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patriciogonzalezvivo/GLSL-Noise.md

Last active Jan 31, 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:

lxsmnsyc commented Mar 7, 2019

in the top most noise (Generic Noise), the second noise function has a 2-D vector 'b' that is passed to the function 'rand' which only accepts float type. I think this is a mistake.

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

akd-io commented Dec 14, 2019

Better to grab them from here

They are better explained there ; )

munrocket commented Jul 5, 2021

First and second noise literally the same. Second just refactored little bit and result are squared.
By the way, what license on noises that without the author?

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