Game of Lifeⁿ

About

This is a framework for expressing Conway's Game of Life in an n-cube of arbitrary size. Game of Lifeⁿ started as an exercise in functional programming using ES2015 inspired by Reginald Braithwaite's JavaScript Allongé. The exercise was more engaging than I expected, and it led to some interesting questions about how to best express certain data structures in JavaScript.

New Game

The Game of Lifeⁿ module exports a generator function. The function accepts two optional arguments. The first argument is an object indicating the size and dimensions of the game field. The second argument is a comma-separated list of points that represent which cells are "alive" at the start of the game.

const {gameFactory} = require('game-of-life-n');
let game = gameFactory({
  size: 4, // length of each side of the square, cube or hypercube
  dimensions: 2 // number of spatial dimensions; 2 = square, 3 = cube, 4+ = hypercube
}, 0, 1, 2, 3);

Game State

JavaScript does not support true multidimensional arrays, so Game of Lifeⁿ uses a single array to represent the game state. This array is one-dimensional and contains 0s and 1s. 1 represents a live cell, and 0 represents a dead cell.

The actual game object is a generator, to be used like so:

let game = gameFactory({
  size: 4,
  dimensions: 2
}, 1, 3, 4, 5, 10, 11);

/* 
The first value represents the initial game state.  Note that the cells
that are alive match the indices specified in the arguments.
*/
game.next().value;
/*
[
  0, 1, 0, 1,
  1, 1, 0, 0,
  0, 0, 1, 1,
  0, 0, 0, 0
]
*/

game.next().value;
/*
[
  0, 1, 1, 0,
  0, 1, 0, 0,
  1, 1, 1, 1,
  1, 0, 0, 1
]
*/

game.next().value;
/*
[
  0, 1, 1, 1,
  0, 0, 0, 0,
  0, 0, 0, 0, 
  0, 0, 0, 0
]
*/

// etc.

Grid Conventions

A single array can effectively represent multidimensional space in Game of Lifeⁿ by using arithmetic to look up coordinates. In a game of 3 dimensions with length 3, the point at coordinates (0, 0, 0) is stored at Array[0]. Point (0, 0, 1) is stored at Array[18]. See ./lib/grid.js for a more detailed look at the arithmetic that powers the grid system.

toCoord Function

In order to translate any array index into an array of cartesian coordinates, use the toCoord function. This may assist you if you are interfacing with graphing libraries.

const gameOfLifeN = require('game-of-life-n'),
  {gameFactory} = gameOfLifeN,
  {toCoord} = gameOfLifeN;

let game = gameFactory({
  size: 3,
  dimensions: 3
}, 0, 1, 2, 3);

toCoord(11);
// returns [2, 0, 1]
// where x = 2, y = 0, z = 1