * p);
    sum += t * amp;
    maxamp += amp;
    amp *= clamp(roughness, 0.0, 1.0);
    fscale *= 2.0;
  }
  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float t = noise(fscale * p);
    float sum2 = sum + t * amp;
    sum /= maxamp;
    sum2 /= maxamp + amp;
    return (1.0 - rmd) * sum + rmd * sum2;
  }
  else {
    return sum / maxamp;
  }
}

/* The fractal_noise functions are all exactly the same except for the input type. */
float fractal_noise(vec3 p, float octaves, float roughness)
{
  float fscale = 1.0;
  float amp = 1.0;
  float maxamp = 0.0;
  float sum = 0.0;
  octaves = clamp(octaves, 0.0, 16.0);
  int n = int(octaves);
  for (int i = 0; i <= n; i++) {
    float t = noise(fscale * p);
    sum += t * amp;
    maxamp += amp;
    amp *= clamp(roughness, 0.0, 1.0);
    fscale *= 2.0;
  }
  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float t = noise(fscale * p);
    float sum2 = sum + t * amp;
    sum /= maxamp;
    sum2 /= maxamp + amp;
    return (1.0 - rmd) * sum + rmd * sum2;
  }
  else {
    return sum / maxamp;
  }
}

/* The fractal_noise functions are all exactly the same except for the input type. */
float fractal_noise(vec4 p, float octaves, float roughness)
{
  float fscale = 1.0;
  float amp = 1.0;
  float maxamp = 0.0;
  float sum = 0.0;
  octaves = clamp(octaves, 0.0, 16.0);
  int n = int(octaves);
  for (int i = 0; i <= n; i++) {
    float t = noise(fscale * p);
    sum += t * amp;
    maxamp += amp;
    amp *= clamp(roughness, 0.0, 1.0);
    fscale *= 2.0;
  }
  float rmd = octaves - floor(octaves);
  if (rmd != 0.0) {
    float t = noise(fscale * p);
    float sum2 = sum + t * amp;
    sum /= maxamp;
    sum2 /= maxamp + amp;
    return (1.0 - rmd) * sum + rmd * sum2;
  }
  else {
    return sum / maxamp;
  }
}