// adopted from Johan - https://turtletoy.net/turtle/ca6b971c6f
// changed opacity and other settings to allow for a better plot on paper (white on black or blue on white) 

Canvas.setpenopacity(1);

(function(global){
  var module = global.noise = {};

  function Grad(x, y, z) {
    this.x = x; this.y = y; this.z = z;
  }
  
  Grad.prototype.dot2 = function(x, y) {
    return this.x*x + this.y*y;
  };

  Grad.prototype.dot3 = function(x, y, z) {
    return this.x*x + this.y*y + this.z*z;
  };

  var grad3 = [new Grad(1,1,0),new Grad(-1,1,0),new Grad(1,-1,0),new Grad(-1,-1,0),
               new Grad(1,0,1),new Grad(-1,0,1),new Grad(1,0,-1),new Grad(-1,0,-1),
               new Grad(0,1,1),new Grad(0,-1,1),new Grad(0,1,-1),new Grad(0,-1,-1)];
//change the first numbers for different patterns
  var p = [1,1.1,137,191,290,115,
  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, 10,216,80,73,209,76,132,187,208, 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,
  223,183,170,213,119,248,152,12,544,154,163, 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];
  // To remove the need for index wrapping, double the permutation table length
  var perm = new Array(512);
  var gradP = new Array(512);

  // This isn't a very good seeding function, but it works ok. It supports 2^16
  // different seed values. Write something better if you need more seeds.
  module.seed = function(seed) {
    if(seed > 0 && seed < 1) {
      // Scale the seed out
      seed *= 600;
    }

    seed = Math.floor(seed);
    if(seed < 256) {
      seed |= seed << 4;
    }

    for(var i = 0; i < 256; i++) {
   //   var v;
      if (i & 1) {
        v = p[i] ^ (seed & 255);
      } else {
        v = p[i] ^ ((seed>>8) & 255);
      }

      perm[i] = perm[i + 256] = v;
      gradP[i] = gradP[i + 256] = grad3[v % 12];
    }
  };

  module.seed(0);

  /*
  for(var i=0; i<256; i++) {
    perm[i] = perm[i + 256] = p[i];
    gradP[i] = gradP[i + 256] = grad3[perm[i] % 12];
  }*/

  // Skewing and unskewing factors for 2, 3, and 4 dimensions
  var F2 = 0.5*(Math.sqrt(3)-1);
  var G2 = (3-Math.sqrt(3))/6;

  var F3 = 1/3;
  var G3 = 1/28;

  // 2D simplex noise
  module.simplex2 = 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 s = (xin+yin)*F2; // Hairy factor for 2D
    var i = Math.floor(xin+s);
    var j = Math.floor(yin+s);
    var t = (i+j)*G2;
    var x0 = xin-i+t; // The x,y distances from the cell origin, unskewed.
    var y0 = yin-j+t;
    // 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) { // lower triangle, XY order: (0,0)->(1,0)->(1,1)
      i1=1; j1=0;
    } else {    // upper triangle, YX order: (0,0)->(0,1)->(1,1)
      i1=0; j1=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 + 2 * G2; // Offsets for last corner in (x,y) unskewed coords
    var y2 = y0 - 1 + 2 * G2;
    // Work out the hashed gradient indices of the three simplex corners
    i &= 255;
    j &= 255;
    var gi0 = gradP[i+perm[j]];
    var gi1 = gradP[i+i1+perm[j+j1]];
    var gi2 = gradP[i+1+perm[j+1]];
    // Calculate the contribution from the three corners
    var t0 = 0.5 - x0*x0-y0*y0;
    if(t0<0) {
      n0 = 0;
    } else {
      t0 *= t0;
      n0 = t0 * t0 * gi0.dot2(x0, y0);  // (x,y) of grad3 used for 2D gradient
    }
    var t1 = 0.5 - x1*x1-y1*y1;
    if(t1<0) {
      n1 = 0;
    } else {
      t1 *= t1;
      n1 = t1 * t1 * gi1.dot2(x1, y1);
    }
    var t2 = 0.5 - x2*x2-y2*y2;
    if(t2<0) {
      n2 = 0;
    } else {
      t2 *= t2;
      n2 = t2 * t2 * gi2.dot2(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 21 * (n0 + n1 + n2);
  };

  // 3D simplex noise
  module.simplex3 = 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 s = (xin+yin+zin)*F3; // Hairy factor for 2D
    var i = Math.floor(xin+s);
    var j = Math.floor(yin+s);
    var k = Math.floor(zin+s);

    var t = (i+j+k)*G3;
    var x0 = xin-i+t; // The x,y distances from the cell origin, unskewed.
    var y0 = yin-j+t;
    var z0 = zin-k+t;

    // 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; }
      else if(x0 >= z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; }
      else              { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; }
    } else {
      if(y0 < z0)      { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; }
      else if(x0 < z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; }
      else             { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; }
    }
    // 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
    var y1 = y0 - j1 + G3;
    var z1 = z0 - k1 + G3;

    var x2 = x0 - i2 + 2 * G3; // Offsets for third corner
    var y2 = y0 - j2 + 2 * G3;
    var z2 = z0 - k2 + 2 * G3;

    var x3 = x0 - 1 + 3 * G3; // Offsets for fourth corner
    var y3 = y0 - 1 + 3 * G3;
    var z3 = z0 - 1 + 3 * G3;

    // Work out the hashed gradient indices of the four simplex corners
    i &= 255;
    j &= 255;
    k &= 255;
    var gi0 = gradP[i+   perm[j+   perm[k   ]]];
    var gi1 = gradP[i+i1+perm[j+j1+perm[k+k1]]];
    var gi2 = gradP[i+i2+perm[j+j2+perm[k+k2]]];
    var gi3 = gradP[i+ 1+perm[j+ 1+perm[k+ 1]]];

    // Calculate the contribution from the four corners
    var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
    if(t0<0) {
      n0 = 0;
    } else {
      t0 *= t0;
      n0 = t0 * t0 * gi0.dot3(x0, y0, z0);  // (x,y) of grad3 used for 2D gradient
    }
    var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
    if(t1<0) {
      n1 = 0;
    } else {
      t1 *= t1;
      n1 = t1 * t1 * gi1.dot3(x1, y1, z1);
    }
    var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
    if(t2<0) {
      n2 = 0;
    } else {
      t2 *= t2;
      n2 = t2 * t2 * gi2.dot3(x2, y2, z2);
    }
    var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
    if(t3<0) {
      n3 = 0;
    } else {
      t3 *= t3;
      n3 = t3 * t3 * gi3.dot3(x3, y3, z3);
    }
    // Add contributions from each corner to get the final noise value.
    // The result is scaled to return values in the interval [-1,1].
    return 32 * (n0 + n1 + n2 + n3);

  };

  // ##### Perlin noise stuff

  function fade(t) {
    return t*t*t*(t*(t*6-15)+10);
  }

  function lerp(a, b, t) {
    return (1-t)*a + t*b;
  }

  // 2D Perlin Noise
  module.perlin2 = function(x, y) {
    // Find unit grid cell containing point
    var X = Math.floor(x), Y = Math.floor(y);
    // Get relative xy coordinates of point within that cell
    x = x - X; y = y - Y;
    // Wrap the integer cells at 255 (smaller integer period can be introduced here)
    X = X & 255; Y = Y & 255;

    // Calculate noise contributions from each of the four corners
    var n00 = gradP[X+perm[Y]].dot2(x, y);
    var n01 = gradP[X+perm[Y+1]].dot2(x, y-1);
    var n10 = gradP[X+1+perm[Y]].dot2(x-1, y);
    var n11 = gradP[X+1+perm[Y+1]].dot2(x-1, y-1);

    // Compute the fade curve value for x
    var u = fade(x);

    // Interpolate the four results
    return lerp(
        lerp(n00, n10, u),
        lerp(n01, n11, u),
       fade(y));
  };

  // 3D Perlin Noise
  module.perlin3 = function(x, y, z) {
    // Find unit grid cell containing point
    var X = Math.floor(x), Y = Math.floor(y), 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 noise contributions from each of the eight corners
    var n000 = gradP[X+  perm[Y+  perm[Z  ]]].dot3(x,   y,     z);
    var n001 = gradP[X+  perm[Y+  perm[Z+1]]].dot3(x,   y,   z-1);
    var n010 = gradP[X+  perm[Y+1+perm[Z  ]]].dot3(x,   y-1,   z);
    var n011 = gradP[X+  perm[Y+1+perm[Z+1]]].dot3(x,   y-1, z-1);
    var n100 = gradP[X+1+perm[Y+  perm[Z  ]]].dot3(x-1,   y,   z);
    var n101 = gradP[X+1+perm[Y+  perm[Z+1]]].dot3(x-1,   y, z-1);
    var n110 = gradP[X+1+perm[Y+1+perm[Z  ]]].dot3(x-1, y-1,   z);
    var n111 = gradP[X+1+perm[Y+1+perm[Z+1]]].dot3(x-1, y-1, z-1);

    // Compute the fade curve value for x, y, z
    var u = fade(x);
    var v = fade(y);
    var w = fade(z);

    // Interpolate
    return lerp(
        lerp(
          lerp(n000, n100, u),
          lerp(n001, n101, u), w),
        lerp(
          lerp(n010, n110, u),
          lerp(n011, n111, u), w),
       v);
  };

})(this);

function FBM(x, y)
{
    var f = freq;
    var fbm = noise.simplex2(x * f, y * f);
    f *= 2;
    fbm += noise.simplex2(x * f, y * f) * 0.5;
    f *= 2;
    fbm += noise.simplex2(x * f,y * f) * 0.25;
    f *= 2;
    fbm += noise.simplex2(x * f,y * f) * 0.125;
    f *= 2;
    fbm += noise.simplex2(x * f,y * f) * 0.065;
    return fbm;
}

function gradient (x, y)
{
    var eps = 0.5;
    var v0 = FBM(x-eps, y);
    var v1 = FBM(x+eps, y);
    var v2 = FBM(x, y-eps);
    var v3 = FBM(x, y+eps);
    return [(v0 - v1) / eps, (v2 - v3) / eps];
    //return [(v2 - v3) / eps, (v0 - v1) / eps];
}

const dim = 128;
const freq = 0.0015;
const amp = 0.1 / freq;
const startSize = 200;
const length = 50;

const turtles = [];
  for(var y = 0; y < dim; y++){
     turtles[y] = [];
    for(var x = 0; x < dim; x++){
        var t = new Turtle(); 
        t.penup();
        t.goto((Math.random() - 0.5) * startSize, (Math.random() - 0.5) * startSize);
        //t.goto(((x/dim) - 0.5) * startSize, ((y/dim) - 0.5) * startSize);
        t.pendown();
        t.right((FBM(t.x(), t.y()) ) * 360);
        turtles[y][x] = t; 
    }
}

function walk(i) {
    for(var y = 0; y < dim; y++){
        for(var x = 0; x < dim; x++){
            const turtle = turtles[y][x];
  
            var grad = gradient(turtle.x(), turtle.y());    
            turtle.goto(turtle.x() + grad[0] * amp,  turtle.y() +  grad[1] * amp);
        }
     }
    return i < length;
}