# LYGIA Shader Library

## pnoise (`lygia`/`generative`/`pnoise`)

Classic Perlin Noise with periodic variant https://github.com/stegu/webgl-noise

Dependencies:

Use:

``````pnoise(<vec2|vec3|vec4> pos, <vec2|vec3|vec4> periodic)
``````

Check it on Github

``````

#ifndef FNC_PNOISE
#define FNC_PNOISE
// Classic Perlin noise, periodic variant
float pnoise(in vec2 P, in vec2 rep) {
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, rep.xyxy); // To create noise with explicit period
Pi = mod289(Pi);        // 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 = fract(i * (1.0 / 41.0)) * 2.0 - 1.0 ;
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 = taylorInvSqrt(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 = quintic(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;
}

float pnoise(in vec3 P, in vec3 rep) {
vec3 Pi0 = mod(floor(P), rep); // Integer part, modulo period
vec3 Pi1 = mod(Pi0 + vec3(1.0), rep); // Integer part + 1, mod period
Pi0 = mod289(Pi0);
Pi1 = mod289(Pi1);
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 * (1.0 / 7.0);
vec4 gy0 = fract(floor(gx0) * (1.0 / 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 * (1.0 / 7.0);
vec4 gy1 = fract(floor(gx1) * (1.0 / 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 = quintic(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;
}

float pnoise(in vec4 P, in vec4 rep) {
vec4 Pi0 = mod(floor(P), rep); // Integer part modulo rep
vec4 Pi1 = mod(Pi0 + 1.0, rep); // Integer part + 1 mod rep
Pi0 = mod289(Pi0);
Pi1 = mod289(Pi1);
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 * (1.0 / 7.0);
vec4 gy00 = floor(gx00) * (1.0 / 7.0);
vec4 gz00 = floor(gy00) * (1.0 / 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 * (1.0 / 7.0);
vec4 gy01 = floor(gx01) * (1.0 / 7.0);
vec4 gz01 = floor(gy01) * (1.0 / 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 * (1.0 / 7.0);
vec4 gy10 = floor(gx10) * (1.0 / 7.0);
vec4 gz10 = floor(gy10) * (1.0 / 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 * (1.0 / 7.0);
vec4 gy11 = floor(gx11) * (1.0 / 7.0);
vec4 gz11 = floor(gy11) * (1.0 / 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 = quintic(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;
}
#endif

``````

Dependencies:

Use:

``````pnoise(<float2|float3|float4> pos, <float2|float3|float4> periodic)
``````

Check it on Github

``````

#ifndef FNC_PNOISE
#define FNC_PNOISE
// Classic Perlin noise, periodic variant
float pnoise(in float2 P, in float2 rep) {
float4 Pi = floor(P.xyxy) + float4(0.0, 0.0, 1.0, 1.0);
float4 Pf = frac(P.xyxy) - float4(0.0, 0.0, 1.0, 1.0);
Pi = Pi % rep.xyxy; // To create noise with explicit period
Pi = mod289(Pi);        // To avoid truncation effects in permutation
float4 ix = Pi.xzxz;
float4 iy = Pi.yyww;
float4 fx = Pf.xzxz;
float4 fy = Pf.yyww;

float4 i = permute(permute(ix) + iy);

float4 gx = frac(i * (1.0 / 41.0)) * 2.0 - 1.0 ;
float4 gy = abs(gx) - 0.5 ;
float4 tx = floor(gx + 0.5);
gx = gx - tx;

float2 g00 = float2(gx.x,gy.x);
float2 g10 = float2(gx.y,gy.y);
float2 g01 = float2(gx.z,gy.z);
float2 g11 = float2(gx.w,gy.w);

float4 norm = taylorInvSqrt(float4(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, float2(fx.x, fy.x));
float n10 = dot(g10, float2(fx.y, fy.y));
float n01 = dot(g01, float2(fx.z, fy.z));
float n11 = dot(g11, float2(fx.w, fy.w));

float2 fade_xy = quintic(Pf.xy);
float2 n_x = lerp(float2(n00, n01), float2(n10, n11), fade_xy.x);
float n_xy = lerp(n_x.x, n_x.y, fade_xy.y);
return 2.3 * n_xy;
}

float pnoise(in float3 P, in float3 rep) {
float3 Pi0 = floor(P) % rep; // Integer part, modulo period
float3 Pi1 = (Pi0 + float3(1.0, 1.0, 1.0)) % rep; // Integer part + 1, mod period
Pi0 = mod289(Pi0);
Pi1 = mod289(Pi1);
float3 Pf0 = frac(P); // Fracional part for interpolation
float3 Pf1 = Pf0 - float3(1.0, 1.0, 1.0); // Fracional part - 1.0
float4 ix = float4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
float4 iy = float4(Pi0.yy, Pi1.yy);
float4 iz0 = Pi0.zzzz;
float4 iz1 = Pi1.zzzz;

float4 ixy = permute(permute(ix) + iy);
float4 ixy0 = permute(ixy + iz0);
float4 ixy1 = permute(ixy + iz1);

float4 gx0 = ixy0 * (1.0 / 7.0);
float4 gy0 = frac(floor(gx0) * (1.0 / 7.0)) - 0.5;
gx0 = frac(gx0);
float4 gz0 = float4(0.5, 0.5, 0.5, 0.5) - abs(gx0) - abs(gy0);
float4 sz0 = step(gz0, float4(0.0, 0.0, 0.0, 0.0));
gx0 -= sz0 * (step(0.0, gx0) - 0.5);
gy0 -= sz0 * (step(0.0, gy0) - 0.5);

float4 gx1 = ixy1 * (1.0 / 7.0);
float4 gy1 = frac(floor(gx1) * (1.0 / 7.0)) - 0.5;
gx1 = frac(gx1);
float4 gz1 = float4(0.5, 0.5, 0.5, 0.5) - abs(gx1) - abs(gy1);
float4 sz1 = step(gz1, float4(0.0, 0.0, 0.0, 0.0));
gx1 -= sz1 * (step(0.0, gx1) - 0.5);
gy1 -= sz1 * (step(0.0, gy1) - 0.5);

float3 g000 = float3(gx0.x,gy0.x,gz0.x);
float3 g100 = float3(gx0.y,gy0.y,gz0.y);
float3 g010 = float3(gx0.z,gy0.z,gz0.z);
float3 g110 = float3(gx0.w,gy0.w,gz0.w);
float3 g001 = float3(gx1.x,gy1.x,gz1.x);
float3 g101 = float3(gx1.y,gy1.y,gz1.y);
float3 g011 = float3(gx1.z,gy1.z,gz1.z);
float3 g111 = float3(gx1.w,gy1.w,gz1.w);

float4 norm0 = taylorInvSqrt(float4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
g000 *= norm0.x;
g010 *= norm0.y;
g100 *= norm0.z;
g110 *= norm0.w;
float4 norm1 = taylorInvSqrt(float4(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, float3(Pf1.x, Pf0.yz));
float n010 = dot(g010, float3(Pf0.x, Pf1.y, Pf0.z));
float n110 = dot(g110, float3(Pf1.xy, Pf0.z));
float n001 = dot(g001, float3(Pf0.xy, Pf1.z));
float n101 = dot(g101, float3(Pf1.x, Pf0.y, Pf1.z));
float n011 = dot(g011, float3(Pf0.x, Pf1.yz));
float n111 = dot(g111, Pf1);

float3 fade_xyz = quintic(Pf0);
float4 n_z = lerp(float4(n000, n100, n010, n110), float4(n001, n101, n011, n111), fade_xyz.z);
float2 n_yz = lerp(n_z.xy, n_z.zw, fade_xyz.y);
float n_xyz = lerp(n_yz.x, n_yz.y, fade_xyz.x);
return 2.2 * n_xyz;
}

float pnoise(in float4 P, in float4 rep) {
float4 Pi0 = floor(P) % rep; // Integer part modulo rep
float4 Pi1 = (Pi0 + 1.0) % rep; // Integer part + 1 mod rep
Pi0 = mod289(Pi0);
Pi1 = mod289(Pi1);
float4 Pf0 = frac(P); // Fracional part for interpolation
float4 Pf1 = Pf0 - 1.0; // Fracional part - 1.0
float4 ix = float4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
float4 iy = float4(Pi0.yy, Pi1.yy);
float4 iz0 = float4(Pi0.zzzz);
float4 iz1 = float4(Pi1.zzzz);
float4 iw0 = float4(Pi0.wwww);
float4 iw1 = float4(Pi1.wwww);

float4 ixy = permute(permute(ix) + iy);
float4 ixy0 = permute(ixy + iz0);
float4 ixy1 = permute(ixy + iz1);
float4 ixy00 = permute(ixy0 + iw0);
float4 ixy01 = permute(ixy0 + iw1);
float4 ixy10 = permute(ixy1 + iw0);
float4 ixy11 = permute(ixy1 + iw1);

float4 gx00 = ixy00 * (1.0 / 7.0);
float4 gy00 = floor(gx00) * (1.0 / 7.0);
float4 gz00 = floor(gy00) * (1.0 / 6.0);
gx00 = frac(gx00) - 0.5;
gy00 = frac(gy00) - 0.5;
gz00 = frac(gz00) - 0.5;
float4 gw00 = float4(0.75, 0.75, 0.75, 0.75) - abs(gx00) - abs(gy00) - abs(gz00);
float4 sw00 = step(gw00, float4(0.0, 0.0, 0.0, 0.0));
gx00 -= sw00 * (step(0.0, gx00) - 0.5);
gy00 -= sw00 * (step(0.0, gy00) - 0.5);

float4 gx01 = ixy01 * (1.0 / 7.0);
float4 gy01 = floor(gx01) * (1.0 / 7.0);
float4 gz01 = floor(gy01) * (1.0 / 6.0);
gx01 = frac(gx01) - 0.5;
gy01 = frac(gy01) - 0.5;
gz01 = frac(gz01) - 0.5;
float4 gw01 = float4(0.75, 0.75, 0.75, 0.75) - abs(gx01) - abs(gy01) - abs(gz01);
float4 sw01 = step(gw01, float4(0.0, 0.0, 0.0, 0.0));
gx01 -= sw01 * (step(0.0, gx01) - 0.5);
gy01 -= sw01 * (step(0.0, gy01) - 0.5);

float4 gx10 = ixy10 * (1.0 / 7.0);
float4 gy10 = floor(gx10) * (1.0 / 7.0);
float4 gz10 = floor(gy10) * (1.0 / 6.0);
gx10 = frac(gx10) - 0.5;
gy10 = frac(gy10) - 0.5;
gz10 = frac(gz10) - 0.5;
float4 gw10 = float4(0.75, 0.75, 0.75, 0.75) - abs(gx10) - abs(gy10) - abs(gz10);
float4 sw10 = step(gw10, float4(0.0, 0.0, 0.0, 0.0));
gx10 -= sw10 * (step(0.0, gx10) - 0.5);
gy10 -= sw10 * (step(0.0, gy10) - 0.5);

float4 gx11 = ixy11 * (1.0 / 7.0);
float4 gy11 = floor(gx11) * (1.0 / 7.0);
float4 gz11 = floor(gy11) * (1.0 / 6.0);
gx11 = frac(gx11) - 0.5;
gy11 = frac(gy11) - 0.5;
gz11 = frac(gz11) - 0.5;
float4 gw11 = float4(0.75, 0.75, 0.75, 0.75) - abs(gx11) - abs(gy11) - abs(gz11);
float4 sw11 = step(gw11, float4(0.0, 0.0, 0.0, 0.0));
gx11 -= sw11 * (step(0.0, gx11) - 0.5);
gy11 -= sw11 * (step(0.0, gy11) - 0.5);

float4 g0000 = float4(gx00.x,gy00.x,gz00.x,gw00.x);
float4 g1000 = float4(gx00.y,gy00.y,gz00.y,gw00.y);
float4 g0100 = float4(gx00.z,gy00.z,gz00.z,gw00.z);
float4 g1100 = float4(gx00.w,gy00.w,gz00.w,gw00.w);
float4 g0010 = float4(gx10.x,gy10.x,gz10.x,gw10.x);
float4 g1010 = float4(gx10.y,gy10.y,gz10.y,gw10.y);
float4 g0110 = float4(gx10.z,gy10.z,gz10.z,gw10.z);
float4 g1110 = float4(gx10.w,gy10.w,gz10.w,gw10.w);
float4 g0001 = float4(gx01.x,gy01.x,gz01.x,gw01.x);
float4 g1001 = float4(gx01.y,gy01.y,gz01.y,gw01.y);
float4 g0101 = float4(gx01.z,gy01.z,gz01.z,gw01.z);
float4 g1101 = float4(gx01.w,gy01.w,gz01.w,gw01.w);
float4 g0011 = float4(gx11.x,gy11.x,gz11.x,gw11.x);
float4 g1011 = float4(gx11.y,gy11.y,gz11.y,gw11.y);
float4 g0111 = float4(gx11.z,gy11.z,gz11.z,gw11.z);
float4 g1111 = float4(gx11.w,gy11.w,gz11.w,gw11.w);

float4 norm00 = taylorInvSqrt(float4(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100)));
g0000 *= norm00.x;
g0100 *= norm00.y;
g1000 *= norm00.z;
g1100 *= norm00.w;

float4 norm01 = taylorInvSqrt(float4(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101)));
g0001 *= norm01.x;
g0101 *= norm01.y;
g1001 *= norm01.z;
g1101 *= norm01.w;

float4 norm10 = taylorInvSqrt(float4(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110)));
g0010 *= norm10.x;
g0110 *= norm10.y;
g1010 *= norm10.z;
g1110 *= norm10.w;

float4 norm11 = taylorInvSqrt(float4(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, float4(Pf1.x, Pf0.yzw));
float n0100 = dot(g0100, float4(Pf0.x, Pf1.y, Pf0.zw));
float n1100 = dot(g1100, float4(Pf1.xy, Pf0.zw));
float n0010 = dot(g0010, float4(Pf0.xy, Pf1.z, Pf0.w));
float n1010 = dot(g1010, float4(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
float n0110 = dot(g0110, float4(Pf0.x, Pf1.yz, Pf0.w));
float n1110 = dot(g1110, float4(Pf1.xyz, Pf0.w));
float n0001 = dot(g0001, float4(Pf0.xyz, Pf1.w));
float n1001 = dot(g1001, float4(Pf1.x, Pf0.yz, Pf1.w));
float n0101 = dot(g0101, float4(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
float n1101 = dot(g1101, float4(Pf1.xy, Pf0.z, Pf1.w));
float n0011 = dot(g0011, float4(Pf0.xy, Pf1.zw));
float n1011 = dot(g1011, float4(Pf1.x, Pf0.y, Pf1.zw));
float n0111 = dot(g0111, float4(Pf0.x, Pf1.yzw));
float n1111 = dot(g1111, Pf1);

float4 fade_xyzw = quintic(Pf0);
float4 n_0w = lerp(float4(n0000, n1000, n0100, n1100), float4(n0001, n1001, n0101, n1101), fade_xyzw.w);
float4 n_1w = lerp(float4(n0010, n1010, n0110, n1110), float4(n0011, n1011, n0111, n1111), fade_xyzw.w);
float4 n_zw = lerp(n_0w, n_1w, fade_xyzw.z);
float2 n_yzw = lerp(n_zw.xy, n_zw.zw, fade_xyzw.y);
float n_xyzw = lerp(n_yzw.x, n_yzw.y, fade_xyzw.x);
return 2.2 * n_xyzw;
}
#endif

``````

## License

Copyright 2021-2023 by Stefan Gustavson and Ian McEwan. Published under the terms of the MIT license: https://opensource.org/license/mit/

LYGIA is dual-licensed under the Prosperity License and the Patron License for sponsors and contributors.

Sponsors and contributors are automatically added to the Patron License and they can ignore the any non-commercial rule of the Prosperity Licensed software (please take a look to the exception).

It's also possible to get a permanent comercial license hook to a single and specific version of LYGIA.

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