### Simplex Noise

A compact Simplex Noise implementation in javascript. Based on: webstaff.itn.liu.se/…ise/simplexnoise.pdf by Stefan Gustavson.

#utility #simplex #noise

```// Simplex Noise. Created by Reinder Nijhoff 2020 - @reindernijhoff
//
// https://turtletoy.net/turtle/6e4e06d42e
//

const turtle = new Turtle();

const frequency = 3; //min=.1, max=10, step=.01
const grid = 50; // min=10, max=100, step=1
const seed = 1; // min=1, max=100, step=1
const noise  = new SimplexNoise(seed);

function walk(i) {
const x = (i % grid)*200/grid - 100;
const y = ((i / grid)|0)*200/grid-100;

const r = .5 + .5 * noise.noise2D([x*frequency/200, y*frequency/200, .5]);

turtle.jump(x+100/grid, y+100*(1-r)/grid);
turtle.circle(r * 100/grid);

return i < grid*grid-1;
}

////////////////////////////////////////////////////////////////
// Simplex Noise utility code. Created by Reinder Nijhoff 2020
// https://turtletoy.net/turtle/6e4e06d42e
// Based on: http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
////////////////////////////////////////////////////////////////
function SimplexNoise(seed = 1) {
const grad = [  [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] ];
const perm = new Uint8Array(512);

const F2 = (Math.sqrt(3) - 1) / 2, F3 = 1/3;
const G2 = (3 - Math.sqrt(3)) / 6, G3 = 1/6;

const dot2 = (a, b) => a[0] * b[0] + a[1] * b[1];
const sub2 = (a, b) => [a[0] - b[0], a[1] - b[1]];
const dot3 = (a, b) => a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
const sub3 = (a, b) => [a[0] - b[0], a[1] - b[1], a[2] - b[2]];

class SimplexNoise {
constructor(seed = 1) {
for (let i = 0; i < 512; i++) {
perm[i] = i & 255;
}
for (let i = 0; i < 255; i++) {
const r = (seed = this.hash(i+seed)) % (256 - i)  + i;
const swp = perm[i];
perm[i + 256] = perm[i] = perm[r];
perm[r + 256] = perm[r] = swp;
}
}
noise2D(p) {
const s = dot2(p, [F2, F2]);
const c = [Math.floor(p[0] + s), Math.floor(p[1] + s)];
const i = c[0] & 255, j = c[1] & 255;
const t = dot2(c, [G2, G2]);

const p0 = sub2(p, sub2(c, [t, t]));
const o  = p0[0] > p0[1] ? [1, 0] : [0, 1];
const p1 = sub2(sub2(p0, o), [-G2, -G2]);
const p2 = sub2(p0, [1-2*G2, 1-2*G2]);

let n =  Math.max(0, 0.5-dot2(p0, p0))**4 * dot2(grad[perm[i+perm[j]] % 12], p0);
n += Math.max(0, 0.5-dot2(p1, p1))**4 * dot2(grad[perm[i+o[0]+perm[j+o[1]]] % 12], p1);
n += Math.max(0, 0.5-dot2(p2, p2))**4 * dot2(grad[perm[i+1+perm[j+1]] % 12], p2);

return 70 * n;
}
noise3D(p) {
const s = dot3(p, [F3, F3, F3]);
const c = [Math.floor(p[0] + s), Math.floor(p[1] + s), Math.floor(p[2] + s)];
const i = c[0] & 255, j = c[1] & 255, k = c[2] & 255;
const t = dot3(c, [G3, G3, G3]);

const p0 = sub3(p, sub3(c, [t, t, t]));
const [o0, o1] = p0[0] >= p0[1] ? p0[1] >= p0[2] ? [ [1, 0, 0], [1, 1, 0] ]
: p0[0] >= p0[2] ? [ [1, 0, 0], [1, 0, 1] ]
: [ [0, 0, 1], [1, 0, 1] ]
: p0[1] < p0[2]  ? [ [0, 0, 1], [0, 1, 1] ]
: p0[0] < p0[2]  ? [ [0, 1, 0], [0, 1, 1] ]
: [ [0, 1, 0], [1, 1, 0] ];
const p1 = sub3(sub3(p0, o0), [-G3, -G3, -G3]);
const p2 = sub3(sub3(p0, o1), [-2*G3, -2*G3, -2*G3]);
const p3 = sub3(p0, [1-3*G3, 1-3*G3, 1-3*G3]);

let n  = Math.max(0, 0.6-dot3(p0, p0))**4 * dot3(grad[perm[i+perm[j+perm[k]]] % 12], p0);
n += Math.max(0, 0.6-dot3(p1, p1))**4 * dot3(grad[perm[i+o0[0]+perm[j+o0[1]+perm[k+o0[2]]]] % 12], p1);
n += Math.max(0, 0.6-dot3(p2, p2))**4 * dot3(grad[perm[i+o1[0]+perm[j+o1[1]+perm[k+o1[2]]]] % 12], p2);
n += Math.max(0, 0.6-dot3(p3, p3))**4 * dot3(grad[perm[i+1+perm[j+1+perm[k+1]]] % 12], p3);

return 32 * n;
}
hash(i) {
i = 1103515245 * ((i >> 1) ^ i);
const h32 = 1103515245 * (i ^ (i>>3));
return h32 ^ (h32 >> 16);
}
}
return new SimplexNoise(seed);
}```