two Perlin noise generators in javascript. The simplex version is about 10% faster (in Chrome at least, haven't tried other browsers)

perlin-noise-classical.js

// Ported from Stefan Gustavson's java implementation
// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
// Read Stefan's excellent paper for details on how this code works.
//
// Sean McCullough banksean@gmail.com

/**
 * You can pass in a random number generator object if you like.
 * It is assumed to have a random() method.
 */
var ClassicalNoise = function(r) { // Classic Perlin noise in 3D, for comparison 
	if (r == undefined) r = Math;
  this.grad3 = [[1,1,0],[-1,1,0],[1,-1,0],[-1,-1,0], 
                                 [1,0,1],[-1,0,1],[1,0,-1],[-1,0,-1], 
                                 [0,1,1],[0,-1,1],[0,1,-1],[0,-1,-1]]; 
  this.p = [];
  for (var i=0; i<256; i++) {
	  this.p[i] = Math.floor(r.random()*256);
  }
  // To remove the need for index wrapping, double the permutation table length 
  this.perm = []; 
  for(var i=0; i<512; i++) {
		this.perm[i]=this.p[i & 255];
  }
};

ClassicalNoise.prototype.dot = function(g, x, y, z) { 
    return g[0]*x + g[1]*y + g[2]*z; 
};

ClassicalNoise.prototype.mix = function(a, b, t) { 
    return (1.0-t)*a + t*b; 
};

ClassicalNoise.prototype.fade = function(t) { 
    return t*t*t*(t*(t*6.0-15.0)+10.0); 
};

  // Classic Perlin noise, 3D version 
ClassicalNoise.prototype.noise = function(x, y, z) { 
  // Find unit grid cell containing point 
  var X = Math.floor(x); 
  var Y = Math.floor(y); 
  var Z = Math.floor(z); 
  
  // Get relative xyz coordinates of point within that cell 
  x = x - X; 
  y = y - Y; 
  z = z - Z; 
  
  // Wrap the integer cells at 255 (smaller integer period can be introduced here) 
  X = X & 255; 
  Y = Y & 255; 
  Z = Z & 255;
  
  // Calculate a set of eight hashed gradient indices 
  var gi000 = this.perm[X+this.perm[Y+this.perm[Z]]] % 12; 
  var gi001 = this.perm[X+this.perm[Y+this.perm[Z+1]]] % 12; 
  var gi010 = this.perm[X+this.perm[Y+1+this.perm[Z]]] % 12; 
  var gi011 = this.perm[X+this.perm[Y+1+this.perm[Z+1]]] % 12; 
  var gi100 = this.perm[X+1+this.perm[Y+this.perm[Z]]] % 12; 
  var gi101 = this.perm[X+1+this.perm[Y+this.perm[Z+1]]] % 12; 
  var gi110 = this.perm[X+1+this.perm[Y+1+this.perm[Z]]] % 12; 
  var gi111 = this.perm[X+1+this.perm[Y+1+this.perm[Z+1]]] % 12; 
  
  // The gradients of each corner are now: 
  // g000 = grad3[gi000]; 
  // g001 = grad3[gi001]; 
  // g010 = grad3[gi010]; 
  // g011 = grad3[gi011]; 
  // g100 = grad3[gi100]; 
  // g101 = grad3[gi101]; 
  // g110 = grad3[gi110]; 
  // g111 = grad3[gi111]; 
  // Calculate noise contributions from each of the eight corners 
  var n000= this.dot(this.grad3[gi000], x, y, z); 
  var n100= this.dot(this.grad3[gi100], x-1, y, z); 
  var n010= this.dot(this.grad3[gi010], x, y-1, z); 
  var n110= this.dot(this.grad3[gi110], x-1, y-1, z); 
  var n001= this.dot(this.grad3[gi001], x, y, z-1); 
  var n101= this.dot(this.grad3[gi101], x-1, y, z-1); 
  var n011= this.dot(this.grad3[gi011], x, y-1, z-1); 
  var n111= this.dot(this.grad3[gi111], x-1, y-1, z-1); 
  // Compute the fade curve value for each of x, y, z 
  var u = this.fade(x); 
  var v = this.fade(y); 
  var w = this.fade(z); 
   // Interpolate along x the contributions from each of the corners 
  var nx00 = this.mix(n000, n100, u); 
  var nx01 = this.mix(n001, n101, u); 
  var nx10 = this.mix(n010, n110, u); 
  var nx11 = this.mix(n011, n111, u); 
  // Interpolate the four results along y 
  var nxy0 = this.mix(nx00, nx10, v); 
  var nxy1 = this.mix(nx01, nx11, v); 
  // Interpolate the two last results along z 
  var nxyz = this.mix(nxy0, nxy1, w); 

  return nxyz; 
};

perlin-noise-simplex.js

// Ported from Stefan Gustavson's java implementation
// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
// Read Stefan's excellent paper for details on how this code works.
//
// Sean McCullough banksean@gmail.com

/**
 * You can pass in a random number generator object if you like.
 * It is assumed to have a random() method.
 */
var SimplexNoise = function(r) {
	if (r == undefined) r = Math;
  this.grad3 = [[1,1,0],[-1,1,0],[1,-1,0],[-1,-1,0], 
                                 [1,0,1],[-1,0,1],[1,0,-1],[-1,0,-1], 
                                 [0,1,1],[0,-1,1],[0,1,-1],[0,-1,-1]]; 
  this.p = [];
  for (var i=0; i<256; i++) {
	  this.p[i] = Math.floor(r.random()*256);
  }
  // To remove the need for index wrapping, double the permutation table length 
  this.perm = []; 
  for(var i=0; i<512; i++) {
		this.perm[i]=this.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. 
  this.simplex = [ 
    [0,1,2,3],[0,1,3,2],[0,0,0,0],[0,2,3,1],[0,0,0,0],[0,0,0,0],[0,0,0,0],[1,2,3,0], 
    [0,2,1,3],[0,0,0,0],[0,3,1,2],[0,3,2,1],[0,0,0,0],[0,0,0,0],[0,0,0,0],[1,3,2,0], 
    [0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0], 
    [1,2,0,3],[0,0,0,0],[1,3,0,2],[0,0,0,0],[0,0,0,0],[0,0,0,0],[2,3,0,1],[2,3,1,0], 
    [1,0,2,3],[1,0,3,2],[0,0,0,0],[0,0,0,0],[0,0,0,0],[2,0,3,1],[0,0,0,0],[2,1,3,0], 
    [0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0], 
    [2,0,1,3],[0,0,0,0],[0,0,0,0],[0,0,0,0],[3,0,1,2],[3,0,2,1],[0,0,0,0],[3,1,2,0], 
    [2,1,0,3],[0,0,0,0],[0,0,0,0],[0,0,0,0],[3,1,0,2],[0,0,0,0],[3,2,0,1],[3,2,1,0]]; 
};

SimplexNoise.prototype.dot = function(g, x, y) { 
	return g[0]*x + g[1]*y;
};

SimplexNoise.prototype.noise = function(xin, yin) { 
  var n0, n1, n2; // Noise contributions from the three corners 
  // Skew the input space to determine which simplex cell we're in 
  var F2 = 0.5*(Math.sqrt(3.0)-1.0); 
  var s = (xin+yin)*F2; // Hairy factor for 2D 
  var i = Math.floor(xin+s); 
  var j = Math.floor(yin+s); 
  var G2 = (3.0-Math.sqrt(3.0))/6.0; 
  var t = (i+j)*G2; 
  var X0 = i-t; // Unskew the cell origin back to (x,y) space 
  var Y0 = j-t; 
  var x0 = xin-X0; // The x,y distances from the cell origin 
  var y0 = yin-Y0; 
  // For the 2D case, the simplex shape is an equilateral triangle. 
  // Determine which simplex we are in. 
  var 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 
  var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords 
  var y1 = y0 - j1 + G2; 
  var x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords 
  var y2 = y0 - 1.0 + 2.0 * G2; 
  // Work out the hashed gradient indices of the three simplex corners 
  var ii = i & 255; 
  var jj = j & 255; 
  var gi0 = this.perm[ii+this.perm[jj]] % 12; 
  var gi1 = this.perm[ii+i1+this.perm[jj+j1]] % 12; 
  var gi2 = this.perm[ii+1+this.perm[jj+1]] % 12; 
  // Calculate the contribution from the three corners 
  var t0 = 0.5 - x0*x0-y0*y0; 
  if(t0<0) n0 = 0.0; 
  else { 
    t0 *= t0; 
    n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0);  // (x,y) of grad3 used for 2D gradient 
  } 
  var t1 = 0.5 - x1*x1-y1*y1; 
  if(t1<0) n1 = 0.0; 
  else { 
    t1 *= t1; 
    n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1); 
  }
  var t2 = 0.5 - x2*x2-y2*y2; 
  if(t2<0) n2 = 0.0; 
  else { 
    t2 *= t2; 
    n2 = t2 * t2 * this.dot(this.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 70.0 * (n0 + n1 + n2); 
};

// 3D simplex noise 
SimplexNoise.prototype.noise3d = function(xin, yin, zin) { 
  var n0, n1, n2, n3; // Noise contributions from the four corners 
  // Skew the input space to determine which simplex cell we're in 
  var F3 = 1.0/3.0; 
  var s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D 
  var i = Math.floor(xin+s); 
  var j = Math.floor(yin+s); 
  var k = Math.floor(zin+s); 
  var G3 = 1.0/6.0; // Very nice and simple unskew factor, too 
  var t = (i+j+k)*G3; 
  var X0 = i-t; // Unskew the cell origin back to (x,y,z) space 
  var Y0 = j-t; 
  var Z0 = k-t; 
  var x0 = xin-X0; // The x,y,z distances from the cell origin 
  var y0 = yin-Y0; 
  var z0 = zin-Z0; 
  // For the 3D case, the simplex shape is a slightly irregular tetrahedron. 
  // Determine which simplex we are in. 
  var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords 
  var 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.
  var x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords 
  var y1 = y0 - j1 + G3; 
  var z1 = z0 - k1 + G3; 
  var x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords 
  var y2 = y0 - j2 + 2.0*G3; 
  var z2 = z0 - k2 + 2.0*G3; 
  var x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords 
  var y3 = y0 - 1.0 + 3.0*G3; 
  var z3 = z0 - 1.0 + 3.0*G3; 
  // Work out the hashed gradient indices of the four simplex corners 
  var ii = i & 255; 
  var jj = j & 255; 
  var kk = k & 255; 
  var gi0 = this.perm[ii+this.perm[jj+this.perm[kk]]] % 12; 
  var gi1 = this.perm[ii+i1+this.perm[jj+j1+this.perm[kk+k1]]] % 12; 
  var gi2 = this.perm[ii+i2+this.perm[jj+j2+this.perm[kk+k2]]] % 12; 
  var gi3 = this.perm[ii+1+this.perm[jj+1+this.perm[kk+1]]] % 12; 
  // Calculate the contribution from the four corners 
  var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0; 
  if(t0<0) n0 = 0.0; 
  else { 
    t0 *= t0; 
    n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0, z0); 
  }
  var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1; 
  if(t1<0) n1 = 0.0; 
  else { 
    t1 *= t1; 
    n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1, z1); 
  } 
  var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2; 
  if(t2<0) n2 = 0.0; 
  else { 
    t2 *= t2; 
    n2 = t2 * t2 * this.dot(this.grad3[gi2], x2, y2, z2); 
  } 
  var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3; 
  if(t3<0) n3 = 0.0; 
  else { 
    t3 *= t3; 
    n3 = t3 * t3 * this.dot(this.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 32.0*(n0 + n1 + n2 + n3); 
};

Thanks for sharing! I found the Classical function to be noticeably faster than the Simplex3D while polling large numbers of points. (Chrome 28.0.1500.95)

yes, thanks for this. I'm using it to generate random numbers to drive a drunk walk function I wrote in javascript for max for live (max/msp in ableton live): https://github.com/blakelymcconnell/m4l_js2liveAPI

Does this have any sort of license? If so, what?

The 3d noise function has a bug. Check line https://gist.github.com/banksean/304522#file-perlin-noise-simplex-js-L156 it calls dot() with x, y, and z arguments, yet the function only deals with x and y, not z. How should it work?

This is awesome thanks! I've been trying to understand Perlin Noise for a very long time now, and this is the simplest form of generation that I found!

I've been wondering, the fade function, t^3*(t*(t*6.0-15.0)+10.0), seems to be the norm, is there any special reason why it is commonly used?

Thanks! I have been using this to create a js random terrain generator

anyone can help me how can i see the result in html? please. thankyou before

anyone can help me how can i see the result in html? please. thankyou before

https://www.17sucai.com/pins/demo-show?id=46732&st=sMlrCMBnHdAKZDuVfEjH2A&e=1725479025

@banksean Can you implement the underwater caustic effect algorithm，like this
https://opengameart.org/content/water-caustics-effect-small