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# patriciogonzalezvivo/GLSL-Noise.md

Last active Jan 27, 2023
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
//

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 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;}

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);

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;}

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 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 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 ));

// ( 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);

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;}

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 ));
// ( 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 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;
}
``````

Articles:

Examples:

### patriciogonzalezvivo commented Jul 5, 2021

Hi! This resource is very old/buggy and not with the right licenses. Please consider using this https://github.com/patriciogonzalezvivo/lygia/tree/main/generative

### asforever commented Aug 19, 2021

Why the constant is 43758.5453123