The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.

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Conway’s Game of Life is *awesome* for being the simplest example of artifical life. It implements a rule-based system for determining whether elements in a grid should be alive or dead, with a very simple rule system. But like with DNA or Ant Colonies (read about it!) a simple set of rules can result in an amazing array of diverse behaviour.

Conway’s Game of Life isn’t hard to implement, and seems like a great target for optimisation. The logic is pretty simple, we need a grid of cells. A lot of people

use two-dimensional arrays for this, but I opted for a 1D array where the rows/columns are calculated through a translation function. Each cell contains a value of 0 or 1 for dead or alive.

## The Code

class Grid { constructor() { this.grid = new Uint8Array(GRID_SIZE); this.next = new Uint8Array(GRID_SIZE); this.init(); } dump() { return this.next; } swap() { this.grid = this.next; this.next = new Uint8Array(GRID_SIZE); } at(x, y) { return y * GRID_WIDTH + x; } init() { this.grid = fast_random(GRID_SIZE); }

The first part of the Grid class, the main meat of the code, is pretty simple. The Grid stores a current grid and a next grid, which is updated and then swapped with the current one during animation cycles. When the Grid is initialized it grabs GRID_SIZE bits using the fast_random function (more on this later).

### Survival Function

For each cell within the “grid”, we need to calculate the number of neighbours to figure out its fate in the next generation. The rules for the game are as follows:

Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.

Any live cell with two or three live neighbours lives on to the next generation.

Any live cell with more than three live neighbours dies, as if by overpopulation.

Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

update() { for (let x = 0; x < GRID_WIDTH; x++) { for (let y = 0; y < GRID_WIDTH; y++) { let score = 0; const CURRENT_LOCATION = this.at(x, y); for (let i = -1; i < 2; i++) { for (let j = -1; j < 2; j++) { if (i == 0 && j == 0) { // skip self } else { score += this.grid[this.at(x + i, y + j) % GRID_SIZE]; } } }

Here we’re just looping over every cell of the grid, and for each of the cells adding up the 1s in the surrounding 8 cells. From this we can figure out whether it’s going to be alive or dead based on its current state and its neighbour count:

switch (this.grid[CURRENT_LOCATION]) { case 0: if (score == 3) { this.next[CURRENT_LOCATION] = 1; } else { this.next[CURRENT_LOCATION] = 0; } break; case 1: if (score > 3 || score < 2) { this.next[CURRENT_LOCATION] = 0; } else { this.next[CURRENT_LOCATION] = 1; } break; } }

Pretty simple!

### Rendering the Output

I wanted to write several potential renderers to test what gave the best performance. Each simply takes a grid as an array and draws it.

const renderer = RectangleRenderer; render = new renderer(); let grid = new Grid(); function iterate() { grid.update(); render.render(grid.dump()); grid.swap(); requestAnimationFrame(iterate); } var ctx; $(document).ready(function() { ctx = $("#game-view")[0].getContext("2d"); iterate(); });

### Initial Optimisations

Ok so, one problem. With a 256×256 grid the initial start-up takes up to 9 seconds. Some quick JS Profiling in chrome seemed to indicate that the culprit was the init() function.

The init() function was seeding the grid by iterating over the entire grid’s X/Y coordinates and filling each cell with a random **0 or **1. But in order to do this, the Math.random() function was being called for each cell (meaning it needs to be called 65535 times) as the following:

cell = Math.floor(Math.random()*2)

As it turns out this is extremely wasteful. In theory, each call to Math.random() could be used to supply up to **32** unique bits per call, which would reduce the number of calls significantly. After implementation, the init() function began to run almost instantaneously:

function random_byte() { let el = Math.round(Math.random() * (Number.MAX_SAFE_INTEGER/2) + Number.MAX_SAFE_INTEGER/2); let bits = []; static_counter += 1; while (el > 1) { let bit = Math.floor(el % 2); bits.push(bit); el = el / 2; } return bits; } function fast_random(size) { let array = []; while (array.length < size) { let c = random_byte(); array = array.concat(c); } return array.slice(0,size); }

With this function added, the initial delay disappeared entirely for a 256x256 grid. In the next article I'm going to look at some of the algorithms used in speeding up the Game of Life as an implementation level.

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