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https://github.com/fibo/games-of-life
is a Mathematical solution of any Game of Life variation
https://github.com/fibo/games-of-life
functional-programming game-of-life
Last synced: about 1 month ago
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is a Mathematical solution of any Game of Life variation
- Host: GitHub
- URL: https://github.com/fibo/games-of-life
- Owner: fibo
- License: mit
- Created: 2015-05-30T18:54:41.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2020-01-06T12:52:31.000Z (almost 5 years ago)
- Last Synced: 2024-10-09T11:51:19.185Z (about 1 month ago)
- Topics: functional-programming, game-of-life
- Language: JavaScript
- Homepage: http://g14n.info/games-of-life/
- Size: 1.02 MB
- Stars: 21
- Watchers: 7
- Forks: 5
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# games-of-life
> is a Mathematical solution to any [Game of Life][1] variation
[Demo](#demo) |
[Installation](#installation) |
[Idea](#idea) |
[Example](#example) |
[See also](#see-also) |
[License](#license)
[](http://badge.fury.io/js/games-of-life)
[](https://github.com/fibo/games-of-life/blob/master/dist/games-of-life.min.js)
[](https://travis-ci.org/fibo/games-of-life?branch=master)
[](https://github.com/fibo/games-of-life)
[](https://standardjs.com)
[](http://g14n.info/games-of-life/changelog)
[](https://github.com/fibo/games-of-life/watchers) [](https://github.com/fibo/games-of-life/stargazers) [](https://github.com/fibo/games-of-life/network/members)
## Demo
I created this hexagonal *Game of Life* demo to show that this package generalize the *Game of Life* in any of its variations.
Click the image below to try it!
[](http://g14n.info/games-of-life/examples/hexagonal/)
## Installation
With [npm](https://npmjs.org/) do
```bash
npm install games-of-life
```
You could also use a CDN adding this to your HTML page
```html
```
## Idea
On the 30th of May 2015, I have participated in a [Coderetreat](http://coderetreat.org/) at Milan XPUG.
We have had so much fun coding implementations of the [Game of Life][1].
As a mathematician, I think it is a very interesting problem. I couldn't resist to generalize it and try to solve it in any of its variations.
Let's start with some abstractions.
A function *getNeighboursOf*, which returns the set of cells adjacent to a given cell, defines the shape of *Game of Life* universe.
Infact, since
getNeighboursOf(cell1) = getNeightboursOf(cell2) ⇒ cell1 = cell2
it can be said that the set of neighbours of a cell is dual to the cell itself, hence the definition of the *getNeighboursOf* function is equivalent to the definition of the space of a *Game of Life* universe. Note that it defines the concept of **nearness**.
In other words,
> if you define a *getNeighbours* function you also shape the space of a *Game of Life* universe
On the other hand, let be given the definition of an *isAlive* function, which returns `true` if the given cell is alive, `false` otherwise.
It can be easily extended to an *areAlive* function which, given a list of cells, returns a list of booleans; following a similar identification we used for the *getNeighboursOf* function, an *isAlive* function describes the state of a *Game of Life* universe at a given moment.
The considerations above allow to implement an **abstract** *Game of Life* in a functional way, in any of its variations, for example:
* finite grid
* infinite grid
* 2-dimensional, 3-dimensional, n-dimensional
* square, triangular, hexagonal tiles
* cylinder, torus, moebius strip, boy surface
Take a look to [createWorld.js](https://github.com/fibo/games-of-life/blob/master/src/createWorld.js) for the implementation's details.
The world has a *transition rule* which defaults to the [classicTransitionRule.js](https://github.com/fibo/games-of-life/blob/master/src/classicTransitionRule.js).
## Example
A simple example is the [infinite grid with two dimensional coordinates](https://github.com/fibo/games-of-life/blob/master/test/example/infiniteGridWithTwoDimensionalCoordinates.js).
Define a *getNeighboursOf* which returns the neighbours of a given cell.
```javascript
function getNeighboursOf (cell) {
var x = cell[0]
var y = cell[1]
var neighbours = []
for (var j = y - 1; j <= y + 1; j++) {
for (var i = x - 1; i <= x + 1; i++) {
if ((i === x) && (j === y)) {
continue
}
neighbours.push([i, j])
}
}
return neighbours
}
// Alias the adjacency function with a more meaningful name,
// to improve semantic in the example code below.
var infiniteGrid2d = getNeighboursOf
```
Create a *Game of Life* world, and get the *evolve* function
```javascript
var gamesOfLife = require('games-of-life')
var createWorld = gamesOfLife.createWorld
var transitionRule = gamesOfLife.classicTransitionRule.bind(null, 2, 3, 3)
var world = createWorld(infiniteGrid2d)
var evolve = world(transitionRule)
```
The empty grid is represented by a function that always returns false, so
```javascript
function emptyGrid () {
return false
}
evolve(emptyGrid) // will always return false
```
Try with a single cell at the origin
```javascript
function singleCellAtTheOrigin (cell) {
return ((cell[0] === 0) && (cell[1] === 0))
}
evolve(singleCellAtTheOrigin) // will always return false too, cause the cell dies
```
Ok, a more interesting example is the blinker
```javascript
function horyzontalBlinker (cell) {
var x = cell[0]
var y = cell[1]
if (y !== 0) {
return false
}
if ((x >= -1) && (x <= 1)) {
return true
}
return false
}
function verticalBlinker (cell) {
var x = cell[0]
var y = cell[1]
if (x !== 0) {
return false
}
if ((y >= -1) && (y <= 1)) {
return true
}
return false
}
```
You may check that the *verticalBlinker* evolves in the *horyzontalBlinker* and vice versa
```javascript
for (var i = -1; i < 1; i++) {
for (var j = -1; j < 1; j++) {
console.log(evolve(verticalBlinker)(i, j) === horyzontalBlinker(i, j)) // true
}
}
```
## License
[MIT](http://g14n.info/mit-license)
[1]: http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life "Game of Life"
[2]: http://www.conwaylife.com/wiki/Main_Page "LikeWiki"
[3]: https://news.ycombinator.com/item?id=9632255 "Hacker News thread"