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              // create a new field:
var field = new field2D(64);

var delta = 0.2;

// initialize with some noise:
field.set(function(x, y) {
  return random();

// duplicate the field for double-buffering:
past = field.clone();

function mix(a, b, t) {
  return a + t*(b-a);

function sigmoid(t) {
  return 1/(1+Math.exp(-t));

// transition function mapping 0..1 input to 0..1 output with sigmoid shape
function d(v) {
  return sigmoid(8*(v-0.5));

// factors to normalize kernel sampling
var rsqrt2 = 1/Math.sqrt(2);
var moorenorm = 1/(4 + 4*rsqrt2);

// approximating the game of life rule:
function game(x, y) {
  // neighbourhood:
  // TODO: use sampling ring (and sampling disk for inner region)
  var N = d(past.get(x, y + 1));
  var E = d(past.get(x + 1, y));
  var S = d(past.get(x, y - 1));
  var W = d(past.get(x - 1, y));
  var NE = d(past.get(x + 1, y + 1))*rsqrt2;
  var SE = d(past.get(x + 1, y - 1))*rsqrt2;
  var SW = d(past.get(x - 1, y - 1))*rsqrt2;
  var NW = d(past.get(x - 1, y + 1))*rsqrt2;
  // sum & normalize to 0..1 "density":
  var near = moorenorm * (N + S + E + W + NW + SW + NE + SE);
  // current state:
  var C = d(past.get(x, y));
  // transition rule:
  // TODO: express without using control flow
  if (C > 0.5) {
    if (near < 0.2) {
      // tend toward death by loneliness:
      return mix(C, 0, delta);
    } else if (near > 0.35) {
      // tend toward death by overcrowding:
      return mix(C, 0, delta);
  } else {
    if (near > 0.34 && near < 0.45) {
      // tend toward rebirth
      return mix(C, 1, delta);
  // else remain the same:
  return C;

// update the simulation (called frequently!)
function update() {
    // swap the buffers (cheaper than copying)
    var tmp = past;
    past = field;
    field = tmp;

     // run the game one step:

// render the simulation (called frequently!)
function draw() {
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