Editing Perlin noise (section)

==Gradient permutation==
In Ken Perlin's original implementation he used a simple hashing scheme to determine what gradient vector is associated with each grid intersection.<ref>{{cite web |last1=Perlin |first1=Ken |title=Perlin noise |url=https://mrl.nyu.edu/~perlin/noise/ |accessdate=26 August 2020}}</ref> A pre-computed permutation table is used to turn a given grid coordinate into a random number. The original implementation worked on a 256 node grid and so included the following permutation table:

<syntaxhighlight lang="c">
int 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 };
</syntaxhighlight>

This specific permutation is not absolutely required, though it does require a randomized array of the integers 0 to 255. If creating a new permutation table, care should be taken to ensure uniform distribution of the values.<ref>{{cite web |title=Perlin Noise: Part 2 |url=https://www.scratchapixel.com/lessons/procedural-generation-virtual-worlds/perlin-noise-part-2 |accessdate=26 August 2020 |archive-date=17 February 2023 |archive-url=https://web.archive.org/web/20230217040756/https://www.scratchapixel.com/lessons/procedural-generation-virtual-worlds/perlin-noise-part-2 |url-status=dead }}</ref>

To get a gradient vector using the permutation table the coordinates of a grid point are looked up sequentially in the permutation table adding the value of each coordinate to the permutation of the previous coordinate. So for example the original implementation did this in 3D as follows:

<syntaxhighlight lang="c">
// Values above 255 were handled by repeating the permutation table twice.
static final int p[] = new int[512];
static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; }

int hash = p[p[p[X] + Y] + Z];
</syntaxhighlight>

The algorithm then looks at the bottom 4 bits of the hash output to pick 1 of 12 gradient vectors for that grid point.