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GLSL Noise Algorithms

Generic 1,2,3 Noise

float rand(float n){return fract(sin(n) * 43758.5453123);}

float noise(float p){
	float fl = floor(p);
  float fc = fract(p);
	return mix(rand(fl), rand(fl + 1.0), fc);
}
	
float noise(vec2 n) {
	const vec2 d = vec2(0.0, 1.0);
  vec2 b = floor(n), f = smoothstep(vec2(0.0), vec2(1.0), fract(n));
	return mix(mix(rand(b), rand(b + d.yx), f.x), mix(rand(b + d.xy), rand(b + d.yy), f.x), f.y);
}
float rand(vec2 n) { 
	return fract(sin(dot(n, vec2(12.9898, 4.1414))) * 43758.5453);
}

float noise(vec2 p){
	vec2 ip = floor(p);
	vec2 u = fract(p);
	u = u*u*(3.0-2.0*u);
	
	float res = mix(
		mix(rand(ip),rand(ip+vec2(1.0,0.0)),u.x),
		mix(rand(ip+vec2(0.0,1.0)),rand(ip+vec2(1.0,1.0)),u.x),u.y);
	return res*res;
}
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);
}
//	<https://www.shadertoy.com/view/4dS3Wd>
//	By Morgan McGuire @morgan3d, http://graphicscodex.com
//
float hash(float n) { return fract(sin(n) * 1e4); }
float hash(vec2 p) { return fract(1e4 * sin(17.0 * p.x + p.y * 0.1) * (0.1 + abs(sin(p.y * 13.0 + p.x)))); }

float noise(float x) {
	float i = floor(x);
	float f = fract(x);
	float u = f * f * (3.0 - 2.0 * f);
	return mix(hash(i), hash(i + 1.0), u);
}

float noise(vec2 x) {
	vec2 i = floor(x);
	vec2 f = fract(x);

	// Four corners in 2D of a tile
	float a = hash(i);
	float b = hash(i + vec2(1.0, 0.0));
	float c = hash(i + vec2(0.0, 1.0));
	float d = hash(i + vec2(1.0, 1.0));

	// Simple 2D lerp using smoothstep envelope between the values.
	// return vec3(mix(mix(a, b, smoothstep(0.0, 1.0, f.x)),
	//			mix(c, d, smoothstep(0.0, 1.0, f.x)),
	//			smoothstep(0.0, 1.0, f.y)));

	// Same code, with the clamps in smoothstep and common subexpressions
	// optimized away.
	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;
}

// This one has non-ideal tiling properties that I'm still tuning
float noise(vec3 x) {
	const vec3 step = vec3(110, 241, 171);

	vec3 i = floor(x);
	vec3 f = fract(x);
 
	// For performance, compute the base input to a 1D hash from the integer part of the argument and the 
	// incremental change to the 1D based on the 3D -> 1D wrapping
    float n = dot(i, step);

	vec3 u = f * f * (3.0 - 2.0 * f);
	return mix(mix(mix( hash(n + dot(step, vec3(0, 0, 0))), hash(n + dot(step, vec3(1, 0, 0))), u.x),
                   mix( hash(n + dot(step, vec3(0, 1, 0))), hash(n + dot(step, vec3(1, 1, 0))), u.x), u.y),
               mix(mix( hash(n + dot(step, vec3(0, 0, 1))), hash(n + dot(step, vec3(1, 0, 1))), u.x),
                   mix( hash(n + dot(step, vec3(0, 1, 1))), hash(n + dot(step, vec3(1, 1, 1))), u.x), u.y), u.z);
}

Perlin Noise

float rand(vec2 c){
	return fract(sin(dot(c.xy ,vec2(12.9898,78.233))) * 43758.5453);
}

float noise(vec2 p, float freq ){
	float unit = screenWidth/freq;
	vec2 ij = floor(p/unit);
	vec2 xy = mod(p,unit)/unit;
	//xy = 3.*xy*xy-2.*xy*xy*xy;
	xy = .5*(1.-cos(PI*xy));
	float a = rand((ij+vec2(0.,0.)));
	float b = rand((ij+vec2(1.,0.)));
	float c = rand((ij+vec2(0.,1.)));
	float d = rand((ij+vec2(1.,1.)));
	float x1 = mix(a, b, xy.x);
	float x2 = mix(c, d, xy.x);
	return mix(x1, x2, xy.y);
}

float pNoise(vec2 p, int res){
	float persistance = .5;
	float n = 0.;
	float normK = 0.;
	float f = 4.;
	float amp = 1.;
	int iCount = 0;
	for (int i = 0; i<50; i++){
		n+=amp*noise(p, f);
		f*=2.;
		normK+=amp;
		amp*=persistance;
		if (iCount == res) break;
		iCount++;
	}
	float nf = n/normK;
	return nf*nf*nf*nf;
}
#define M_PI 3.14159265358979323846

float rand(vec2 co){return fract(sin(dot(co.xy ,vec2(12.9898,78.233))) * 43758.5453);}
float rand (vec2 co, float l) {return rand(vec2(rand(co), l));}
float rand (vec2 co, float l, float t) {return rand(vec2(rand(co, l), t));}

float perlin(vec2 p, float dim, float time) {
	vec2 pos = floor(p * dim);
	vec2 posx = pos + vec2(1.0, 0.0);
	vec2 posy = pos + vec2(0.0, 1.0);
	vec2 posxy = pos + vec2(1.0);
	
	float c = rand(pos, dim, time);
	float cx = rand(posx, dim, time);
	float cy = rand(posy, dim, time);
	float cxy = rand(posxy, dim, time);
	
	vec2 d = fract(p * dim);
	d = -0.5 * cos(d * M_PI) + 0.5;
	
	float ccx = mix(c, cx, d.x);
	float cycxy = mix(cy, cxy, d.x);
	float center = mix(ccx, cycxy, d.y);
	
	return center * 2.0 - 1.0;
}

// p must be normalized!
float perlin(vec2 p, float dim) {
	
	/*vec2 pos = floor(p * dim);
	vec2 posx = pos + vec2(1.0, 0.0);
	vec2 posy = pos + vec2(0.0, 1.0);
	vec2 posxy = pos + vec2(1.0);
	
	// For exclusively black/white noise
	/*float c = step(rand(pos, dim), 0.5);
	float cx = step(rand(posx, dim), 0.5);
	float cy = step(rand(posy, dim), 0.5);
	float cxy = step(rand(posxy, dim), 0.5);*/
	
	/*float c = rand(pos, dim);
	float cx = rand(posx, dim);
	float cy = rand(posy, dim);
	float cxy = rand(posxy, dim);
	
	vec2 d = fract(p * dim);
	d = -0.5 * cos(d * M_PI) + 0.5;
	
	float ccx = mix(c, cx, d.x);
	float cycxy = mix(cy, cxy, d.x);
	float center = mix(ccx, cycxy, d.y);
	
	return center * 2.0 - 1.0;*/
	return perlin(p, dim, 0.0);
}

Classic Perlin Noise

//	Classic Perlin 2D Noise 
//	by Stefan Gustavson
//
vec2 fade(vec2 t) {return t*t*t*(t*(t*6.0-15.0)+10.0);}

float cnoise(vec2 P){
  vec4 Pi = floor(P.xyxy) + vec4(0.0, 0.0, 1.0, 1.0);
  vec4 Pf = fract(P.xyxy) - vec4(0.0, 0.0, 1.0, 1.0);
  Pi = mod(Pi, 289.0); // To avoid truncation effects in permutation
  vec4 ix = Pi.xzxz;
  vec4 iy = Pi.yyww;
  vec4 fx = Pf.xzxz;
  vec4 fy = Pf.yyww;
  vec4 i = permute(permute(ix) + iy);
  vec4 gx = 2.0 * fract(i * 0.0243902439) - 1.0; // 1/41 = 0.024...
  vec4 gy = abs(gx) - 0.5;
  vec4 tx = floor(gx + 0.5);
  gx = gx - tx;
  vec2 g00 = vec2(gx.x,gy.x);
  vec2 g10 = vec2(gx.y,gy.y);
  vec2 g01 = vec2(gx.z,gy.z);
  vec2 g11 = vec2(gx.w,gy.w);
  vec4 norm = 1.79284291400159 - 0.85373472095314 * 
    vec4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11));
  g00 *= norm.x;
  g01 *= norm.y;
  g10 *= norm.z;
  g11 *= norm.w;
  float n00 = dot(g00, vec2(fx.x, fy.x));
  float n10 = dot(g10, vec2(fx.y, fy.y));
  float n01 = dot(g01, vec2(fx.z, fy.z));
  float n11 = dot(g11, vec2(fx.w, fy.w));
  vec2 fade_xy = fade(Pf.xy);
  vec2 n_x = mix(vec2(n00, n01), vec2(n10, n11), fade_xy.x);
  float n_xy = mix(n_x.x, n_x.y, fade_xy.y);
  return 2.3 * n_xy;
}
//	Classic Perlin 3D Noise 
//	by Stefan Gustavson
//
vec4 permute(vec4 x){return mod(((x*34.0)+1.0)*x, 289.0);}
vec4 taylorInvSqrt(vec4 r){return 1.79284291400159 - 0.85373472095314 * r;}
vec3 fade(vec3 t) {return t*t*t*(t*(t*6.0-15.0)+10.0);}

float cnoise(vec3 P){
  vec3 Pi0 = floor(P); // Integer part for indexing
  vec3 Pi1 = Pi0 + vec3(1.0); // Integer part + 1
  Pi0 = mod(Pi0, 289.0);
  Pi1 = mod(Pi1, 289.0);
  vec3 Pf0 = fract(P); // Fractional part for interpolation
  vec3 Pf1 = Pf0 - vec3(1.0); // Fractional part - 1.0
  vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
  vec4 iy = vec4(Pi0.yy, Pi1.yy);
  vec4 iz0 = Pi0.zzzz;
  vec4 iz1 = Pi1.zzzz;

  vec4 ixy = permute(permute(ix) + iy);
  vec4 ixy0 = permute(ixy + iz0);
  vec4 ixy1 = permute(ixy + iz1);

  vec4 gx0 = ixy0 / 7.0;
  vec4 gy0 = fract(floor(gx0) / 7.0) - 0.5;
  gx0 = fract(gx0);
  vec4 gz0 = vec4(0.5) - abs(gx0) - abs(gy0);
  vec4 sz0 = step(gz0, vec4(0.0));
  gx0 -= sz0 * (step(0.0, gx0) - 0.5);
  gy0 -= sz0 * (step(0.0, gy0) - 0.5);

  vec4 gx1 = ixy1 / 7.0;
  vec4 gy1 = fract(floor(gx1) / 7.0) - 0.5;
  gx1 = fract(gx1);
  vec4 gz1 = vec4(0.5) - abs(gx1) - abs(gy1);
  vec4 sz1 = step(gz1, vec4(0.0));
  gx1 -= sz1 * (step(0.0, gx1) - 0.5);
  gy1 -= sz1 * (step(0.0, gy1) - 0.5);

  vec3 g000 = vec3(gx0.x,gy0.x,gz0.x);
  vec3 g100 = vec3(gx0.y,gy0.y,gz0.y);
  vec3 g010 = vec3(gx0.z,gy0.z,gz0.z);
  vec3 g110 = vec3(gx0.w,gy0.w,gz0.w);
  vec3 g001 = vec3(gx1.x,gy1.x,gz1.x);
  vec3 g101 = vec3(gx1.y,gy1.y,gz1.y);
  vec3 g011 = vec3(gx1.z,gy1.z,gz1.z);
  vec3 g111 = vec3(gx1.w,gy1.w,gz1.w);

  vec4 norm0 = taylorInvSqrt(vec4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
  g000 *= norm0.x;
  g010 *= norm0.y;
  g100 *= norm0.z;
  g110 *= norm0.w;
  vec4 norm1 = taylorInvSqrt(vec4(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
  g001 *= norm1.x;
  g011 *= norm1.y;
  g101 *= norm1.z;
  g111 *= norm1.w;

  float n000 = dot(g000, Pf0);
  float n100 = dot(g100, vec3(Pf1.x, Pf0.yz));
  float n010 = dot(g010, vec3(Pf0.x, Pf1.y, Pf0.z));
  float n110 = dot(g110, vec3(Pf1.xy, Pf0.z));
  float n001 = dot(g001, vec3(Pf0.xy, Pf1.z));
  float n101 = dot(g101, vec3(Pf1.x, Pf0.y, Pf1.z));
  float n011 = dot(g011, vec3(Pf0.x, Pf1.yz));
  float n111 = dot(g111, Pf1);

  vec3 fade_xyz = fade(Pf0);
  vec4 n_z = mix(vec4(n000, n100, n010, n110), vec4(n001, n101, n011, n111), fade_xyz.z);
  vec2 n_yz = mix(n_z.xy, n_z.zw, fade_xyz.y);
  float n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); 
  return 2.2 * n_xyz;
}
//	Classic Perlin 3D Noise 
//	by Stefan Gustavson
//
vec4 permute(vec4 x){return mod(((x*34.0)+1.0)*x, 289.0);}
vec4 taylorInvSqrt(vec4 r){return 1.79284291400159 - 0.85373472095314 * r;}
vec4 fade(vec4 t) {return t*t*t*(t*(t*6.0-15.0)+10.0);}

float cnoise(vec4 P){
  vec4 Pi0 = floor(P); // Integer part for indexing
  vec4 Pi1 = Pi0 + 1.0; // Integer part + 1
  Pi0 = mod(Pi0, 289.0);
  Pi1 = mod(Pi1, 289.0);
  vec4 Pf0 = fract(P); // Fractional part for interpolation
  vec4 Pf1 = Pf0 - 1.0; // Fractional part - 1.0
  vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
  vec4 iy = vec4(Pi0.yy, Pi1.yy);
  vec4 iz0 = vec4(Pi0.zzzz);
  vec4 iz1 = vec4(Pi1.zzzz);
  vec4 iw0 = vec4(Pi0.wwww);
  vec4 iw1 = vec4(Pi1.wwww);

  vec4 ixy = permute(permute(ix) + iy);
  vec4 ixy0 = permute(ixy + iz0);
  vec4 ixy1 = permute(ixy + iz1);
  vec4 ixy00 = permute(ixy0 + iw0);
  vec4 ixy01 = permute(ixy0 + iw1);
  vec4 ixy10 = permute(ixy1 + iw0);
  vec4 ixy11 = permute(ixy1 + iw1);

  vec4 gx00 = ixy00 / 7.0;
  vec4 gy00 = floor(gx00) / 7.0;
  vec4 gz00 = floor(gy00) / 6.0;
  gx00 = fract(gx00) - 0.5;
  gy00 = fract(gy00) - 0.5;
  gz00 = fract(gz00) - 0.5;
  vec4 gw00 = vec4(0.75) - abs(gx00) - abs(gy00) - abs(gz00);
  vec4 sw00 = step(gw00, vec4(0.0));
  gx00 -= sw00 * (step(0.0, gx00) - 0.5);
  gy00 -= sw00 * (step(0.0, gy00) - 0.5);

  vec4 gx01 = ixy01 / 7.0;
  vec4 gy01 = floor(gx01) / 7.0;
  vec4 gz01 = floor(gy01) / 6.0;
  gx01 = fract(gx01) - 0.5;
  gy01 = fract(gy01) - 0.5;
  gz01 = fract(gz01) - 0.5;
  vec4 gw01 = vec4(0.75) - abs(gx01) - abs(gy01) - abs(gz01);
  vec4 sw01 = step(gw01, vec4(0.0));
  gx01 -= sw01 * (step(0.0, gx01) - 0.5);
  gy01 -= sw01 * (step(0.0, gy01) - 0.5);

  vec4 gx10 = ixy10 / 7.0;
  vec4 gy10 = floor(gx10) / 7.0;
  vec4 gz10 = floor(gy10) / 6.0;
  gx10 = fract(gx10) - 0.5;
  gy10 = fract(gy10) - 0.5;
  gz10 = fract(gz10) - 0.5;
  vec4 gw10 = vec4(0.75) - abs(gx10) - abs(gy10) - abs(gz10);
  vec4 sw10 = step(gw10, vec4(0.0));
  gx10 -= sw10 * (step(0.0, gx10) - 0.5);
  gy10 -= sw10 * (step(0.0, gy10) - 0.5);

  vec4 gx11 = ixy11 / 7.0;
  vec4 gy11 = floor(gx11) / 7.0;
  vec4 gz11 = floor(gy11) / 6.0;
  gx11 = fract(gx11) - 0.5;
  gy11 = fract(gy11) - 0.5;
  gz11 = fract(gz11) - 0.5;
  vec4 gw11 = vec4(0.75) - abs(gx11) - abs(gy11) - abs(gz11);
  vec4 sw11 = step(gw11, vec4(0.0));
  gx11 -= sw11 * (step(0.0, gx11) - 0.5);
  gy11 -= sw11 * (step(0.0, gy11) - 0.5);

  vec4 g0000 = vec4(gx00.x,gy00.x,gz00.x,gw00.x);
  vec4 g1000 = vec4(gx00.y,gy00.y,gz00.y,gw00.y);
  vec4 g0100 = vec4(gx00.z,gy00.z,gz00.z,gw00.z);
  vec4 g1100 = vec4(gx00.w,gy00.w,gz00.w,gw00.w);
  vec4 g0010 = vec4(gx10.x,gy10.x,gz10.x,gw10.x);
  vec4 g1010 = vec4(gx10.y,gy10.y,gz10.y,gw10.y);
  vec4 g0110 = vec4(gx10.z,gy10.z,gz10.z,gw10.z);
  vec4 g1110 = vec4(gx10.w,gy10.w,gz10.w,gw10.w);
  vec4 g0001 = vec4(gx01.x,gy01.x,gz01.x,gw01.x);
  vec4 g1001 = vec4(gx01.y,gy01.y,gz01.y,gw01.y);
  vec4 g0101 = vec4(gx01.z,gy01.z,gz01.z,gw01.z);
  vec4 g1101 = vec4(gx01.w,gy01.w,gz01.w,gw01.w);
  vec4 g0011 = vec4(gx11.x,gy11.x,gz11.x,gw11.x);
  vec4 g1011 = vec4(gx11.y,gy11.y,gz11.y,gw11.y);
  vec4 g0111 = vec4(gx11.z,gy11.z,gz11.z,gw11.z);
  vec4 g1111 = vec4(gx11.w,gy11.w,gz11.w,gw11.w);

  vec4 norm00 = taylorInvSqrt(vec4(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100)));
  g0000 *= norm00.x;
  g0100 *= norm00.y;
  g1000 *= norm00.z;
  g1100 *= norm00.w;

  vec4 norm01 = taylorInvSqrt(vec4(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101)));
  g0001 *= norm01.x;
  g0101 *= norm01.y;
  g1001 *= norm01.z;
  g1101 *= norm01.w;

  vec4 norm10 = taylorInvSqrt(vec4(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110)));
  g0010 *= norm10.x;
  g0110 *= norm10.y;
  g1010 *= norm10.z;
  g1110 *= norm10.w;

  vec4 norm11 = taylorInvSqrt(vec4(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111)));
  g0011 *= norm11.x;
  g0111 *= norm11.y;
  g1011 *= norm11.z;
  g1111 *= norm11.w;

  float n0000 = dot(g0000, Pf0);
  float n1000 = dot(g1000, vec4(Pf1.x, Pf0.yzw));
  float n0100 = dot(g0100, vec4(Pf0.x, Pf1.y, Pf0.zw));
  float n1100 = dot(g1100, vec4(Pf1.xy, Pf0.zw));
  float n0010 = dot(g0010, vec4(Pf0.xy, Pf1.z, Pf0.w));
  float n1010 = dot(g1010, vec4(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
  float n0110 = dot(g0110, vec4(Pf0.x, Pf1.yz, Pf0.w));
  float n1110 = dot(g1110, vec4(Pf1.xyz, Pf0.w));
  float n0001 = dot(g0001, vec4(Pf0.xyz, Pf1.w));
  float n1001 = dot(g1001, vec4(Pf1.x, Pf0.yz, Pf1.w));
  float n0101 = dot(g0101, vec4(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
  float n1101 = dot(g1101, vec4(Pf1.xy, Pf0.z, Pf1.w));
  float n0011 = dot(g0011, vec4(Pf0.xy, Pf1.zw));
  float n1011 = dot(g1011, vec4(Pf1.x, Pf0.y, Pf1.zw));
  float n0111 = dot(g0111, vec4(Pf0.x, Pf1.yzw));
  float n1111 = dot(g1111, Pf1);

  vec4 fade_xyzw = fade(Pf0);
  vec4 n_0w = mix(vec4(n0000, n1000, n0100, n1100), vec4(n0001, n1001, n0101, n1101), fade_xyzw.w);
  vec4 n_1w = mix(vec4(n0010, n1010, n0110, n1110), vec4(n0011, n1011, n0111, n1111), fade_xyzw.w);
  vec4 n_zw = mix(n_0w, n_1w, fade_xyzw.z);
  vec2 n_yzw = mix(n_zw.xy, n_zw.zw, fade_xyzw.y);
  float n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x);
  return 2.2 * n_xyzw;
}

// Classic Perlin noise, periodic version
float cnoise(vec4 P, vec4 rep){
  vec4 Pi0 = mod(floor(P), rep); // Integer part modulo rep
  vec4 Pi1 = mod(Pi0 + 1.0, rep); // Integer part + 1 mod rep
  vec4 Pf0 = fract(P); // Fractional part for interpolation
  vec4 Pf1 = Pf0 - 1.0; // Fractional part - 1.0
  vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
  vec4 iy = vec4(Pi0.yy, Pi1.yy);
  vec4 iz0 = vec4(Pi0.zzzz);
  vec4 iz1 = vec4(Pi1.zzzz);
  vec4 iw0 = vec4(Pi0.wwww);
  vec4 iw1 = vec4(Pi1.wwww);

  vec4 ixy = permute(permute(ix) + iy);
  vec4 ixy0 = permute(ixy + iz0);
  vec4 ixy1 = permute(ixy + iz1);
  vec4 ixy00 = permute(ixy0 + iw0);
  vec4 ixy01 = permute(ixy0 + iw1);
  vec4 ixy10 = permute(ixy1 + iw0);
  vec4 ixy11 = permute(ixy1 + iw1);

  vec4 gx00 = ixy00 / 7.0;
  vec4 gy00 = floor(gx00) / 7.0;
  vec4 gz00 = floor(gy00) / 6.0;
  gx00 = fract(gx00) - 0.5;
  gy00 = fract(gy00) - 0.5;
  gz00 = fract(gz00) - 0.5;
  vec4 gw00 = vec4(0.75) - abs(gx00) - abs(gy00) - abs(gz00);
  vec4 sw00 = step(gw00, vec4(0.0));
  gx00 -= sw00 * (step(0.0, gx00) - 0.5);
  gy00 -= sw00 * (step(0.0, gy00) - 0.5);

  vec4 gx01 = ixy01 / 7.0;
  vec4 gy01 = floor(gx01) / 7.0;
  vec4 gz01 = floor(gy01) / 6.0;
  gx01 = fract(gx01) - 0.5;
  gy01 = fract(gy01) - 0.5;
  gz01 = fract(gz01) - 0.5;
  vec4 gw01 = vec4(0.75) - abs(gx01) - abs(gy01) - abs(gz01);
  vec4 sw01 = step(gw01, vec4(0.0));
  gx01 -= sw01 * (step(0.0, gx01) - 0.5);
  gy01 -= sw01 * (step(0.0, gy01) - 0.5);

  vec4 gx10 = ixy10 / 7.0;
  vec4 gy10 = floor(gx10) / 7.0;
  vec4 gz10 = floor(gy10) / 6.0;
  gx10 = fract(gx10) - 0.5;
  gy10 = fract(gy10) - 0.5;
  gz10 = fract(gz10) - 0.5;
  vec4 gw10 = vec4(0.75) - abs(gx10) - abs(gy10) - abs(gz10);
  vec4 sw10 = step(gw10, vec4(0.0));
  gx10 -= sw10 * (step(0.0, gx10) - 0.5);
  gy10 -= sw10 * (step(0.0, gy10) - 0.5);

  vec4 gx11 = ixy11 / 7.0;
  vec4 gy11 = floor(gx11) / 7.0;
  vec4 gz11 = floor(gy11) / 6.0;
  gx11 = fract(gx11) - 0.5;
  gy11 = fract(gy11) - 0.5;
  gz11 = fract(gz11) - 0.5;
  vec4 gw11 = vec4(0.75) - abs(gx11) - abs(gy11) - abs(gz11);
  vec4 sw11 = step(gw11, vec4(0.0));
  gx11 -= sw11 * (step(0.0, gx11) - 0.5);
  gy11 -= sw11 * (step(0.0, gy11) - 0.5);

  vec4 g0000 = vec4(gx00.x,gy00.x,gz00.x,gw00.x);
  vec4 g1000 = vec4(gx00.y,gy00.y,gz00.y,gw00.y);
  vec4 g0100 = vec4(gx00.z,gy00.z,gz00.z,gw00.z);
  vec4 g1100 = vec4(gx00.w,gy00.w,gz00.w,gw00.w);
  vec4 g0010 = vec4(gx10.x,gy10.x,gz10.x,gw10.x);
  vec4 g1010 = vec4(gx10.y,gy10.y,gz10.y,gw10.y);
  vec4 g0110 = vec4(gx10.z,gy10.z,gz10.z,gw10.z);
  vec4 g1110 = vec4(gx10.w,gy10.w,gz10.w,gw10.w);
  vec4 g0001 = vec4(gx01.x,gy01.x,gz01.x,gw01.x);
  vec4 g1001 = vec4(gx01.y,gy01.y,gz01.y,gw01.y);
  vec4 g0101 = vec4(gx01.z,gy01.z,gz01.z,gw01.z);
  vec4 g1101 = vec4(gx01.w,gy01.w,gz01.w,gw01.w);
  vec4 g0011 = vec4(gx11.x,gy11.x,gz11.x,gw11.x);
  vec4 g1011 = vec4(gx11.y,gy11.y,gz11.y,gw11.y);
  vec4 g0111 = vec4(gx11.z,gy11.z,gz11.z,gw11.z);
  vec4 g1111 = vec4(gx11.w,gy11.w,gz11.w,gw11.w);

  vec4 norm00 = taylorInvSqrt(vec4(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100)));
  g0000 *= norm00.x;
  g0100 *= norm00.y;
  g1000 *= norm00.z;
  g1100 *= norm00.w;

  vec4 norm01 = taylorInvSqrt(vec4(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101)));
  g0001 *= norm01.x;
  g0101 *= norm01.y;
  g1001 *= norm01.z;
  g1101 *= norm01.w;

  vec4 norm10 = taylorInvSqrt(vec4(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110)));
  g0010 *= norm10.x;
  g0110 *= norm10.y;
  g1010 *= norm10.z;
  g1110 *= norm10.w;

  vec4 norm11 = taylorInvSqrt(vec4(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111)));
  g0011 *= norm11.x;
  g0111 *= norm11.y;
  g1011 *= norm11.z;
  g1111 *= norm11.w;

  float n0000 = dot(g0000, Pf0);
  float n1000 = dot(g1000, vec4(Pf1.x, Pf0.yzw));
  float n0100 = dot(g0100, vec4(Pf0.x, Pf1.y, Pf0.zw));
  float n1100 = dot(g1100, vec4(Pf1.xy, Pf0.zw));
  float n0010 = dot(g0010, vec4(Pf0.xy, Pf1.z, Pf0.w));
  float n1010 = dot(g1010, vec4(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
  float n0110 = dot(g0110, vec4(Pf0.x, Pf1.yz, Pf0.w));
  float n1110 = dot(g1110, vec4(Pf1.xyz, Pf0.w));
  float n0001 = dot(g0001, vec4(Pf0.xyz, Pf1.w));
  float n1001 = dot(g1001, vec4(Pf1.x, Pf0.yz, Pf1.w));
  float n0101 = dot(g0101, vec4(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
  float n1101 = dot(g1101, vec4(Pf1.xy, Pf0.z, Pf1.w));
  float n0011 = dot(g0011, vec4(Pf0.xy, Pf1.zw));
  float n1011 = dot(g1011, vec4(Pf1.x, Pf0.y, Pf1.zw));
  float n0111 = dot(g0111, vec4(Pf0.x, Pf1.yzw));
  float n1111 = dot(g1111, Pf1);

  vec4 fade_xyzw = fade(Pf0);
  vec4 n_0w = mix(vec4(n0000, n1000, n0100, n1100), vec4(n0001, n1001, n0101, n1101), fade_xyzw.w);
  vec4 n_1w = mix(vec4(n0010, n1010, n0110, n1110), vec4(n0011, n1011, n0111, n1111), fade_xyzw.w);
  vec4 n_zw = mix(n_0w, n_1w, fade_xyzw.z);
  vec2 n_yzw = mix(n_zw.xy, n_zw.zw, fade_xyzw.y);
  float n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x);
  return 2.2 * n_xyzw;
}

Simplex Noise

// Simplex 2D noise
//
vec3 permute(vec3 x) { return mod(((x*34.0)+1.0)*x, 289.0); }

float snoise(vec2 v){
  const vec4 C = vec4(0.211324865405187, 0.366025403784439,
           -0.577350269189626, 0.024390243902439);
  vec2 i  = floor(v + dot(v, C.yy) );
  vec2 x0 = v -   i + dot(i, C.xx);
  vec2 i1;
  i1 = (x0.x > x0.y) ? vec2(1.0, 0.0) : vec2(0.0, 1.0);
  vec4 x12 = x0.xyxy + C.xxzz;
  x12.xy -= i1;
  i = mod(i, 289.0);
  vec3 p = permute( permute( i.y + vec3(0.0, i1.y, 1.0 ))
  + i.x + vec3(0.0, i1.x, 1.0 ));
  vec3 m = max(0.5 - vec3(dot(x0,x0), dot(x12.xy,x12.xy),
    dot(x12.zw,x12.zw)), 0.0);
  m = m*m ;
  m = m*m ;
  vec3 x = 2.0 * fract(p * C.www) - 1.0;
  vec3 h = abs(x) - 0.5;
  vec3 ox = floor(x + 0.5);
  vec3 a0 = x - ox;
  m *= 1.79284291400159 - 0.85373472095314 * ( a0*a0 + h*h );
  vec3 g;
  g.x  = a0.x  * x0.x  + h.x  * x0.y;
  g.yz = a0.yz * x12.xz + h.yz * x12.yw;
  return 130.0 * dot(m, g);
}
//	Simplex 3D Noise 
//	by Ian McEwan, Ashima Arts
//
vec4 permute(vec4 x){return mod(((x*34.0)+1.0)*x, 289.0);}
vec4 taylorInvSqrt(vec4 r){return 1.79284291400159 - 0.85373472095314 * r;}

float snoise(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 * C 
  vec3 x1 = x0 - i1 + 1.0 * C.xxx;
  vec3 x2 = x0 - i2 + 2.0 * C.xxx;
  vec3 x3 = x0 - 1. + 3.0 * C.xxx;

// Permutations
  i = mod(i, 289.0 ); 
  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
// ( N*N points uniformly over a square, mapped onto an octahedron.)
  float n_ = 1.0/7.0; // N=7
  vec3  ns = n_ * D.wyz - D.xzx;

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

  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 = 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) ) );
}
//	Simplex 4D Noise 
//	by Ian McEwan, Ashima Arts
//
vec4 permute(vec4 x){return mod(((x*34.0)+1.0)*x, 289.0);}
float permute(float x){return floor(mod(((x*34.0)+1.0)*x, 289.0));}
vec4 taylorInvSqrt(vec4 r){return 1.79284291400159 - 0.85373472095314 * r;}
float taylorInvSqrt(float r){return 1.79284291400159 - 0.85373472095314 * r;}

vec4 grad4(float j, vec4 ip){
  const vec4 ones = vec4(1.0, 1.0, 1.0, -1.0);
  vec4 p,s;

  p.xyz = floor( fract (vec3(j) * ip.xyz) * 7.0) * ip.z - 1.0;
  p.w = 1.5 - dot(abs(p.xyz), ones.xyz);
  s = vec4(lessThan(p, vec4(0.0)));
  p.xyz = p.xyz + (s.xyz*2.0 - 1.0) * s.www; 

  return p;
}

float snoise(vec4 v){
  const vec2  C = vec2( 0.138196601125010504,  // (5 - sqrt(5))/20  G4
                        0.309016994374947451); // (sqrt(5) - 1)/4   F4
// First corner
  vec4 i  = floor(v + dot(v, C.yyyy) );
  vec4 x0 = v -   i + dot(i, C.xxxx);

// Other corners

// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
  vec4 i0;

  vec3 isX = step( x0.yzw, x0.xxx );
  vec3 isYZ = step( x0.zww, x0.yyz );
//  i0.x = dot( isX, vec3( 1.0 ) );
  i0.x = isX.x + isX.y + isX.z;
  i0.yzw = 1.0 - isX;

//  i0.y += dot( isYZ.xy, vec2( 1.0 ) );
  i0.y += isYZ.x + isYZ.y;
  i0.zw += 1.0 - isYZ.xy;

  i0.z += isYZ.z;
  i0.w += 1.0 - isYZ.z;

  // i0 now contains the unique values 0,1,2,3 in each channel
  vec4 i3 = clamp( i0, 0.0, 1.0 );
  vec4 i2 = clamp( i0-1.0, 0.0, 1.0 );
  vec4 i1 = clamp( i0-2.0, 0.0, 1.0 );

  //  x0 = x0 - 0.0 + 0.0 * C 
  vec4 x1 = x0 - i1 + 1.0 * C.xxxx;
  vec4 x2 = x0 - i2 + 2.0 * C.xxxx;
  vec4 x3 = x0 - i3 + 3.0 * C.xxxx;
  vec4 x4 = x0 - 1.0 + 4.0 * C.xxxx;

// Permutations
  i = mod(i, 289.0); 
  float j0 = permute( permute( permute( permute(i.w) + i.z) + i.y) + i.x);
  vec4 j1 = permute( permute( permute( permute (
             i.w + vec4(i1.w, i2.w, i3.w, 1.0 ))
           + i.z + vec4(i1.z, i2.z, i3.z, 1.0 ))
           + i.y + vec4(i1.y, i2.y, i3.y, 1.0 ))
           + i.x + vec4(i1.x, i2.x, i3.x, 1.0 ));
// Gradients
// ( 7*7*6 points uniformly over a cube, mapped onto a 4-octahedron.)
// 7*7*6 = 294, which is close to the ring size 17*17 = 289.

  vec4 ip = vec4(1.0/294.0, 1.0/49.0, 1.0/7.0, 0.0) ;

  vec4 p0 = grad4(j0,   ip);
  vec4 p1 = grad4(j1.x, ip);
  vec4 p2 = grad4(j1.y, ip);
  vec4 p3 = grad4(j1.z, ip);
  vec4 p4 = grad4(j1.w, ip);

// 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;
  p4 *= taylorInvSqrt(dot(p4,p4));

// Mix contributions from the five corners
  vec3 m0 = max(0.6 - vec3(dot(x0,x0), dot(x1,x1), dot(x2,x2)), 0.0);
  vec2 m1 = max(0.6 - vec2(dot(x3,x3), dot(x4,x4)            ), 0.0);
  m0 = m0 * m0;
  m1 = m1 * m1;
  return 49.0 * ( dot(m0*m0, vec3( dot( p0, x0 ), dot( p1, x1 ), dot( p2, x2 )))
               + dot(m1*m1, vec2( dot( p3, x3 ), dot( p4, x4 ) ) ) ) ;

}
// 	<www.shadertoy.com/view/XsX3zB>
//	by Nikita Miropolskiy

/* discontinuous pseudorandom uniformly distributed in [-0.5, +0.5]^3 */
vec3 random3(vec3 c) {
	float j = 4096.0*sin(dot(c,vec3(17.0, 59.4, 15.0)));
	vec3 r;
	r.z = fract(512.0*j);
	j *= .125;
	r.x = fract(512.0*j);
	j *= .125;
	r.y = fract(512.0*j);
	return r-0.5;
}

const float F3 =  0.3333333;
const float G3 =  0.1666667;
float snoise(vec3 p) {

	vec3 s = floor(p + dot(p, vec3(F3)));
	vec3 x = p - s + dot(s, vec3(G3));
	 
	vec3 e = step(vec3(0.0), x - x.yzx);
	vec3 i1 = e*(1.0 - e.zxy);
	vec3 i2 = 1.0 - e.zxy*(1.0 - e);
	 	
	vec3 x1 = x - i1 + G3;
	vec3 x2 = x - i2 + 2.0*G3;
	vec3 x3 = x - 1.0 + 3.0*G3;
	 
	vec4 w, d;
	 
	w.x = dot(x, x);
	w.y = dot(x1, x1);
	w.z = dot(x2, x2);
	w.w = dot(x3, x3);
	 
	w = max(0.6 - w, 0.0);
	 
	d.x = dot(random3(s), x);
	d.y = dot(random3(s + i1), x1);
	d.z = dot(random3(s + i2), x2);
	d.w = dot(random3(s + 1.0), x3);
	 
	w *= w;
	w *= w;
	d *= w;
	 
	return dot(d, vec4(52.0));
}

float snoiseFractal(vec3 m) {
	return   0.5333333* snoise(m)
				+0.2666667* snoise(2.0*m)
				+0.1333333* snoise(4.0*m)
				+0.0666667* snoise(8.0*m);
}


NormalMap Noise

vec3 normalNoise(vec2 _st, float _zoom, float _speed){
	vec2 v1 = _st;
	vec2 v2 = _st;
	vec2 v3 = _st;
	float expon = pow(10.0, _zoom*2.0);
	v1 /= 1.0*expon;
	v2 /= 0.62*expon;
	v3 /= 0.83*expon;
	float n = time*_speed;
	float nr = (simplexNoise(vec3(v1, n)) + simplexNoise(vec3(v2, n)) + simplexNoise(vec3(v3, n))) / 6.0 + 0.5;
	n = time * _speed + 1000.0;
	float ng = (simplexNoise(vec3(v1, n)) + simplexNoise(vec3(v2, n)) + simplexNoise(vec3(v3, n))) / 6.0 + 0.5;
	return vec3(nr,ng,0.5);
}

VoroNoise

//	<https://www.shadertoy.com/view/Xd23Dh>
//	by inigo quilez <http://iquilezles.org/www/articles/voronoise/voronoise.htm>
//

vec3 hash3( vec2 p ){
    vec3 q = vec3( dot(p,vec2(127.1,311.7)), 
				   dot(p,vec2(269.5,183.3)), 
				   dot(p,vec2(419.2,371.9)) );
	return fract(sin(q)*43758.5453);
}

float iqnoise( in vec2 x, float u, float v ){
    vec2 p = floor(x);
    vec2 f = fract(x);
		
	float k = 1.0+63.0*pow(1.0-v,4.0);
	
	float va = 0.0;
	float wt = 0.0;
    for( int j=-2; j<=2; j++ )
    for( int i=-2; i<=2; i++ )
    {
        vec2 g = vec2( float(i),float(j) );
		vec3 o = hash3( p + g )*vec3(u,u,1.0);
		vec2 r = g - f + o.xy;
		float d = dot(r,r);
		float ww = pow( 1.0-smoothstep(0.0,1.414,sqrt(d)), k );
		va += o.z*ww;
		wt += ww;
    }
	
    return va/wt;
}

//	https://www.shadertoy.com/view/lsjGWD
//	by Pietro De Nicola
//
#define OCTAVES   		1		// 7
#define SWITCH_TIME 	60.0		// seconds

float t = time/SWITCH_TIME;

float function 			= mod(t,4.0);
bool  multiply_by_F1	= mod(t,8.0)  >= 4.0;
bool  inverse				= mod(t,16.0) >= 8.0;
float distance_type	= mod(t/16.0,4.0);

vec2 hash( vec2 p ){
	p = vec2( dot(p,vec2(127.1,311.7)),dot(p,vec2(269.5,183.3)));
	return fract(sin(p)*43758.5453);
}

float voronoi( in vec2 x ){
	vec2 n = floor( x );
	vec2 f = fract( x );
	
	float F1 = 8.0;
	float F2 = 8.0;
	
	for( int j=-1; j<=1; j++ )
		for( int i=-1; i<=1; i++ ){
			vec2 g = vec2(i,j);
			vec2 o = hash( n + g );

			o = 0.5 + 0.41*sin( time + 6.2831*o );	
			vec2 r = g - f + o;

		float d = 	distance_type < 1.0 ? dot(r,r)  :				// euclidean^2
				  	distance_type < 2.0 ? sqrt(dot(r,r)) :			// euclidean
					distance_type < 3.0 ? abs(r.x) + abs(r.y) :		// manhattan
					distance_type < 4.0 ? max(abs(r.x), abs(r.y)) :	// chebyshev
					0.0;

		if( d<F1 ) { 
			F2 = F1; 
			F1 = d; 
		} else if( d<F2 ) {
			F2 = d;
		}
    }
	
	float c = function < 1.0 ? F1 : 
			  function < 2.0 ? F2 : 
			  function < 3.0 ? F2-F1 :
			  function < 4.0 ? (F1+F2)/2.0 : 
			  0.0;
		
	if( multiply_by_F1 )	c *= F1;
	if( inverse )			c = 1.0 - c;
	
    return c;
}

float fbm( in vec2 p ){
	float s = 0.0;
	float m = 0.0;
	float a = 0.5;
	
	for( int i=0; i<OCTAVES; i++ ){
		s += a * voronoi(p);
		m += a;
		a *= 0.5;
		p *= 2.0;
	}
	return s/m;
}

// Use:
//		vec2 p = gl_FragCoord.xy/iResolution.xx;
//    float c = POWER*fbm( SCALE*p ) + BIAS;

Fractional Brownian motion

#define NUM_OCTAVES 5

float fbm(float x) {
	float v = 0.0;
	float a = 0.5;
	float shift = float(100);
	for (int i = 0; i < NUM_OCTAVES; ++i) {
		v += a * noise(x);
		x = x * 2.0 + shift;
		a *= 0.5;
	}
	return v;
}


float fbm(vec2 x) {
	float v = 0.0;
	float a = 0.5;
	vec2 shift = vec2(100);
	// Rotate to reduce axial bias
    mat2 rot = mat2(cos(0.5), sin(0.5), -sin(0.5), cos(0.50));
	for (int i = 0; i < NUM_OCTAVES; ++i) {
		v += a * noise(x);
		x = rot * x * 2.0 + shift;
		a *= 0.5;
	}
	return v;
}


float fbm(vec3 x) {
	float v = 0.0;
	float a = 0.5;
	vec3 shift = vec3(100);
	for (int i = 0; i < NUM_OCTAVES; ++i) {
		v += a * noise(x);
		x = x * 2.0 + shift;
		a *= 0.5;
	}
	return v;
}
// 	<https://www.shadertoy.com/view/MdX3Rr>
//	by inigo quilez
//
const mat2 m2 = mat2(0.8,-0.6,0.6,0.8);
float fbm( in vec2 p ){
    float f = 0.0;
    f += 0.5000*noise( p ); p = m2*p*2.02;
    f += 0.2500*noise( p ); p = m2*p*2.03;
    f += 0.1250*noise( p ); p = m2*p*2.01;
    f += 0.0625*noise( p );

    return f/0.9375;
}

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