Code adapted and cleaned up from the C# implementation here http://flafla2.github.io/2014/08/09/perlinnoise.html. Specific changes: conversion to JS, removal of classes and stateful classes.

perlin-noise.js

// Hash lookup table as defined by Ken Perlin.  This is a randomly
// arranged array of all numbers from 0-255 inclusive.
const permutation = [ 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
];

const pp = [];
for (let i = 0; i < 512; i++) {
  pp[i] = permutation[i % 256];
}


// Source: http://riven8192.blogspot.com/2010/08/calculate-perlinnoise-twice-as-fast.html
function grad(hash, x, y, z) {
  switch(hash & 0xF) {
    case 0x0: return  x + y;
    case 0x1: return -x + y;
    case 0x2: return  x - y;
    case 0x3: return -x - y;
    case 0x4: return  x + z;
    case 0x5: return -x + z;
    case 0x6: return  x - z;
    case 0x7: return -x - z;
    case 0x8: return  y + z;
    case 0x9: return -y + z;
    case 0xA: return  y - z;
    case 0xB: return -y - z;
    case 0xC: return  y + x;
    case 0xD: return -y + z;
    case 0xE: return  y - x;
    case 0xF: return -y - z;
    default: return 0; // never happens
  }
}

// Fade function as defined by Ken Perlin.  This eases coordinate values
// so that they will "ease" towards integral values.  This ends up smoothing
// the final output.
function fade(t) {
  // 6t^5 - 15t^4 + 10t^3
  return t * t * t * (t * (t * 6 - 15) + 10);
}

function inc(num, repeat) {
  num++;
  if (repeat > 0) num %= repeat;
  return num;
}

function lerp(a, b, x) {
  return a + x * (b - a);
}

// Make sure that x, y, z are within 0-1! Otherwise you will just see 0.5.
export function Perlin(x, y, z, repeat = 0) {
  // If we have any repeat on, change the coordinates to their "local" repetitions
  if (repeat > 0) {
    x = x % repeat;
    y = y % repeat;
    z = z % repeat;
  }

  // Calculate the "unit cube" that the point asked will be located in
  // The left bound is ( |_x_|,|_y_|,|_z_| ) and the right bound is that
  // plus 1.  Next we calculate the location (from 0.0 to 1.0) in that cube.
  // We also fade the location to smooth the result.
  const xi = Math.floor(x) & 255;
  const yi = Math.floor(y) & 255;
  const zi = Math.floor(z) & 255;
  const xf = x - Math.floor(x);
  const yf = y - Math.floor(y);
  const zf = z - Math.floor(z);
  const u = fade(xf);
  const v = fade(yf);
  const w = fade(zf);

  const aaa = pp[pp[pp[xi] + yi] + zi];
  const aba = pp[pp[pp[xi] + inc(yi, repeat)] + zi];
  const aab = pp[pp[pp[xi] + yi] + inc(zi, repeat)];
  const abb = pp[pp[pp[xi] + inc(yi, repeat)] + inc(zi, repeat)];
  const baa = pp[pp[pp[inc(xi, repeat)] + yi] + zi];
  const bba = pp[pp[pp[inc(xi, repeat)] + inc(yi, repeat)] + zi];
  const bab = pp[pp[pp[inc(xi, repeat)] + yi] + inc(zi, repeat)];
  const bbb = pp[pp[pp[inc(xi, repeat)] + inc(yi, repeat)] + inc(zi, repeat)];

  // The gradient function calculates the dot product between a pseudorandom
  // gradient vector and the vector from the input coordinate to the 8
  // surrounding points in its unit cube.
  // This is all then lerped together as a sort of weighted average based on the faded (u,v,w)
  // values we made earlier.
  let x1, x2, y1, y2;
  x1 = lerp(grad(aaa, xf, yf, zf), grad(baa, xf - 1, yf, zf), u);
  x2 = lerp(grad(aba, xf, yf - 1, zf), grad(bba, xf - 1, yf - 1, zf), u);
  y1 = lerp(x1, x2, v);

  x1 = lerp(grad(aab, xf, yf, zf - 1), grad(bab, xf - 1, yf, zf - 1), u);
  x2 = lerp(grad(abb, xf, yf - 1, zf - 1), grad(bbb, xf - 1, yf - 1, zf - 1), u);
  y2 = lerp(x1, x2, v);

  // For convenience we bound it to 0 - 1 (theoretical min/max before is -1 - 1)
  return (lerp (y1, y2, w)+1)/2;
}

// Make sure that x, y, z are within 0-1! Otherwise you will just see 0.5.
export function OctavePerlin(x, y, z, octaves, persistence, repeat=0) {
  let total = 0;
  let frequency = 1;
  let amplitude = 1;
  // Used for normalizing result to 0.0 - 1.0
  let maxValue = 0;
  for(let i = 0; i < octaves; i++) {
    total += Perlin(x * frequency, y * frequency, z * frequency, repeat) * amplitude;

    maxValue += amplitude;

    amplitude *= persistence;
    frequency *= 2;
  }

  return total/maxValue;
}