康威的生命游戏 - 超越网格

Question

Ok so there are a lot of "Conway's Game of Life" questions but this one is pretty specific. I'm going to have to throw a bunch of code at you first, break it down and show you where the issue is.

So here is my Conway's Game of Life implementation so far, right now it is limited to the console for debugging (JSfiddle - http://jsfiddle.net/georeith/C9Gyr/8/ - fire it up, open your console):

var utils = {};

/*
 * utils.extend()
 * - Extend initial object with all properties of following objects, objects later in the argument list take precedence.
 */
utils.extend = function(obj) {
  var args = Array.prototype.slice.call(arguments, 1);
  for (var i = args.length; i--;) {
    for (var prop in args[i]) {
      obj[prop] = args[i][prop];
    }
  }
  return obj;
}

/*
 * utils.defaults()
 * - Overwrite initial object with properties of following objects only if key is present in the initial object.
 */
utils.defaults = function(obj) {
  var args = Array.prototype.slice.call(arguments, 1);
  for (var i = args.length; i--;) {
    for (var prop in args[i]) {
      if (obj.hasOwnProperty(prop)) {
        obj[prop] = args[i][prop];
      }
    }
  }
  return obj;
}

/* no-wrap positioning functions */
var calcPos = {
  ul: function(cell) {
    return [cell.x - 1, cell.y - 1];
  },
  um: function(cell) {
    return [cell.x, cell.y - 1];
  },
  ur: function(cell) {
    return [cell.x + 1, cell.y - 1];
  },
  l: function(cell) {
    return [cell.x - 1, cell.y];
  },
  r: function(cell) {
    return [cell.x + 1, cell.y];
  },
  ll: function(cell) {
    return [cell.x - 1, cell.y + 1];
  },
  lm: function(cell) {
    return [cell.x, cell.y + 1];
  },
  lr: function(cell) {
    return [cell.x + 1, cell.y + 1];
  }
}

var worldDefaults = {
  rows: 50,
  columns: 50,
  wrap: true, // left edge is mirrored on right, top edge is mirrored on bottom. Vice versa
  speed: -1, // milliseconds (minimum time, waits until end of last tick to calculate from)
  grid: []
}
var World = function (opts) {
  this.settings = utils.defaults(worldDefaults, opts);

  this.maxX = this.settings.columns - 1;
  this.maxY = this.settings.rows -1;
  for (var y = 0, yLen = this.settings.rows; y < yLen; ++y) {
    for (var x = 0, xLen = this.settings.columns; x < xLen; ++x) { 
      if (y === 0) {
        this.cellList.push([]);
        if (this.settings.grid.length <= x) {
          this.settings.grid.push([]);
        }
      }
      var cell = new Cell();
      cell.x = x;
      cell.y = y;
      cell.alive = !!this.settings.grid[x][y];

      if (cell.alive) {
        this.lifeList.push(cell);
      }

      var lx = (x) ? x - 1 : this.maxX;
      var uy = (y) ? y - 1 : this.maxY;
      var ux = (x == this.maxX) ? 0 : x + 1;
      var ly = (y == this.maxY) ? 0 : y + 1;

      cell.neighbourCoords = (this.settings.wrap) ?
      [
        [lx, uy],   [x, uy],  [ux, uy],
        [lx,  y], /*[x,  y]*/ [ux,  y],
        [lx, ly],   [x, ly],  [ux, ly]
      ]
      :
      [
        calcPos.ul, calcPos.um, calcPos.ur,
        calcPos.l, calcPos.r,
        calcPos.ll, calcPos.lm, calcPos.lr
      ]
      ;
      this.cellList[x][y] = cell;
    }
  }
}
World.prototype.generation = 0;
World.prototype.cellList = [];
World.prototype.lifeList = [];
World.prototype.changeList = [];
World.prototype.nextTick = null;

/* Progresses the world */
World.prototype.tick = function() {
  var newLifeList = [];
  this.changeList = [];

  // This hash goes out of scope after each tick allowing any dead shadowCells to be garbage collected
  if (!this.settings.wrap) {
    var shadowCellHash = {};
  }

  for (var i = 0, iLen = this.lifeList.length; i < iLen; ++i) {
    var cell = this.lifeList[i];
    if (cell.key) {
      shadowCellHash[cell.key] = cell;
    }
    cell.neighbours = 0;
    cell.lastIterated = this.generation;

    for (var j = 0, jLen = cell.neighbourCoords.length; j < jLen; ++j) {

      var coords;
      var neighbour;
      if (this.settings.wrap) {
        coords = cell.neighbourCoords[j];
        neighbour = this.cellList[coords[0]][coords[1]];

      } else {
        coords = cell.neighbourCoords[j](cell);
        if (coords[0] > this.maxX || coords[0] < 0 || coords[1] > this.maxY || coords[1] < 0) {
          // This neighbour is off the screen so will require a shadowCell
          var key = ''+coords[0]+','+coords[1];
          if (!shadowCellHash[key]) {
            neighbour = shadowCellHash[key] = new ShadowCell(coords[0], coords[1]);
            neighbour.neighbourCoords = cell.neighbourCoords;
          } else {
            neighbour = shadowCellHash[key];
          }
        } else {
          neighbour = this.cellList[coords[0]][coords[1]];
        }
      }


      if (neighbour.lastIterated !== this.generation) {
        neighbour.neighbours = 0;
        neighbour.lastIterated = this.generation;
      }
      if (neighbour.alive !== neighbour.changed) {
        // neighbour started as alive
        ++cell.neighbours;
      } else {
        // neighbour started as dead
        ++neighbour.neighbours;
        if (neighbour.neighbours === 3) {
          neighbour.alive = true;
          neighbour.changed = true;
          neighbour.changeIndex = this.changeList.push(neighbour) - 1;
        } else if (neighbour.neighbours === 4) {
          // neighbour has reverted to dead
          neighbour.alive = false;
          neighbour.changed = false;
          neighbour.changeIndex = -1;
          this.changeList[neighbour.changeIndex] = undefined;
        }
      }
    }
    if (cell.neighbours < 2 || cell.neighbours > 3) {
      cell.changed = true;
      cell.alive = false;
      cell.changeIndex = this.changeList.push(cell) - 1;
    } else {
      newLifeList.push(cell);
    }
  }

  for (var i = 0, iLen = this.changeList.length; i < iLen; ++i) {
    var cell = this.changeList[i];
    if (cell !== undefined) {
      cell.changeIndex = -1;
      if (cell.alive) {
        newLifeList.push(cell);
      }
      cell.update();
      cell.changed = false;
    }
  }

  this.lifeList = newLifeList;
  ++this.generation;
  this.onTick();

  var that = this;
  if (this.settings.speed >= 0) {
    this.nextTick = setTimeout(function() {
      that.tick();
    }, this.settings.speed);
  }
  return this;
}

World.prototype.out = function() {
  var s = '';
  for (var y = 0, yLen = this.settings.rows; y < yLen; ++y) {
    for (var x = 0, xLen = this.settings.columns; x < xLen; ++x) {
      s += (this.cellList[x][y].alive)? '\u2B1B' : '\u2B1C';
    }
    s += '\n';
  }
  s += '\u21B3 Generation: ' + this.generation + ' -- Cells: ' + this.lifeList.length + ' \u21B5';
  s += '\n';
  return s;    
}

World.prototype.stop = function() {
  this.speed = -1;
}

World.prototype.onTick = function() {
  return this;
}

var Cell = function() {
  return this;
}
Cell.prototype.x = 0;
Cell.prototype.y = 0;
Cell.prototype.neighbours = 0;
Cell.prototype.alive = false;
Cell.prototype.changed = false;
Cell.prototype.changeIndex = -1;
Cell.prototype.lastIterated = -1;

/*
 * ShadowCell
 * - non rendered cell for use in no-wrap
 */
var ShadowCell = function(x,y) {
  this.x = x;
  this.y = y;
  this.key = ''+this.x+','+this.y;
  return this;
}
ShadowCell.prototype = utils.extend({}, Cell.prototype);
ShadowCell.prototype.isShadow = true;
ShadowCell.prototype.update = function(){
  return this;
};

/*
 * Cell.update()
 * - Update cell after tick
 */
Cell.prototype.update = function() {
  this.render();
  return this;
}

/*
 * Cell.render()
 * - Placeholder function to be overwritten by rendering engine
 */
Cell.prototype.render = function() {
  return this;
}

The method I have chosen involves an array of all the cells that are alive at the start of each generation. I then iterate over each of their 8 neighbours and decide whether to create/delete them.

This works great when I pass wrap: false to the World constructor (see JSfiddle for implementation), this tells it to mirror the sides and not allow overflow. However that style of layout breaks a lot of patterns as it causes cells to come back on themselves so I also want to allow it to calculate beyond the grid.

For this purpose I created the ShadowCell class which behaves mostly the same as the Cell class (each grid cell dead or alive is an instance of it) except that the ShadowClass is only created when a non-existent cell is required outside of the grid and is offered for garbage collection the moment it is no longer required (if it is dead after each generation). Otherwise it mimics the Cell classes attributes and fits directly into the same logic that Cell does.

The issue

If you go to "generation 4" in the console output you may notice it isn't quite right...

I have narrowed this issue down to the ShadowCell implementation because this works if I provide enough padding around the shape so that it does not overflow the grid (which is when ShadowCell kicks in), although like I said earlier ShadowCell is a copy of the Cell class, it has the same attributes and gets passed in as if it was a Cell .

Because I want these to be garbage collected I do not include these in the overall grid array World.cellList ... this leads me to believe the problem lies in this section of code:

// This hash goes out of scope after each tick allowing any dead shadowCells to be garbage collected

if (!this.settings.wrap) {
  var shadowCellHash = {};
}

for (var i = 0, iLen = this.lifeList.length; i < iLen; ++i) {
  var cell = this.lifeList[i];
  if (cell.key) {
    shadowCellHash[cell.key] = cell;
  }
  cell.neighbours = 0;
  cell.lastIterated = this.generation;

  for (var j = 0, jLen = cell.neighbourCoords.length; j < jLen; ++j) {

    var coords;
    var neighbour;
    if (this.settings.wrap) {
      coords = cell.neighbourCoords[j];
      neighbour = this.cellList[coords[0]][coords[1]];

    } else {
      coords = cell.neighbourCoords[j](cell);
      if (coords[0] > this.maxX || coords[0] < 0 || coords[1] > this.maxY || coords[1] < 0) {
        // This neighbour is off the screen so will require a shadowCell
        var key = ''+coords[0]+','+coords[1];
        if (!shadowCellHash[key]) {
          // ShadowCell not in hash, let's create one
          neighbour = shadowCellHash[key] = new ShadowCell(coords[0], coords[1]);
          neighbour.neighbourCoords = cell.neighbourCoords; 
          // NOTE: neighbourCoords are a set of functions that return values relative to the cell you pass to them. I am not literally giving the `ShadowCell` the same neighbour positions here.
        } else {
          neighbour = shadowCellHash[key];
        }
      } else {
        // This neighbour is on screen, grab its cell.
        neighbour = this.cellList[coords[0]][coords[1]];
      }
    }
    ...

Note: Alive ShadowCell s will not be garbage collected as they get stored in an Array with the other cells (I am certain of this from my debugging, see the cell count in your console output and count the visible cells).

For some reason the ShadowCell class appears to cause incorrect reporting of neighbours. I have attempted to debug it by following the creation, deletion and counted neighbours of each individual cell during each generation but my brain dies before it can put it all together. For all my debugging efforts I can't see why this behaviour should occur . ShadowCell is pretty much the same as a Cell to everything else that uses it (they use the exact same position functions .etc), the fact it doesn't get rendered shouldn't be the cause of this.

For generation 4 I get the following output by logging the creation of shadow maps, I can see that each is being created once per generation (note: The class doesn't show because I used utils.extend() to create a snapshot of them):

Object {x: 5, y: -1, key: "5,-1", neighbourCoords: Array[8], neighbours: 0…}
Object {x: 6, y: -1, key: "6,-1", neighbourCoords: Array[8], neighbours: 0…}
Object {x: 7, y: -1, key: "7,-1", neighbourCoords: Array[8], neighbours: 0…}
Object {x: 4, y: -1, key: "4,-1", neighbourCoords: Array[8], neighbours: 0…}
Object {x: -1, y: 1, key: "-1,1", neighbourCoords: Array[8], neighbours: 0…}
Object {x: -1, y: 2, key: "-1,2", neighbourCoords: Array[8], neighbours: 0…}
Object {x: -1, y: 3, key: "-1,3", neighbourCoords: Array[8], neighbours: 0…}
Object {x: 5, y: -2, key: "5,-2", neighbourCoords: Array[8], neighbours: 0…}
Object {x: 6, y: -2, key: "6,-2", neighbourCoords: Array[8], neighbours: 0…}
Object {x: 7, y: -2, key: "7,-2", neighbourCoords: Array[8], neighbours: 0…}
Object {x: -1, y: 4, key: "-1,4", neighbourCoords: Array[8], neighbours: 0…}

Logged on line 152 like so:

if (!shadowCellHash[key]) {
  neighbour = shadowCellHash[key] = new ShadowCell(coords[0], coords[1]);
  neighbour.neighbourCoords = cell.neighbourCoords;
  console.log(utils.extend({}, neighbour));
} else {

Answer 1

shadowCellHash is not initialized with all of the ShadowCell s before you start looping through every cell looking for neighbours. When the loop checks [5,-1] for neighbors, it doesn't find [6,-1] because it's not in shadowCellHash . Since [6,-1] is not found, a new dead [6,-1] is created, and [5,-1] is not born because it does not have enough live neighbours.

I think I've resolved your issue by eagerly re-populating shadowCellHash at the beginning of each World.tick

JSFiddle

  // This hash goes out of scope after each tick allowing any dead shadowCells to be garbage collected
  if (!this.settings.wrap) {
    var shadowCellHash = {};
    for (var i = 0; i < this.lifeList.length; i++) {
        var cell = this.lifeList[i];
        if (cell.key) {
          shadowCellHash[cell.key] = cell;
        }
    }
  }