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 [email protected]

/**
 * 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 [email protected]

/**
 * 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); 
};

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