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// Ported from Stefan Gustavson's java implementation
// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
// Read Stefan's excellent paper for details on how this code works.
//
// Sean McCullough banksean@gmail.com
//
// Added 4D noise
// Joshua Koo zz85nus@gmail.com
/**
* You can pass in a random number generator object if you like.
* It is assumed to have a random() method.
*/
var SimplexNoise = function(r) {
if (r == undefined) r = Math;
this.grad3 = [[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]];
this.grad4 = [[0,1,1,1], [0,1,1,-1], [0,1,-1,1], [0,1,-1,-1],
[0,-1,1,1], [0,-1,1,-1], [0,-1,-1,1], [0,-1,-1,-1],
[1,0,1,1], [1,0,1,-1], [1,0,-1,1], [1,0,-1,-1],
[-1,0,1,1], [-1,0,1,-1], [-1,0,-1,1], [-1,0,-1,-1],
[1,1,0,1], [1,1,0,-1], [1,-1,0,1], [1,-1,0,-1],
[-1,1,0,1], [-1,1,0,-1], [-1,-1,0,1], [-1,-1,0,-1],
[1,1,1,0], [1,1,-1,0], [1,-1,1,0], [1,-1,-1,0],
[-1,1,1,0], [-1,1,-1,0], [-1,-1,1,0], [-1,-1,-1,0]];
this.p = [];
for (var i=0; i<256; i++) {
this.p[i] = Math.floor(r.random()*256);
}
// To remove the need for index wrapping, double the permutation table length
this.perm = [];
for(var i=0; i<512; i++) {
this.perm[i]=this.p[i & 255];
}
// A lookup table to traverse the simplex around a given point in 4D.
// Details can be found where this table is used, in the 4D noise method.
this.simplex = [
[0,1,2,3],[0,1,3,2],[0,0,0,0],[0,2,3,1],[0,0,0,0],[0,0,0,0],[0,0,0,0],[1,2,3,0],
[0,2,1,3],[0,0,0,0],[0,3,1,2],[0,3,2,1],[0,0,0,0],[0,0,0,0],[0,0,0,0],[1,3,2,0],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[1,2,0,3],[0,0,0,0],[1,3,0,2],[0,0,0,0],[0,0,0,0],[0,0,0,0],[2,3,0,1],[2,3,1,0],
[1,0,2,3],[1,0,3,2],[0,0,0,0],[0,0,0,0],[0,0,0,0],[2,0,3,1],[0,0,0,0],[2,1,3,0],
[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0],
[2,0,1,3],[0,0,0,0],[0,0,0,0],[0,0,0,0],[3,0,1,2],[3,0,2,1],[0,0,0,0],[3,1,2,0],
[2,1,0,3],[0,0,0,0],[0,0,0,0],[0,0,0,0],[3,1,0,2],[0,0,0,0],[3,2,0,1],[3,2,1,0]];
};
SimplexNoise.prototype.dot = function(g, x, y) {
return g[0]*x + g[1]*y;
};
SimplexNoise.prototype.noise = 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 F2 = 0.5*(Math.sqrt(3.0)-1.0);
var s = (xin+yin)*F2; // Hairy factor for 2D
var i = Math.floor(xin+s);
var j = Math.floor(yin+s);
var G2 = (3.0-Math.sqrt(3.0))/6.0;
var t = (i+j)*G2;
var X0 = i-t; // Unskew the cell origin back to (x,y) space
var Y0 = j-t;
var x0 = xin-X0; // The x,y distances from the cell origin
var y0 = yin-Y0;
// 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) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// 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 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
var y2 = y0 - 1.0 + 2.0 * G2;
// Work out the hashed gradient indices of the three simplex corners
var ii = i & 255;
var jj = j & 255;
var gi0 = this.perm[ii+this.perm[jj]] % 12;
var gi1 = this.perm[ii+i1+this.perm[jj+j1]] % 12;
var gi2 = this.perm[ii+1+this.perm[jj+1]] % 12;
// Calculate the contribution from the three corners
var t0 = 0.5 - x0*x0-y0*y0;
if(t0<0) n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
}
var t1 = 0.5 - x1*x1-y1*y1;
if(t1<0) n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1);
}
var t2 = 0.5 - x2*x2-y2*y2;
if(t2<0) n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * this.dot(this.grad3[gi2], 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 70.0 * (n0 + n1 + n2);
};
// 3D simplex noise
SimplexNoise.prototype.noise3d = 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 F3 = 1.0/3.0;
var s = (xin+yin+zin)*F3; // Very nice and simple skew factor for 3D
var i = Math.floor(xin+s);
var j = Math.floor(yin+s);
var k = Math.floor(zin+s);
var G3 = 1.0/6.0; // Very nice and simple unskew factor, too
var t = (i+j+k)*G3;
var X0 = i-t; // Unskew the cell origin back to (x,y,z) space
var Y0 = j-t;
var Z0 = k-t;
var x0 = xin-X0; // The x,y,z distances from the cell origin
var y0 = yin-Y0;
var z0 = zin-Z0;
// 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; } // X Y Z order
else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order
else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order
}
else { // x0<y0
if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order
else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order
else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order
}
// 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 in (x,y,z) coords
var y1 = y0 - j1 + G3;
var z1 = z0 - k1 + G3;
var x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords
var y2 = y0 - j2 + 2.0*G3;
var z2 = z0 - k2 + 2.0*G3;
var x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords
var y3 = y0 - 1.0 + 3.0*G3;
var z3 = z0 - 1.0 + 3.0*G3;
// Work out the hashed gradient indices of the four simplex corners
var ii = i & 255;
var jj = j & 255;
var kk = k & 255;
var gi0 = this.perm[ii+this.perm[jj+this.perm[kk]]] % 12;
var gi1 = this.perm[ii+i1+this.perm[jj+j1+this.perm[kk+k1]]] % 12;
var gi2 = this.perm[ii+i2+this.perm[jj+j2+this.perm[kk+k2]]] % 12;
var gi3 = this.perm[ii+1+this.perm[jj+1+this.perm[kk+1]]] % 12;
// Calculate the contribution from the four corners
var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
if(t0<0) n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0, z0);
}
var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
if(t1<0) n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1, z1);
}
var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
if(t2<0) n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * this.dot(this.grad3[gi2], x2, y2, z2);
}
var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
if(t3<0) n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * this.dot(this.grad3[gi3], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0*(n0 + n1 + n2 + n3);
};
// 4D simplex noise
SimplexNoise.prototype.noise4d = function( x, y, z, w ) {
// For faster and easier lookups
var grad4 = this.grad4;
var simplex = this.simplex;
var perm = this.perm;
// The skewing and unskewing factors are hairy again for the 4D case
var F4 = (Math.sqrt(5.0)-1.0)/4.0;
var G4 = (5.0-Math.sqrt(5.0))/20.0;
var n0, n1, n2, n3, n4; // Noise contributions from the five corners
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
var s = (x + y + z + w) * F4; // Factor for 4D skewing
var i = Math.floor(x + s);
var j = Math.floor(y + s);
var k = Math.floor(z + s);
var l = Math.floor(w + s);
var t = (i + j + k + l) * G4; // Factor for 4D unskewing
var X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
var Y0 = j - t;
var Z0 = k - t;
var W0 = l - t;
var x0 = x - X0; // The x,y,z,w distances from the cell origin
var y0 = y - Y0;
var z0 = z - Z0;
var w0 = w - W0;
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// The method below is a good way of finding the ordering of x,y,z,w and
// then find the correct traversal order for the simplex we’re in.
// First, six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to add up binary bits
// for an integer index.
var c1 = (x0 > y0) ? 32 : 0;
var c2 = (x0 > z0) ? 16 : 0;
var c3 = (y0 > z0) ? 8 : 0;
var c4 = (x0 > w0) ? 4 : 0;
var c5 = (y0 > w0) ? 2 : 0;
var c6 = (z0 > w0) ? 1 : 0;
var c = c1 + c2 + c3 + c4 + c5 + c6;
var i1, j1, k1, l1; // The integer offsets for the second simplex corner
var i2, j2, k2, l2; // The integer offsets for the third simplex corner
var i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// The number 3 in the "simplex" array is at the position of the largest coordinate.
i1 = simplex[c][0]>=3 ? 1 : 0;
j1 = simplex[c][1]>=3 ? 1 : 0;
k1 = simplex[c][2]>=3 ? 1 : 0;
l1 = simplex[c][3]>=3 ? 1 : 0;
// The number 2 in the "simplex" array is at the second largest coordinate.
i2 = simplex[c][0]>=2 ? 1 : 0;
j2 = simplex[c][1]>=2 ? 1 : 0; k2 = simplex[c][2]>=2 ? 1 : 0;
l2 = simplex[c][3]>=2 ? 1 : 0;
// The number 1 in the "simplex" array is at the second smallest coordinate.
i3 = simplex[c][0]>=1 ? 1 : 0;
j3 = simplex[c][1]>=1 ? 1 : 0;
k3 = simplex[c][2]>=1 ? 1 : 0;
l3 = simplex[c][3]>=1 ? 1 : 0;
// The fifth corner has all coordinate offsets = 1, so no need to look that up.
var x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
var y1 = y0 - j1 + G4;
var z1 = z0 - k1 + G4;
var w1 = w0 - l1 + G4;
var x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
var y2 = y0 - j2 + 2.0*G4;
var z2 = z0 - k2 + 2.0*G4;
var w2 = w0 - l2 + 2.0*G4;
var x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
var y3 = y0 - j3 + 3.0*G4;
var z3 = z0 - k3 + 3.0*G4;
var w3 = w0 - l3 + 3.0*G4;
var x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
var y4 = y0 - 1.0 + 4.0*G4;
var z4 = z0 - 1.0 + 4.0*G4;
var w4 = w0 - 1.0 + 4.0*G4;
// Work out the hashed gradient indices of the five simplex corners
var ii = i & 255;
var jj = j & 255;
var kk = k & 255;
var ll = l & 255;
var gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
var gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
var gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
var gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
var gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32;
// Calculate the contribution from the five corners
var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
if(t0<0) n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * this.dot(grad4[gi0], x0, y0, z0, w0);
}
var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
if(t1<0) n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * this.dot(grad4[gi1], x1, y1, z1, w1);
}
var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
if(t2<0) n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * this.dot(grad4[gi2], x2, y2, z2, w2);
} var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
if(t3<0) n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * this.dot(grad4[gi3], x3, y3, z3, w3);
}
var t4 = 0.6 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
if(t4<0) n4 = 0.0;
else {
t4 *= t4;
n4 = t4 * t4 * this.dot(grad4[gi4], x4, y4, z4, w4);
}
// Sum up and scale the result to cover the range [-1,1]
return 27.0 * (n0 + n1 + n2 + n3 + n4);
};
var context;
var simplex = new SimplexNoise();
function createAurora(width, height) {
var canvas = document.createElement("canvas");
canvas.width = width;
canvas.height = height;
context = canvas.getContext('2d');
document.body.appendChild(canvas);
this.redraw = function() {
var now = Date.now();
var time = now / 4000;
context.clearRect(0, 0, width, height);
var gradient = context.createLinearGradient( 0, 0, height/.4, height * .9);
gradient.addColorStop( 0, 'rgba(86,59,148,1)' );
gradient.addColorStop( (Math.sin(time)+1) * 0.5 * 0.2, 'rgba(178,64,95,.3)' );
gradient.addColorStop( (Math.cos(time)+1) * 0.5 * 0.2 + 0.444 , 'rgba(0,200,0,.6)' ); // 0.6
gradient.addColorStop( 0.7, 'rgba(55,60,140,.3)' );
gradient.addColorStop( 1, 'rgba(0,200,0,.5)' );
context.fillStyle = gradient;
context.fillRect(0,0, width, height);
context.save();
context.globalCompositeOperation = 'source-over';
var gradient = context.createLinearGradient( 0, 0, 0, height*.5 );
gradient.addColorStop( 0, 'rgba(0,0,0,0.01)' );
gradient.addColorStop( 1, 'rgba(0,0,0,1)' );
context.fillStyle = gradient;
context.fillRect(0,0, width, height);
context.restore();
var image = context.createImageData( width, height );
var image2 = context.getImageData( 0, 0, width, height );
var imageData = image.data;
var imageData2 = image2.data;
var w,h, n;
// settings
var octaves = .3;
var scaleX = 4 /octaves, scaleY = 0.25 /octaves;
for ( var i = 0, j = 0, l = imageData.length; i < l; i += 4, j ++ ) {
h = Math.floor( j/width );
w = j % width;
n = 0;
var frequency = .3;
var persistance = 1.5;
var amptitude ;
for (var oi=0; oi < octaves; oi++) {
frequency *= 2;
amptitude = Math.pow(persistance, oi);
n += simplex.noise3d(w/width * frequency * scaleX, h/height* frequency * scaleY, time) * amptitude ;
}
var m = n;
var factor = n* 0.5 + 0.5;
n = Math.floor( factor * 255);
imageData[ i ] = Math.floor( factor * imageData2[ i ]);
imageData[ i + 1 ] = Math.floor( factor * imageData2[ i + 1]);
imageData[ i + 2 ] = Math.floor( factor * imageData2[ i + 2 ]);
imageData[ i + 3 ] = 255;
}
context.putImageData( image, 0, 0 );
}
this.redraw();
return this;
}
var canvas = createAurora(900, 600)
animate();
function animate() {
requestAnimationFrame( animate );
render();
}
function render() {
canvas.redraw();
}
!
