# Tileable Noise

Author: Ilya Suzdalnitski

## Description

Ported Java Simplex Noise source code to C# from toxiclibs. Implemented tileable noise by mapping 4d noise into 2d plane as described in GameDev.net forum

The method itself:

```
SeamlessNoise( float x, float y, float dx, float dy, float xyOffset );```

where: x, y are normalized coordinates (in [0..1] space).
dx, dy are noise scale in x and y axes.
xyOffset is noise offset (same offset will result in having the same noise).

The method returns a float value in [-1..1] space. You might have to normalize it to [0..1] space by doing something like this:

```
noise = SeamlessNoise( x, y, 10.0f, 10.0f, 0.0f);
noise = (noise + 1.0f) * .5f;```

## Usage example

```
int seed = System.DateTime.Now.Millisecond;

for (int x = 0; x < _texture.width; x++) {
for (int y = 0; y < _texture.height; y++) {
float noise = SimplexNoise.SeamlessNoise( ( (float)x ) / ( (float)_texture.width ),
( (float)y ) / ( (float)_texture.height ),
10.0f, 10.0f, (float)seed );
}
}```

## Noise class source code - Noise.cs

```
using UnityEngine;

public class SimplexNoise
{
private static int[][] grad3 = new int[][]{
new int[]{1, 1, 0},
new int[]{-1, 1, 0},
new int[]{1, -1, 0},
new int[]{-1, -1, 0},
new int[]{1, 0, 1},
new int[]{-1, 0, 1},
new int[]{1, 0, -1},
new int[]{-1, 0, -1},
new int[]{0, 1, 1},
new int[]{0, -1, 1},
new int[]{0, 1, -1},
new int[]{0, -1, -1} };

private static int[][] grad4 = new int[][]{
new int[]{ 0, 1, 1, 1 },
new int[]{ 0, 1, 1, -1 },
new int[]{ 0, 1, -1, 1 },
new int[]{ 0, 1, -1, -1 },
new int[]{ 0, -1, 1, 1 },
new int[]{ 0, -1, 1, -1 },
new int[]{ 0, -1, -1, 1 },
new int[]{ 0, -1, -1, -1 },
new int[]{ 1, 0, 1, 1 },
new int[]{ 1, 0, 1, -1 },
new int[]{ 1, 0, -1, 1 },
new int[]{ 1, 0, -1, -1 },
new int[]{ -1, 0, 1, 1 },
new int[]{ -1, 0, 1, -1 },
new int[]{ -1, 0, -1, 1 },
new int[]{ -1, 0, -1, -1 },
new int[]{ 1, 1, 0, 1 },
new int[]{ 1, 1, 0, -1 },
new int[]{ 1, -1, 0, 1 },
new int[]{ 1, -1, 0, -1 },
new int[]{ -1, 1, 0, 1 },
new int[]{ -1, 1, 0, -1 },
new int[]{ -1, -1, 0, 1 },
new int[]{ -1, -1, 0, -1 },
new int[]{ 1, 1, 1, 0 },
new int[]{ 1, 1, -1, 0 },
new int[]{ 1, -1, 1, 0 },
new int[]{ 1, -1, -1, 0 },
new int[]{ -1, 1, 1, 0 },
new int[]{ -1, 1, -1, 0 },
new int[]{ -1, -1, 1, 0 },
new int[]{ -1, -1, -1, 0 } };

private static int[] p = {
151,160,137,91,90,15,
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180};
// To remove the need for index wrapping, float the permutation table length
private static int[] perm = new int[512];
static SimplexNoise()
{
for( int i = 0; i < 512; i++ )
perm[i] = p[i & 255];
}
// A lookup table to traverse the simplex around a given point in 4D.
// Details can be found where this table is used, in the 4D Noise method.
private static int[][] simplex = new int[][]{
new int[]{0,1,2,3}, new int[]{0,1,3,2}, new int[]{0,0,0,0}, new int[]{0,2,3,1}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{1,2,3,0},
new int[]{0,2,1,3}, new int[]{0,0,0,0}, new int[]{0,3,1,2}, new int[]{0,3,2,1}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{1,3,2,0},
new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0},
new int[]{1,2,0,3}, new int[]{0,0,0,0}, new int[]{1,3,0,2}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{2,3,0,1}, new int[]{2,3,1,0},
new int[]{1,0,2,3}, new int[]{1,0,3,2}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{2,0,3,1}, new int[]{0,0,0,0}, new int[]{2,1,3,0},
new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0},
new int[]{2,0,1,3}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{3,0,1,2}, new int[]{3,0,2,1}, new int[]{0,0,0,0}, new int[]{3,1,2,0},
new int[]{2,1,0,3}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{0,0,0,0}, new int[]{3,1,0,2}, new int[]{0,0,0,0}, new int[]{3,2,0,1}, new int[]{3,2,1,0}};
// This method is a *lot* faster than using (int)Math.floor(x)
private static int fastfloor( float x )
{
return x > 0 ? ( int )x : ( int )x - 1;
}
private static float dot( int[] g, float x, float y )
{
return g[0] * x + g[1] * y;
}
private static float dot( int[] g, float x, float y, float z )
{
return g[0] * x + g[1] * y + g[2] * z;
}
private static float dot( int[] g, float x, float y, float z, float w )
{
return g[0] * x + g[1] * y + g[2] * z + g[3] * w;
}
// 2D simplex Noise
public static float Noise( float xin, float yin )
{
float n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
float F2 = 0.5f * ( Mathf.Sqrt( 3.0f ) - 1.0f );
float s = ( xin + yin ) * F2; // Hairy factor for 2D
int i = fastfloor( xin + s );
int j = fastfloor( yin + s );
float G2 = ( 3.0f - Mathf.Sqrt( 3.0f ) ) / 6.0f;
float t = ( i + j ) * G2;
float X0 = i - t; // Unskew the cell origin back to (x,y) space
float Y0 = j - t;
float x0 = xin - X0; // The x,y distances from the cell origin
float y0 = yin - Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
if( x0 > y0 )
{
i1 = 1;
j1 = 0;
} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else
{
i1 = 0;
j1 = 1;
} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
float y1 = y0 - j1 + G2;
float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
float y2 = y0 - 1.0f + 2.0f * G2;
// Work out the hashed gradient indices of the three simplex corners
int ii = i & 255;
int jj = j & 255;
int gi0 = perm[ii + perm[jj]] % 12;
int gi1 = perm[ii + i1 + perm[jj + j1]] % 12;
int gi2 = perm[ii + 1 + perm[jj + 1]] % 12;
// Calculate the contribution from the three corners
float t0 = 0.5f - x0 * x0 - y0 * y0;
if( t0 < 0 )
n0 = 0.0f;
else
{
t0 *= t0;
n0 = t0 * t0 * dot( grad3[gi0], x0, y0 ); // (x,y) of grad3 used for 2D gradient
}
float t1 = 0.5f - x1 * x1 - y1 * y1;
if( t1 < 0 )
n1 = 0.0f;
else
{
t1 *= t1;
n1 = t1 * t1 * dot( grad3[gi1], x1, y1 );
}
float t2 = 0.5f - x2 * x2 - y2 * y2;
if( t2 < 0 )
n2 = 0.0f;
else
{
t2 *= t2;
n2 = t2 * t2 * dot( grad3[gi2], x2, y2 );
}
// Add contributions from each corner to get the final Noise value.
// The result is scaled to return values in the interval [-1,1].
return 70.0f * ( n0 + n1 + n2 );
}
// 3D simplex Noise
public static float Noise( float xin, float yin, float zin )
{
float n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
const float F3 = 1.0f / 3.0f;
float s = ( xin + yin + zin ) * F3; // Very nice and simple skew factor for 3D
int i = fastfloor( xin + s );
int j = fastfloor( yin + s );
int k = fastfloor( zin + s );
const float G3 = 1.0f / 6.0f; // Very nice and simple unskew factor, too
float t = ( i + j + k ) * G3;
float X0 = i - t; // Unskew the cell origin back to (x,y,z) space
float Y0 = j - t;
float Z0 = k - t;
float x0 = xin - X0; // The x,y,z distances from the cell origin
float y0 = yin - Y0;
float z0 = zin - Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
if( x0 >= y0 )
{
if( y0 >= z0 )
{
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // X Y Z order
else if( x0 >= z0 )
{
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
} // X Z Y order
else
{
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
} // Z X Y order
}
else
{ // x0<y0
if( y0 < z0 )
{
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
} // Z Y X order
else if( x0 < z0 )
{
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
} // Y Z X order
else
{
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // Y X Z order
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
float y1 = y0 - j1 + G3;
float z1 = z0 - k1 + G3;
float x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
float y2 = y0 - j2 + 2.0f * G3;
float z2 = z0 - k2 + 2.0f * G3;
float x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
float y3 = y0 - 1.0f + 3.0f * G3;
float z3 = z0 - 1.0f + 3.0f * G3;
// Work out the hashed gradient indices of the four simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int gi0 = perm[ii + perm[jj + perm[kk]]] % 12;
int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12;
int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12;
int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12;
// Calculate the contribution from the four corners
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
if( t0 < 0 )
n0 = 0.0f;
else
{
t0 *= t0;
n0 = t0 * t0 * dot( grad3[gi0], x0, y0, z0 );
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
if( t1 < 0 )
n1 = 0.0f;
else
{
t1 *= t1;
n1 = t1 * t1 * dot( grad3[gi1], x1, y1, z1 );
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
if( t2 < 0 )
n2 = 0.0f;
else
{
t2 *= t2;
n2 = t2 * t2 * dot( grad3[gi2], x2, y2, z2 );
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
if( t3 < 0 )
n3 = 0.0f;
else
{
t3 *= t3;
n3 = t3 * t3 * dot( grad3[gi3], x3, y3, z3 );
}
// Add contributions from each corner to get the final Noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0f * ( n0 + n1 + n2 + n3 );
}
// 4D simplex Noise
public static float Noise( float x, float y, float z, float w )
{
// The skewing and unskewing factors are hairy again for the 4D case
float F4 = ( Mathf.Sqrt( 5.0f ) - 1.0f ) / 4.0f;
float G4 = ( 5.0f - Mathf.Sqrt( 5.0f ) ) / 20.0f;
float n0, n1, n2, n3, n4; // Noise contributions from the five corners
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
float s = ( x + y + z + w ) * F4; // Factor for 4D skewing
int i = fastfloor( x + s );
int j = fastfloor( y + s );
int k = fastfloor( z + s );
int l = fastfloor( w + s );
float t = ( i + j + k + l ) * G4; // Factor for 4D unskewing
float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
float Y0 = j - t;
float Z0 = k - t;
float W0 = l - t;
float x0 = x - X0; // The x,y,z,w distances from the cell origin
float y0 = y - Y0;
float z0 = z - Z0;
float w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// The method below is a good way of finding the ordering of x,y,z,w and
// then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to add up binary bits
// for an integer index.
int c1 = ( x0 > y0 ) ? 32 : 0;
int c2 = ( x0 > z0 ) ? 16 : 0;
int c3 = ( y0 > z0 ) ? 8 : 0;
int c4 = ( x0 > w0 ) ? 4 : 0;
int c5 = ( y0 > w0 ) ? 2 : 0;
int c6 = ( z0 > w0 ) ? 1 : 0;
int c = c1 + c2 + c3 + c4 + c5 + c6;
int i1, j1, k1, l1; // The integer offsets for the second simplex corner
int i2, j2, k2, l2; // The integer offsets for the third simplex corner
int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = simplex[c][0] >= 3 ? 1 : 0;
j1 = simplex[c][1] >= 3 ? 1 : 0;
k1 = simplex[c][2] >= 3 ? 1 : 0;
l1 = simplex[c][3] >= 3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0] >= 2 ? 1 : 0;
j2 = simplex[c][1] >= 2 ? 1 : 0;
k2 = simplex[c][2] >= 2 ? 1 : 0;
l2 = simplex[c][3] >= 2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0] >= 1 ? 1 : 0;
j3 = simplex[c][1] >= 1 ? 1 : 0;
k3 = simplex[c][2] >= 1 ? 1 : 0;
l3 = simplex[c][3] >= 1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
float y1 = y0 - j1 + G4;
float z1 = z0 - k1 + G4;
float w1 = w0 - l1 + G4;
float x2 = x0 - i2 + 2.0f * G4; // Offsets for third corner in (x,y,z,w) coords
float y2 = y0 - j2 + 2.0f * G4;
float z2 = z0 - k2 + 2.0f * G4;
float w2 = w0 - l2 + 2.0f * G4;
float x3 = x0 - i3 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
float y3 = y0 - j3 + 3.0f * G4;
float z3 = z0 - k3 + 3.0f * G4;
float w3 = w0 - l3 + 3.0f * G4;
float x4 = x0 - 1.0f + 4.0f * G4; // Offsets for last corner in (x,y,z,w) coords
float y4 = y0 - 1.0f + 4.0f * G4;
float z4 = z0 - 1.0f + 4.0f * G4;
float w4 = w0 - 1.0f + 4.0f * G4;
// Work out the hashed gradient indices of the five simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int ll = l & 255;
int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
// Calculate the contribution from the five corners
float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
if( t0 < 0 )
n0 = 0.0f;
else
{
t0 *= t0;
n0 = t0 * t0 * dot( grad4[gi0], x0, y0, z0, w0 );
}
float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
if( t1 < 0 )
n1 = 0.0f;
else
{
t1 *= t1;
n1 = t1 * t1 * dot( grad4[gi1], x1, y1, z1, w1 );
}
float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
if( t2 < 0 )
n2 = 0.0f;
else
{
t2 *= t2;
n2 = t2 * t2 * dot( grad4[gi2], x2, y2, z2, w2 );
}
float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
if( t3 < 0 )
n3 = 0.0f;
else
{
t3 *= t3;
n3 = t3 * t3 * dot( grad4[gi3], x3, y3, z3, w3 );
}
float t4 = 0.6f - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
if( t4 < 0 )
n4 = 0.0f;
else
{
t4 *= t4;
n4 = t4 * t4 * dot( grad4[gi4], x4, y4, z4, w4 );
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0f * ( n0 + n1 + n2 + n3 + n4 );
}

//
//Blurred noise
public static float BlurredNoise( float stepSize, float x, float y) {
int totalIterations = 0;
float noiseSum = 0.0f;

for (float xx = x - stepSize; xx <= x + stepSize; xx += stepSize) {
for (float yy = y - stepSize; yy <= y + stepSize; yy += stepSize) {
noiseSum += Noise(xx, yy);
totalIterations++;
}
}

return noiseSum / (float)totalIterations;
}

public static float BlurredNoise( float stepSize, float x, float y, float z, float w ) {
int totalIterations = 0;
float noiseSum = 0.0f;

for (float xx = x - stepSize; xx <= x + stepSize; xx += stepSize) {
for (float yy = y - stepSize; yy <= y + stepSize; yy += stepSize) {
for (float zz = z - stepSize; zz <= z + stepSize; zz += stepSize) {
for (float ww = w - stepSize; ww <= w + stepSize; ww += stepSize) {
noiseSum += Noise(xx, yy, zz, ww);

totalIterations++;
}
}
}
}

return noiseSum / (float)totalIterations;
}

//X, Y is [0..1]
public static float SeamlessNoise( float x, float y, float dx, float dy, float xyOffset ) {
float s = x;
float t = y;

float nx = xyOffset + Mathf.Cos(s * 2.0f * Mathf.PI) * dx / (2.0f * Mathf.PI);
float ny = xyOffset + Mathf.Cos(t * 2.0f * Mathf.PI) * dy / (2.0f * Mathf.PI);
float nz = xyOffset + Mathf.Sin(s * 2.0f * Mathf.PI) * dx / (2.0f * Mathf.PI);
float nw = xyOffset + Mathf.Sin(t * 2.0f * Mathf.PI) * dy / (2.0f * Mathf.PI);

return Noise(nx, ny, nz, nw);
}
}```