Perlin noise: Difference between revisions

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{{trans|Go}}
{{trans|Go}}
<lang rexx>/*REXX program implements a Perlin noise algorithm of a point in 3D─space. */
<lang rexx>/*REXX program implements a Perlin noise algorithm of a point in 3D─space. */
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
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,
113 224 232 178 185 112 104 218 246 97 228 251 34 242 193 238 210 144 12 191 179 162 241 81,
108 110 79 113 224 232 178 185 112 104 218 246 97 228 251 34 242 193 238 210 144 12 191 179,
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,
162 241 81 51 145 235 249 14 239 107 49 192 214 31 181 199 106 157 184 84 204 176 115 121,
150 254 138 236 205 93 222 114 67 29 24 72 243 141 128 195 78 66 215 61 156 180
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
numeric digits 100 /*use 100 decimal digits for precision.*/
numeric digits 100 /*use 100 decimal digits for precision.*/
parse arg x y z . /*get optional arguments from the C.L. */
parse arg x y z . /*get optional arguments from the C.L. */

Revision as of 00:07, 7 September 2015

Perlin noise is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Perlin noise is a kind of gradient noise invented by Ken Perlin around the end of the twentieth century and still currently heavily used in computer graphics, most notably to procedurally generate textures or heightmaps. The Perlin noise is basically a pseudo-random mapping of into with an integer which can be arbitrarily large but which is usually 2, 3 or 4.

Either by using a dedicated library or by implementing the algorithm, show that the Perlin noise (as defined in 2002 in the Java implementation below) of the point in 3D-space with coordinates 3.14, 42, 7 is 0.13691995878400012.

OCaml

<lang ocaml> let 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]

let lerp(t, a, b) = a +. t *. (b -. a)

let fade t = 

 (t *. t *. t) *. (t *. (t *. 6. -. 15.) +. 10.)

let grad (hash, x, y, z) = 

 let h = hash land 15 in
 let u = if (h < 8) then x else y in
 let v = if (h < 4) then y else (if (h = 12 || h = 14) then x else z) in
 (if (h land 1 = 0) then u else (0. -. u)) +.
   (if (h land 2 = 0) then v else (0. -. v))

let perlin_init p = 

 List.rev (List.fold_left (fun i x -> x :: i) (List.rev p) p);;

let perlin_noise p x y z = 

 let x1 = (int_of_float x) land 255 and
     y1 = (int_of_float y) land 255 and
     z1 = (int_of_float z) land 255 and
     xi = x -. (float (int_of_float x)) and
     yi = y -. (float (int_of_float y)) and
     zi = z -. (float (int_of_float z)) in
 let u = fade xi and
     v = fade yi and
     w = fade zi and
     a = (List.nth p x1) + y1 in
 let aa = (List.nth p a) + z1 and
     ab = (List.nth p (a + 1)) + z1 and
     b = (List.nth p (x1 + 1)) + y1 in
 let ba = (List.nth p b) + z1 and
     bb = (List.nth p (b + 1)) + z1 in
 lerp(w, lerp(v, lerp(u, (grad((List.nth p aa), xi, yi, zi)),
                         (grad((List.nth p ba), xi -. 1., yi , zi))),
                 lerp(u, (grad((List.nth p ab), xi , yi -. 1., zi)),
                         (grad((List.nth p bb), xi -. 1., yi -. 1., zi)))),
         lerp(v, lerp(u, (grad((List.nth p (aa + 1)), xi, yi, zi -. 1.)),
                         (grad((List.nth p (ba + 1)), xi -. 1., yi , zi -. 1.))),
                 lerp(u, (grad((List.nth p (ab + 1)), xi , yi -. 1., zi -.  1.)),
                         (grad((List.nth p (bb + 1)), xi -. 1., yi -.  1., zi -. 1.)))))

let p = perlin_init permutation in 

 print_string((Printf.sprintf "%0.17f" (perlin_noise p 3.14 42.0 7.0)) ^ "\n")

</lang>

Output:
0.13691995878400012

Common Lisp

<lang lisp>;;;; Translation from: Java

(declaim (optimize (speed 3) (debug 0)))

(defconstant +p+ 

 (let ((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)) (aux (make-array 512 :element-type 'fixnum))) 

   (dotimes (i 256 aux)
     (setf (aref aux i) (aref permutation i))
     (setf (aref aux (+ 256 i)) (aref permutation i)))))

(defun fade (te) 

 (declare (type double-float te))
 (the double-float (* te te te (+ (* te (- (* te 6) 15)) 10))))

(defun lerp (te a b) 

 (declare (type double-float te a b))
 (the double-float (+ a (* te (- b a)))))

(defun grad (hash x y z) 

 (declare (type fixnum hash)

(type double-float x y z)) 

 (let* ((h (logand hash 15)) ;; convert lo 4 bits of hash code into 12 gradient directions

(u (if (< h 8) x y)) (v (cond ((< h 4) y) ((or (= h 12) (= h 14)) x) (t z)))) 

   (the
    double-float
    (+
     (if (zerop (logand h 1)) u (- u))
     (if (zerop (logand h 2)) v (- v))))))

(defun noise (x y z) 

 (declare (type double-float x y z))
 ;; find unit cube that contains point.
 (let ((cx (logand (floor x) 255))

(cy (logand (floor y) 255)) (cz (logand (floor z) 255))) 

   ;; find relative x, y, z of point in cube.
   (let ((x (- x (floor x)))

(y (- y (floor y))) (z (- z (floor z)))) 

     ;; compute fade curves for each of x, y, z.
     (let ((u (fade x))

(v (fade y)) (w (fade z))) ;; hash coordinates of the 8 cube corners, (let* ((ca (+ (aref +p+ cx) cy)) (caa (+ (aref +p+ ca) cz)) (cab (+ (aref +p+ (1+ ca)) cz)) (cb (+ (aref +p+ (1+ cx)) cy)) (cba (+ (aref +p+ cb) cz)) (cbb (+ (aref +p+ (1+ cb)) cz)))  ;; ... and add blended results from 8 corners of cube (the double-float (lerp w (lerp v (lerp u (grad (aref +p+ caa) x y z) (grad (aref +p+ cba) (1- x) y z)) (lerp u (grad (aref +p+ cab) x (1- y) z) (grad (aref +p+ cbb) (1- x) (1- y) z))) (lerp v (lerp u (grad (aref +p+ (1+ caa)) x y (1- z)) (grad (aref +p+ (1+ cba)) (1- x) y (1- z))) (lerp u (grad (aref +p+ (1+ cab)) x (1- y) (1- z)) (grad (aref +p+ (1+ cbb)) (1- x) (1- y) (1- z)))))))))))

(print (noise 3.14d0 42d0 7d0)) </lang>

Output:
0.13691995878400012d0

D

<lang d>import std.stdio, std.math;

struct PerlinNoise { 

   private static double fade(in double t) pure nothrow @safe @nogc {
       return t ^^ 3 * (t * (t * 6 - 15) + 10);
   }

   private static double lerp(in double t, in double a, in double b)
   pure nothrow @safe @nogc {
       return a + t * (b - a);
   }

   private static double grad(in ubyte hash,
                              in double x, in double y, in double z)
   pure nothrow @safe @nogc {
       // Convert lo 4 bits of hash code into 12 gradient directions.
       immutable h = hash & 0xF;
       immutable double u = (h < 8) ? x : y,
                        v = (h < 4) ? y : (h == 12 || h == 14 ? x : z);
       return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
   }

   static immutable ubyte[512] p;

   static this() pure nothrow @safe @nogc {
       static immutable permutation = cast(ubyte[256])x"97 A0 89 5B 5A
           0F 83 0D C9 5F 60 35 C2 E9 07 E1 8C 24 67 1E 45 8E 08 63 25
           F0 15 0A 17 BE 06 94 F7 78 EA 4B 00 1A C5 3E 5E FC DB CB 75
           23 0B 20 39 B1 21 58 ED 95 38 57 AE 14 7D 88 AB A8 44 AF 4A
           A5 47 86 8B 30 1B A6 4D 92 9E E7 53 6F E5 7A 3C D3 85 E6 DC
           69 5C 29 37 2E F5 28 F4 66 8F 36 41 19 3F A1 01 D8 50 49 D1
           4C 84 BB D0 59 12 A9 C8 C4 87 82 74 BC 9F 56 A4 64 6D C6 AD
           BA 03 40 34 D9 E2 FA 7C 7B 05 CA 26 93 76 7E FF 52 55 D4 CF
           CE 3B E3 2F 10 3A 11 B6 BD 1C 2A DF B7 AA D5 77 F8 98 02 2C
           9A A3 46 DD 99 65 9B A7 2B AC 09 81 16 27 FD 13 62 6C 6E 4F
           71 E0 E8 B2 B9 70 68 DA F6 61 E4 FB 22 F2 C1 EE D2 90 0C BF
           B3 A2 F1 51 33 91 EB F9 0E EF 6B 31 C0 D6 1F B5 C7 6A 9D B8
           54 CC B0 73 79 32 2D 7F 04 96 FE 8A EC CD 5D DE 72 43 1D 18
           48 F3 8D 80 C3 4E 42 D7 3D 9C B4";

       // Two copies of permutation.
       p[0 .. permutation.length] = permutation[];
       p[permutation.length .. $] = permutation[];
   }

   /// x0, y0 and z0 can be any real numbers, but the result is
   /// zero if they are all integers.
   /// The result is probably in [-1.0, 1.0].
   static double opCall(in double x0, in double y0, in double z0)
   pure nothrow @safe @nogc {
       // Find unit cube that contains point.
       immutable ubyte X = cast(int)x0.floor & 0xFF,
                       Y = cast(int)y0.floor & 0xFF,
                       Z = cast(int)z0.floor & 0xFF;

       // Find relative x,y,z of point in cube.
       immutable x = x0 - x0.floor,
                 y = y0 - y0.floor,
                 z = z0 - z0.floor;

       // Compute fade curves for each of x,y,z.
       immutable u = fade(x),
                 v = fade(y),
                 w = fade(z);

       // Hash coordinates of the 8 cube corners.
       immutable A  = p[X  ]   + Y,
                 AA = p[A]     + Z,
                 AB = p[A + 1] + Z,
                 B  = p[X + 1] + Y,
                 BA = p[B]     + Z,
                 BB = p[B + 1] + Z;

       // And add blended results from  8 corners of cube.
       return lerp(w, lerp(v, lerp(u, grad(p[AA  ], x  , y  , z  ),
                                      grad(p[BA  ], x-1, y  , z  )),
                              lerp(u, grad(p[AB  ], x  , y-1, z  ),
                                      grad(p[BB  ], x-1, y-1, z  ))),
                      lerp(v, lerp(u, grad(p[AA+1], x  , y  , z-1),
                                      grad(p[BA+1], x-1, y  , z-1)),
                              lerp(u, grad(p[AB+1], x  , y-1, z-1),
                                      grad(p[BB+1], x-1, y-1, z-1))));
   }

}

void main() { 

   writefln("%1.17f", PerlinNoise(3.14, 42, 7));

   /*
   // Generate a demo image using the Gray Scale task module.
   import grayscale_image;
   enum N = 200;
   auto im = new Image!Gray(N, N);
   foreach (immutable y; 0 .. N)
       foreach (immutable x; 0 .. N) {
           immutable p = PerlinNoise(x / 30.0, y / 30.0, 0.1);
           im[x, y] = Gray(cast(ubyte)((p + 1) / 2 * 256));
       }
   im.savePGM("perlin_noise.pgm");
   */

}</lang>

Output:
0.13691995878400012

Go

<lang go>package main

import ( 

   "fmt"
   "math"

)

func main() { 

   fmt.Println(noise(3.14, 42, 7))

}

func noise(x, y, z float64) float64 { 

   X := int(math.Floor(x)) & 255
   Y := int(math.Floor(y)) & 255
   Z := int(math.Floor(z)) & 255
   x -= math.Floor(x)
   y -= math.Floor(y)
   z -= math.Floor(z)
   u := fade(x)
   v := fade(y)
   w := fade(z)
   A := p[X] + Y
   AA := p[A] + Z
   AB := p[A+1] + Z
   B := p[X+1] + Y
   BA := p[B] + Z
   BB := p[B+1] + Z
   return lerp(w, lerp(v, lerp(u, grad(p[AA], x, y, z),
       grad(p[BA], x-1, y, z)),
       lerp(u, grad(p[AB], x, y-1, z),
           grad(p[BB], x-1, y-1, z))),
       lerp(v, lerp(u, grad(p[AA+1], x, y, z-1),
           grad(p[BA+1], x-1, y, z-1)),
           lerp(u, grad(p[AB+1], x, y-1, z-1),
               grad(p[BB+1], x-1, y-1, z-1))))

} func fade(t float64) float64 { return t * t * t * (t*(t*6-15) + 10) } func lerp(t, a, b float64) float64 { return a + t*(b-a) } func grad(hash int, x, y, z float64) float64 { 

   // Go doesn't have a ternary.  Ternaries can be translated directly
   // with if statements, but chains of if statements are often better
   // expressed with switch statements.
   switch hash & 15 {
   case 0, 12:
       return x + y
   case 1, 14:
       return y - x
   case 2:
       return x - y
   case 3:
       return -x - y
   case 4:
       return x + z
   case 5:
       return z - x
   case 6:
       return x - z
   case 7:
       return -x - z
   case 8:
       return y + z
   case 9, 13:
       return z - y
   case 10:
       return y - z
   }
   // case 11, 16:
   return -y - z

}

var permutation = []int{ 

   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,

} var p = append(permutation, permutation...)</lang>

Output:
0.13691995878400012

J

We can trivially copy the java implementation:

<lang J>band=:17 b. ImprovedNoise=:3 :0 

 'x y z'=. y
 X=. (<. x) band 255
 Y=. (<. y) band 255
 Z=. (<. z) band 255
 x=. x-<.!.0 x
 y=. y-<.!.0 y
 z=. z-<.!.0 z
 u=. fade x
 v=. fade y
 w=. fade z
 A=. (p{~X)+Y
 AA=.(p{~A)+Z
 AB=.(p{~A+1)+Z
 B=. (p{~X+1)+Y
 BA=.(p{~B)+Z
 BB=.(p{~B+1)+Z

 t1=. (grad(p{~BB+1),(x-1),(y-1),z-1)
 t2=. (lerp u,(grad(p{~AB+1),x,(y-1),z-1),t1)
 t3=. (grad(p{~BA+1),(x-1),y,z-1)
 t4=. (lerp v,(lerp u,(grad(p{~AA+1),x,y,z-1),t3),t2)
 t5=. (grad(p{~BB),(x-1),(y-1),z)
 t6=. (lerp u,(grad(p{~AB),x,(y-1),z),t5)
 t7=. (grad(p{~BA),(x-1),y,z)
 (lerp w,(lerp v,(lerp u,(grad(p{~AA),x,y,z),t7),t6),t4)

)

fade=:3 :0 

 t=.y
 t * t * t * ((t * ((t * 6) - 15)) + 10)

)

lerp=:3 :0 

 't a b'=. y
 a + t * (b - a)

)

grad=:3 :0 

 'hash x y z'=. y
 h =. hash band 15 NB.                 CONVERT LO 4 BITS OF HASH CODE
 u =. x [^:(h<8) y NB.                 INTO 12 GRADIENT DIRECTIONS.
 v =. y [^:(h<4) x [^:((h=12)+.(h=14)) z
 (u [^:((h band 1) = 0) -u) + v [^:((h band 2) = 0) -v

)


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

fade=: 0 0 0 10 _15 6&p.

ImprovedNoise=:3 :0 

 'XYZ xyz'=. |:256 1 #:y
 uvw=. fade xyz
 hash=. 0 1+/(+ p{~0 1+/])/|. XYZ

 t1=.                 (grad(p{~BB+1),(x-1),(y-1),z-1)
 t2=.         (lerp u,(grad(p{~AB+1), x,   (y-1),z-1),t1)
 t3=.                 (grad(p{~BA+1),(x-1), y,   z-1)
 t4=. (lerp v,(lerp u,(grad(p{~AA+1), x,    y,   z-1),t3),t2)
 t5=.                 (grad(p{~BB),  (x-1),(y-1),z)
 t6=.         (lerp u,(grad(p{~AB),   x,   (y-1),z),  t5)
 t7=.                 (grad(p{~BA),  (x-1), y,   z)
 (lerp w,(lerp v,(lerp u,(grad(p{~AA),x,    y,   z),  t7),t6),t4)

) </lang>

And this gives us our desired result:

<lang J> ImprovedNoise 3.14 42 7 0.13692</lang>

Or, asking to see 20 digits after the decimal point:

<lang J> 

  22j20": ImprovedNoise 3.14 42 7

0.13691995878400012000</lang>

Simplified Expression

It's tempting, though, to express this more concisely. We are limited, there, by some of the arbitrary choices in the algorithm, but we can still exploit regularities in its structure:

<lang J>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

fade=: 0 0 0 10 _15 6&p.

grad=:4 :0 

 dir=. (16|x){_1+3 3 3#:25 7 19 1 23 5 21 3 17 11 15 9 25 11 7 9
 dir+/ .*"1 y

)

lerp=:4 :0 

 'a b'=. y
 a + x * (b - a)

)

ImprovedNoise=:3 :0 

 'XYZ xyz'=. |:256 1 #:y
 uvw=. fade xyz
 hash=. p{~0 1+/(+ p{~0 1+/])/|. XYZ
 g=. hash grad xyz-"1|."1#:i.$hash
 u=. (0{uvw) lerp"1 g
 v=. (1{uvw) lerp"1 u
 w=. (2{uvw) lerp"1 v

)</lang>

And we can see that there's no difference in this result:

<lang J> 0.13691995878400012 - ImprovedNoise 3.14 42 7 0</lang>

It's probably possible to simplify this further.

Java

The original code from Perlin was originally published in java. <lang java>// JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN.

public final class ImprovedNoise { 

  static public double noise(double x, double y, double z) {
     int X = (int)Math.floor(x) & 255,                  // FIND UNIT CUBE THAT
         Y = (int)Math.floor(y) & 255,                  // CONTAINS POINT.
         Z = (int)Math.floor(z) & 255;
     x -= Math.floor(x);                                // FIND RELATIVE X,Y,Z
     y -= Math.floor(y);                                // OF POINT IN CUBE.
     z -= Math.floor(z);
     double u = fade(x),                                // COMPUTE FADE CURVES
            v = fade(y),                                // FOR EACH OF X,Y,Z.
            w = fade(z);
     int A = p[X  ]+Y, AA = p[A]+Z, AB = p[A+1]+Z,      // HASH COORDINATES OF
         B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z;      // THE 8 CUBE CORNERS,

     return lerp(w, lerp(v, lerp(u, grad(p[AA  ], x  , y  , z   ),  // AND ADD
                                    grad(p[BA  ], x-1, y  , z   )), // BLENDED
                            lerp(u, grad(p[AB  ], x  , y-1, z   ),  // RESULTS
                                    grad(p[BB  ], x-1, y-1, z   ))),// FROM  8
                    lerp(v, lerp(u, grad(p[AA+1], x  , y  , z-1 ),  // CORNERS
                                    grad(p[BA+1], x-1, y  , z-1 )), // OF CUBE
                            lerp(u, grad(p[AB+1], x  , y-1, z-1 ),
                                    grad(p[BB+1], x-1, y-1, z-1 ))));
  }
  static double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); }
  static double lerp(double t, double a, double b) { return a + t * (b - a); }
  static double grad(int hash, double x, double y, double z) {
     int h = hash & 15;                      // CONVERT LO 4 BITS OF HASH CODE
     double u = h<8 ? x : y,                 // INTO 12 GRADIENT DIRECTIONS.
            v = h<4 ? y : h==12||h==14 ? x : z;
     return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
  }
  static final int p[] = new int[512], 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
  };
  static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; }

}</lang>

Perl

Translation of: Java

<lang perl>use strict; use warnings;

use constant permutation => qw{ 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 }; use constant p => (permutation, permutation);

sub floor { 

   my $x = shift;
   my $xi = int($x);
   return $x < $xi ? $xi - 1 : $xi;

}

sub fade { $_ = shift; $_ * $_ * $_ * ($_ * ($_ * 6 - 15) + 10) } sub lerp { $_[1] + $_[0] * ($_[2] - $_[1]) } sub grad { 

   my ($h, $x, $y, $z) = @_[0..3];
   $h &= 15;
   my $u = $h < 8 ? $x : $y;
   my $v = $h < 4 ? $y :
   $h == 12 || $h == 14 ? $x : $z;
   return (($h & 1) == 0 ? $u : -$u) + (($h & 2) == 0 ? $v : -$v);

}

sub noise { 

   my ($X, $Y, $Z) = map { floor($_) & 255 }
   my ($x, $y, $z) = @_[0,1,2];
   my ($u, $v, $w) = map { fade($_) }
   $x -= $X, $y -= $Y, $z -= $Z;
   my $A = (p)[$X] + $Y;
   my ($AA, $AB) = ( (p)[$A] + $Z, (p)[$A + 1] + $Z );
   my $B = (p)[$X + 1] + $Y;
   my ($BA, $BB) = ( (p)[$B] + $Z, (p)[$B + 1] + $Z );   
   lerp($w, lerp($v, lerp($u,

grad( (p)[$AA], $x, $y, $z ), grad( (p)[$BA], $x - 1, $y, $z ) ), lerp($u, grad( (p)[$AB], $x, $y - 1, $z ), grad( (p)[$BB], $x - 1, $y - 1, $z ) ) ), lerp($v, lerp($u, grad((p)[$AA + 1], $x, $y, $z - 1 ), grad((p)[$BA + 1], $x - 1, $y, $z - 1 )), lerp($u, grad((p)[$AB + 1], $x, $y - 1, $z - 1 ), grad((p)[$BB + 1], $x - 1, $y - 1, $z - 1 )) ) 

   );

}

print noise 3.14, 42, 7;</lang>

Output:
0.136919958784

Perl 6

Translation of: Java

<lang perl6>constant @p = map {:36($_)}, < 47 4G 3T 2J 2I F 3N D 5L 2N 2O 1H 5E 6H 7 69 3W 10 2V U 1X 3Y 8 2R 11 6O L A N 5A 6 44 6V 3C 6I 23 0 Q 5H 1Q 2M 70 63 5N 39 Z B W 1L 4X X 2G 6L 45 1K 2F 4U K 3H 3S 4R 4O 1W 4V 22 4L 1Z 3Q 3V 1C R 4M 25 42 4E 6F 2B 33 6D 3E 1O 5V 3P 6E 64 2X 2K 15 1J 1A 6T 14 6S 2U 3Z 1I 1T P 1R 4H 1 60 28 21 5T 24 3O 57 5S 2H I 4P 5K 5G 3R 3M 38 58 4F 2E 4K 2S 31 5I 4T 56 3 1S 1G 61 6A 6Y 3G 3F 5 5M 12 43 3A 3I 73 2A 2D 5W 5R 5Q 1N 6B 1B G 1M H 52 59 S 16 67 53 4Q 5X 3B 6W 48 2 18 4A 4J 1Y 65 49 2T 4B 4N 17 4S 9 3L M 13 71 J 2Q 30 32 27 35 68 6G 4Y 55 34 2W 62 6U 2P 6C 6Z Y 6Q 5D 6M 5U 40 C 5B 4Z 4I 6P 29 1F 41 6J 6X E 6N 2Z 1D 5C 5Y V 51 5J 2Y 4D 54 2C 5O 4W 37 3D 1E 19 3J 4 46 72 3U 6K 5P 2L 66 36 1V T O 20 6R 3X 3K 5F 26 1U 5Z 1P 4C 50 > xx 2;

sub fade($_) { $_ * $_ * $_ * ($_ * ($_ * 6 - 15) + 10) } sub lerp($t, $a, $b) { $a + $t * ($b - $a) } sub grad($h is copy, $x, $y, $z) { 

   $h +&= 15;
   my $u = $h < 8 ?? $x !! $y;
   my $v = $h < 4 ?? $y !! $h == 12|14 ?? $x !! $z;
   ($h +& 1 ?? -$u !! $u) + ($h +& 2 ?? -$v !! $v);

}

sub noise($x is copy, $y is copy, $z is copy) is export { 

   my ($X, $Y, $Z) = ($x, $y, $z)».floor »+&» 255;
   my ($u, $v, $w) = map &fade, $x -= $X, $y -= $Y, $z -= $Z;
   my ($AA, $AB) = @p[$_] + $Z, @p[$_ + 1] + $Z given @p[$X] + $Y;
   my ($BA, $BB) = @p[$_] + $Z, @p[$_ + 1] + $Z given @p[$X + 1] + $Y;
   lerp($w, lerp($v, lerp($u, grad(@p[$AA    ], $x    , $y    , $z     ),  
                              grad(@p[$BA    ], $x - 1, $y    , $z     )), 
                     lerp($u, grad(@p[$AB    ], $x    , $y - 1, $z     ),  
                              grad(@p[$BB    ], $x - 1, $y - 1, $z     ))),
            lerp($v, lerp($u, grad(@p[$AA + 1], $x    , $y    , $z - 1 ),  
                              grad(@p[$BA + 1], $x - 1, $y    , $z - 1 )), 
                     lerp($u, grad(@p[$AB + 1], $x    , $y - 1, $z - 1 ),
                              grad(@p[$BB + 1], $x - 1, $y - 1, $z - 1 ))));

}

say noise 3.14, 42, 7;</lang>

Output:
0.13691995878

Python

Translation of: Java

<lang python>def perlin_noise(x, y, z): 

   X = int(x) & 255                  # FIND UNIT CUBE THAT
   Y = int(y) & 255                  # CONTAINS POINT.
   Z = int(z) & 255
   x -= int(x)                                # FIND RELATIVE X,Y,Z
   y -= int(y)                                # OF POINT IN CUBE.
   z -= int(z)
   u = fade(x)                                # COMPUTE FADE CURVES
   v = fade(y)                                # FOR EACH OF X,Y,Z.
   w = fade(z)
   A = p[X  ]+Y; AA = p[A]+Z; AB = p[A+1]+Z      # HASH COORDINATES OF
   B = p[X+1]+Y; BA = p[B]+Z; BB = p[B+1]+Z      # THE 8 CUBE CORNERS,

   return lerp(w, lerp(v, lerp(u, grad(p[AA  ], x  , y  , z   ),  # AND ADD
                                  grad(p[BA  ], x-1, y  , z   )), # BLENDED
                          lerp(u, grad(p[AB  ], x  , y-1, z   ),  # RESULTS
                                  grad(p[BB  ], x-1, y-1, z   ))),# FROM  8
                  lerp(v, lerp(u, grad(p[AA+1], x  , y  , z-1 ),  # CORNERS
                                  grad(p[BA+1], x-1, y  , z-1 )), # OF CUBE
                          lerp(u, grad(p[AB+1], x  , y-1, z-1 ),
                                  grad(p[BB+1], x-1, y-1, z-1 ))))

def fade(t): 

   return t ** 3 * (t * (t * 6 - 15) + 10)

def lerp(t, a, b): 

   return a + t * (b - a)

def grad(hash, x, y, z): 

   h = hash & 15                      # CONVERT LO 4 BITS OF HASH CODE
   u = x if h<8 else y                # INTO 12 GRADIENT DIRECTIONS.
   v = y if h<4 else (x if h in (12, 14) else z)
   return (u if (h&1) == 0 else -u) + (v if (h&2) == 0 else -v)

p = [None] * 512 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]

for i in range(256): 

   p[256+i] = p[i] = permutation[i]

if __name__ == '__main__': 

   print("%1.17f" % perlin_noise(3.14, 42, 7))</lang>
Output:
0.13691995878400012

Racket

Translation of: Java

-- because we were asked to

<lang racket>#lang racket (define (floor-to-255 x) 

 (bitwise-and (exact-floor x) #xFF))

(define (fade t) 

 (* t t t (+ 10 (* t (- (* t 6) 15)))))

(define (lerp t a b) 

 (+ a (* t (- b a))))
CONVERT LO 4 BITS OF HASH CODE INTO 12 GRADIENT DIRECTIONS.

(define (grad hsh x y z) 

 (define h (bitwise-and hsh #x0F))
 (define u (if (< h 8) x y))
 (define v (cond [(< h 4) y] [(or (= h 12) (= h 14)) x] [else z]))
 (+ (if (bitwise-bit-set? h 0) (- u) u) (if (bitwise-bit-set? h 1) (- v) v)))

(define permutation 

 (vector
  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))

(define p (make-vector 512)) (for ((offset (in-list '(0 256)))) 

 (vector-copy! p offset permutation))

(define-syntax-rule (p-ref n) 

 (vector-ref p n))

(define (noise x y z) 

 (let*
     (
      ;; FIND UNIT CUBE THAT CONTAINS POINT.
      (X (floor-to-255 x))
      (Y (floor-to-255 y))
      (Z (floor-to-255 z))
      ; FIND RELATIVE X,Y,Z OF POINT IN CUBE.
      (x (- x (floor x)))
      (y (- y (floor y)))
      (z (- z (floor z)))
      ;; COMPUTE FADE CURVES FOR EACH OF X,Y,Z.
      (u (fade x))
      (v (fade y))
      (w (fade z))
      ;; HASH COORDINATES OF THE 8 CUBE CORNERS...
      (A  (+ (p-ref X) Y))
      (AA (+ (p-ref A) Z))
      (AB (+ (p-ref (add1 A)) Z))
      (B  (+ (p-ref (add1 X)) Y))
      (BA (+ (p-ref B) Z))
      (BB (+ (p-ref (add1 B)) Z)))
   ;; .. AND ADD BLENDED RESULTS FROM 8 CORNERS OF CUBE
   (lerp
    w
    (lerp
     v (lerp u (grad (p-ref AA) x y z) (grad (p-ref BA) (sub1 x) y z))
     (lerp u (grad (p-ref AB) x (sub1 y) z) (grad (p-ref BB) (sub1 x) (sub1 y) z)))
    (lerp
     v
     (lerp u (grad (p-ref (add1 AA)) x y (sub1 z)) (grad (p-ref (add1 BA)) (sub1 x) y (sub1 z)))
     (lerp u (grad (vector-ref p (add1 AB)) x (sub1 y) (sub1 z))
           (grad (vector-ref p (add1 BB)) (sub1 x) (sub1 y) (sub1 z)))))))

(module+ test 

 (noise 3.14 42 7))</lang>
Output:
0.13691995878400012

REXX

Translation of: Go

<lang rexx>/*REXX program implements a Perlin noise algorithm of a point in 3D─space. */ 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

numeric digits 100 /*use 100 decimal digits for precision.*/ parse arg x y z . /*get optional arguments from the C.L. */ if x== | x==',' then x= 3.14 if y== | y==',' then y= 42 if z== | z==',' then z= 7 say 'Perlin noise for ' x " " y ' ' z " ───► " PerlinNoise(x,y,z) exit /*stick a fork in it, we're all done. */ /*────────────────────────────────────────────────────────────────────────────*/ fade: procedure; parse arg t; return t**3 * (t * (t * 6 - 15) + 10) floor: procedure; parse arg x; _=x%1; return _-(x<0)*(x\=_) lerp: procedure: parse arg t,a,b; return a + t * (b - a) p: /*return a number in P list.*/ return word(p, arg(1) // 256 + 1) /*────────────────────────────────────────────────────────────────────────────*/ grad: procedure; parse arg hash,x,y,z; _=hash // 16 

                     select
                     when _= 0 | _==12  then return  x+y
                     when _= 1 | _==14  then return  y-x
                     when _= 2          then return  x-y
                     when _= 3          then return -x-y
                     when _= 4          then return  x+z
                     when _= 5          then return  z-x
                     when _= 6          then return  x-z
                     when _= 7          then return -x-z
                     when _= 8          then return  y+z
                     when _= 9 | _==13  then return  z-y
                     when _=10          then return  y-z
                     otherwise               return -y-z
                     end   /*select*/

/*────────────────────────────────────────────────────────────────────────────*/ PerlinNoise: procedure expose p; parse arg x,y,z 

            x$= floor(x) // 256;   x = x-floor(x);        u = fade(x)
            y$= floor(y) // 256;   y = y-floor(y);        v = fade(y)
            z$= floor(z) // 256;   z = z-floor(z);        w = fade(z)
            a = p(x$  ) + y$;      aa= p(a) + z$;        ab = p(a+1) + z$
            b = p(x$+1) + y$;      ba= p(b) + z$;        bb = p(b+1) + z$
            return lerp(w, lerp(v, lerp(u, grad(p(aa  ), x,    y,    z   ),,
                                           grad(p(ba  ), x-1,  y,    z   )),,
                                   lerp(u, grad(p(ab  ), x,    y-1,  z   ),,
                                           grad(p(bb  ), x-1,  y-1,  z   ))),,
                           lerp(v, lerp(u, grad(p(aa+1), x,    y,    z-1 ),,
                                           grad(p(ba+1), x-1,  y,    z-1 )),,
                                   lerp(u, grad(p(ab+1), x,    y-1,  z-1 ),,
                                           grad(p(BB+1), x-1,  y-1,  z-1 ))))</lang>

output   when using the default inputs:

(Note that REXX uses decimal floating point, not binary.) 

Perlin noise for  3.14   42   7  ───►  0.136919958784

Tcl

Works with: Tcl version 8.6

<lang tcl>namespace eval perlin { 

   proc noise {x y z} {

# Find unit cube that contains point. set X [expr {int(floor($x)) & 255}] set Y [expr {int(floor($y)) & 255}] set Z [expr {int(floor($z)) & 255}]

# Find relative x,y,z of point in cube. set x [expr {$x - floor($x)}] set y [expr {$y - floor($y)}] set z [expr {$z - floor($z)}]

# Compute fade curves for each of x,y,z. set u [expr {fade($x)}] set v [expr {fade($y)}] set w [expr {fade($z)}]

# Hash coordinates of the 8 cube corners... variable p set A [expr {p($X) + $Y}] set AA [expr {p($A) + $Z}] set AB [expr {p($A+1) + $Z}] set B [expr {p($X+1) + $Y}] set BA [expr {p($B) + $Z}] set BB [expr {p($B+1) + $Z}]

# And add blended results from 8 corners of cube return [expr { lerp($w, lerp($v, lerp($u, grad(p($AA), $x, $y, $z ), grad(p($BA), $x-1, $y, $z )), lerp($u, grad(p($AB), $x, $y-1, $z ), grad(p($BB), $x-1, $y-1, $z ))), lerp($v, lerp($u, grad(p($AA+1), $x, $y, $z-1 ), grad(p($BA+1), $x-1, $y, $z-1 )), lerp($u, grad(p($AB+1), $x, $y-1, $z-1 ), grad(p($BB+1), $x-1, $y-1, $z-1 )))) }] 

   }

   namespace eval tcl::mathfunc {

proc p {idx} {lindex $::perlin::permutation $idx} proc fade {t} {expr { $t**3 * ($t * ($t * 6 - 15) + 10) }} proc lerp {t a b} {expr { $a + $t * ($b - $a) }} proc grad {hash x y z} { # Convert low 4 bits of hash code into 12 gradient directions set h [expr { $hash & 15 }] set u [expr { $h<8 ? $x : $y }] set v [expr { $h<4 ? $y : ($h==12 || $h==14) ? $x : $z }] expr { (($h&1)==0 ? $u : -$u) + (($h&2)==0 ? $v : -$v) } } 

   }

   apply {{} {

binary scan [binary format H* [join { 97A0895B5A0F830DC95F6035C2E907E18C24671E458E086325F0150A17BE0694F7 78EA4B001AC53E5EFCDBCB75230B2039B12158ED953857AE147D88ABA844AF4AA5 

           47868B301BA64D929EE7536FE57A3CD385E6DC695C29372EF528F4668F3641193F

A101D85049D14C84BBD05912A9C8C4878274BC9F56A4646DC6ADBA034034D9E2FA 

           7C7B05CA2693767EFF5255D4CFCE3BE32F103A11B6BD1C2ADFB7AAD577F898022C

9AA346DD99659BA72BAC09811627FD13626C6E4F71E0E8B2B97068DAF661E4FB22 

           F2C1EED2900CBFB3A2F1513391EBF90EEF6B31C0D61FB5C76A9DB854CCB0737932

2D7F0496FE8AECCD5DDE72431D1848F38D80C34E42D73D9CB4 } ""]] cu* p variable ::perlin::permutation [concat $p $p] 

   }}

}

puts [perlin::noise 3.14 42 7]</lang>

Output:
0.13691995878400012

zkl

Translation of: Java

<lang zkl>class [static] ImprovedNoise{ // a container, not an object 

  fcn noise(xyz){ xyz=vm.arglist.apply("toFloat");
     X,Y,Z:=	// FIND UNIT CUBE THAT CONTAINS POINT.
        xyz.apply(fcn(x){ x.floor().toInt().bitAnd(255) });
     xyz=      // FIND RELATIVE X,Y,Z OF POINT IN CUBE.
        xyz.apply(fcn(x){ x - x.floor() });
     u,v,w:= xyz.apply(fade);  // COMPUTE FADE CURVES FOR EACH OF X,Y,Z.
     A,AA,AB:= p[X  ]+Y, p[A]+Z, p[A+1]+Z;      // HASH COORDINATES OF
     B,BA,BB:= p[X+1]+Y, p[B]+Z, p[B+1]+Z;      // THE 8 CUBE CORNERS,
     x,y,z:=xyz;
     lerp(w, lerp(v, lerp(u, grad(p[AA  ], x  , y  , z   ),  // AND ADD
                             grad(p[BA  ], x-1, y  , z   )), // BLENDED
                     lerp(u, grad(p[AB  ], x  , y-1, z   ),  // RESULTS
                             grad(p[BB  ], x-1, y-1, z   ))),// FROM  8
             lerp(v, lerp(u, grad(p[AA+1], x  , y  , z-1 ),  // CORNERS
                             grad(p[BA+1], x-1, y  , z-1 )), // OF CUBE
                     lerp(u, grad(p[AB+1], x  , y-1, z-1 ),
                             grad(p[BB+1], x-1, y-1, z-1 ))));
  }
  fcn [private] fade(t){ t*t*t*(t*(t*6 - 15) + 10) }
  fcn [private] lerp(t,a,b){ a + t*(b - a) }
  fcn [private] grad(hash,x,y,z){
     h:=hash.bitAnd(15);		// CONVERT LO 4 BITS OF HASH CODE
     u:=(if(h<8) x else y);		// INTO 12 GRADIENT DIRECTIONS.
     v:=(if(h<4) y else ((h==12 or h==14) and x or z));
     (if(h.isEven) u else -u) + (if(h.bitAnd(2)==0) v else -v)
  }
  var [const,private] permutation=Data(Void, 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),
   p=Data(Void,permutation,permutation);

}</lang> <lang zkl>ImprovedNoise.noise(3.14, 42, 7).println();</lang>

Output:
0.13692
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