float taylorInvSqrt(in float r) { return 1.79284291400159 - 0.85373472095314 * r; }
vec2 taylorInvSqrt(in vec2 r) { return 1.79284291400159 - 0.85373472095314 * r; }
vec3 taylorInvSqrt(in vec3 r) { return 1.79284291400159 - 0.85373472095314 * r; }
vec4 taylorInvSqrt(in vec4 r) { return 1.79284291400159 - 0.85373472095314 * r; }

float permute(const in float x) { return mod289(((x * 34.0) + 1.0) * x); }
vec2 permute(const in vec2 x) { return mod289(((x * 34.0) + 1.0) * x); }
vec3 permute(const in vec3 x) { return mod289(((x * 34.0) + 1.0) * x); }
vec4 permute(const in vec4 x) { return mod289(((x * 34.0) + 1.0) * x); }

float mod289(const in float x) { return x - floor(x * (1. / 289.)) * 289.; }
vec2 mod289(const in vec2 x) { return x - floor(x * (1. / 289.)) * 289.; }
vec3 mod289(const in vec3 x) { return x - floor(x * (1. / 289.)) * 289.; }
vec4 mod289(const in vec4 x) { return x - floor(x * (1. / 289.)) * 289.; }

float snoise(in vec3 v) {
    const vec2  C = vec2(1.0/6.0, 1.0/3.0) ;
    const vec4  D = vec4(0.0, 0.5, 1.0, 2.0);

    // First corner
    vec3 i  = floor(v + dot(v, C.yyy) );
    vec3 x0 =   v - i + dot(i, C.xxx) ;

    // Other corners
    vec3 g = step(x0.yzx, x0.xyz);
    vec3 l = 1.0 - g;
    vec3 i1 = min( g.xyz, l.zxy );
    vec3 i2 = max( g.xyz, l.zxy );

    //   x0 = x0 - 0.0 + 0.0 * C.xxx;
    //   x1 = x0 - i1  + 1.0 * C.xxx;
    //   x2 = x0 - i2  + 2.0 * C.xxx;
    //   x3 = x0 - 1.0 + 3.0 * C.xxx;
    vec3 x1 = x0 - i1 + C.xxx;
    vec3 x2 = x0 - i2 + C.yyy; // 2.0*C.x = 1/3 = C.y
    vec3 x3 = x0 - D.yyy;      // -1.0+3.0*C.x = -0.5 = -D.y

    // Permutations
    i = mod289(i);
    vec4 p = permute( permute( permute(
                i.z + vec4(0.0, i1.z, i2.z, 1.0 ))
            + i.y + vec4(0.0, i1.y, i2.y, 1.0 ))
            + i.x + vec4(0.0, i1.x, i2.x, 1.0 ));

    // Gradients: 7x7 points over a square, mapped onto an octahedron.
    // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294)
    float n_ = 0.142857142857; // 1.0/7.0
    vec3  ns = n_ * D.wyz - D.xzx;

    vec4 j = p - 49.0 * floor(p * ns.z * ns.z);  //  mod(p,7*7)

    vec4 x_ = floor(j * ns.z);
    vec4 y_ = floor(j - 7.0 * x_ );    // mod(j,N)

    vec4 x = x_ *ns.x + ns.yyyy;
    vec4 y = y_ *ns.x + ns.yyyy;
    vec4 h = 1.0 - abs(x) - abs(y);

    vec4 b0 = vec4( x.xy, y.xy );
    vec4 b1 = vec4( x.zw, y.zw );

    //vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0;
    //vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0;
    vec4 s0 = floor(b0)*2.0 + 1.0;
    vec4 s1 = floor(b1)*2.0 + 1.0;
    vec4 sh = -step(h, vec4(0.0));

    vec4 a0 = b0.xzyw + s0.xzyw*sh.xxyy ;
    vec4 a1 = b1.xzyw + s1.xzyw*sh.zzww ;

    vec3 p0 = vec3(a0.xy,h.x);
    vec3 p1 = vec3(a0.zw,h.y);
    vec3 p2 = vec3(a1.xy,h.z);
    vec3 p3 = vec3(a1.zw,h.w);

    //Normalise gradients
    vec4 norm = taylorInvSqrt(vec4(dot(p0,p0), dot(p1,p1), dot(p2, p2), dot(p3,p3)));
    p0 *= norm.x;
    p1 *= norm.y;
    p2 *= norm.z;
    p3 *= norm.w;

    // Mix final noise value
    vec4 m = max(0.6 - vec4(dot(x0,x0), dot(x1,x1), dot(x2,x2), dot(x3,x3)), 0.0);
    m = m * m;
    return 42.0 * dot( m*m, vec4( dot(p0,x0), dot(p1,x1),
                                dot(p2,x2), dot(p3,x3) ) );
}

vec3 snoiseVec3( vec3 x ){

  float s  = snoise(vec3( x ));
  float s1 = snoise(vec3( x.y - 19.1 , x.z + 33.4 , x.x + 47.2 ));
  float s2 = snoise(vec3( x.z + 74.2 , x.x - 124.5 , x.y + 99.4 ));
  vec3 c = vec3( s , s1 , s2 );
  return c;

}


vec3 curlNoise( vec3 p ){
  
  const float e = .1;
  vec3 dx = vec3( e   , 0.0 , 0.0 );
  vec3 dy = vec3( 0.0 , e   , 0.0 );
  vec3 dz = vec3( 0.0 , 0.0 , e   );

  vec3 p_x0 = snoiseVec3( p - dx );
  vec3 p_x1 = snoiseVec3( p + dx );
  vec3 p_y0 = snoiseVec3( p - dy );
  vec3 p_y1 = snoiseVec3( p + dy );
  vec3 p_z0 = snoiseVec3( p - dz );
  vec3 p_z1 = snoiseVec3( p + dz );

  float x = p_y1.z - p_y0.z - p_z1.y + p_z0.y;
  float y = p_z1.x - p_z0.x - p_x1.z + p_x0.z;
  float z = p_x1.y - p_x0.y - p_y1.x + p_y0.x;

  const float divisor = 1.0 / ( 2.0 * e );
  return normalize( vec3( x , y , z ) * divisor );

}