Building Langton's Ant in Elm

Last week I attended the Elm London meetup, arranged by Kris Jenkins, who always produces a great selection of challenges for people to take on for all skill levels. Along with Isaac, we decided to take on Kris’ challenge to build Langton’s Ant in Elm.

Langton’s Ant

Langton’s Ant is a game similar to Conway’s Game of Life in that cells on a game board change from being alive to dead based on their surroundings and certain criteria. In Langton’s Ant there is a small ant on the board that moves and changes squares as it goes. The ant starts on any random square, and on each move it:

  1. Based on the colour of the square, it either turns 90 degrees right, or 90 degrees left.
  2. Changes the colour of the square it’s on from black to white, or vice versa.
  3. Moves forward one square in the direction it’s facing.

The fact that the game has well defined rules makes it perfect for a short hack event, so we set about building it in Elm.

Getting started

I used create-elm-app to quickly get the app going. It’s a really handy way to get a working application and local server up without having to think about it, and I highly recommend it.

Defining types

When working in Elm the first thing I always do is define the types for the key concepts of the application. Looking through Langton’s ant, we could see we’d need to model:

  • The concept of an Ant.
  • Cells on a game Board.
  • Coords which cells are positioned at on the board.
  • The Direction of the ant.
  • The Colour of a cell.

Starting with the easier ones, a Direction is a union type that can be one of Up, Down, Left or Right:

type Direction
    = Up
    | Down
    | Left
    | Right

And similarly, a Colour is either White or Black:

type Colour
    = White
    | Black

And a coordinate, or Coord, is a tuple of (x, y):

type alias Coord =
    ( Int, Int )

Once you have these, it’s easy to combine them to make up the “bigger” types. A cell is a record that has a coordinate pair and a colour:

type alias Cell =
    { position : Coord
    , colour : Colour
    }

And the Ant is a record with a position and a direction:

type alias Ant =
    { position : Coord
    , direction : Direction
    }

The board is then a dictionary (quite similar to a JavaScript object, or a Ruby hash) that has coordinates as its keys, and then Cells as its values. There’s a bit of duplication here because you’re using the coordinates for the keys of the dictionary, and then storing the keys in the cell, but we left it like that because it’s nice to be able to have a cell tell you its position, without having to keep a reference to the coordinates around.

type alias Board =
    Dict Coord Cell

Finally, the Model has a board and an ant:

type alias Model =
    { board : Board
    , ant : Ant
    }

This method of defining the types is such a good way to think about your application and I highly recommend doing so. Even if you realise that you haven’t quite modelled your types right later, it’s easy to change them and let the compiler walk you through fixing them. They say if you define your types right, the rest of your application easily falls into place, and I’d say that’s definitely true of Elm.

Initial State

The initial state of the world is an ant at position (0, 0) facing Left (you could pick any direction, it doesn’t matter) and an empty list of cells:

initialCells : Board
initialCells =
    Dict.empty


initialAnt : Ant
initialAnt =
    Ant ( 0, 0 ) Left


init : ( Model, Cmd Msg )
init =
    ( Model initialCells initialAnt, Cmd.none )

The reason we have no cells to start with is because we don’t actually need a cell to exist until the ant moves off it. When an ant reaches a square, it will turn the cell black if it’s white, or white if it’s black, and by default all cells are white. That means if there’s no cell under the ant, we can just create a white one, and go from there.

Moving on a tick

There is no user input in Langton’s Ant, and as such we needed a way to run the game every millisecond to advance it to the next stage. We can use subscriptions in Elm to do this.

In The Elm Architecture we define a subscriptions function which we can use to subscribe to events. Elm’s Time module provides a way to send a Msg at defined time intervals:

subscriptions : Model -> Sub Msg
subscriptions model =
    Time.every (Time.millisecond) Tick

This instructs Elm’s runtime to send a Tick message every millisecond.

Dealing with a Tick

The first thing to do is define our Msg type, that is, the types of messages we expect to flow through our system. In our case it’s just one, Tick:

type Msg
    = Tick Time

When Time.every sends a Tick it will also send the current time with it, which we’ll ignore, but we have to define our Msg type as Tick Time to keep the compiler happy. In our update function we’ll simply hand off to a tick function that will run the actual game:

update : Msg -> Model -> ( Model, Cmd Msg )
update msg model =
    case msg of
        Tick _ ->
            ( tick model, Cmd.none )

Defining tick

Recall that there are three parts to a move in Langton’s Ant:

  1. Based on the colour of the square, it either turns 90 degrees right, or 90 degrees left.
  2. Changes the colour of the square it’s on from black to white, or vice versa.
  3. Moves forward one square in the direction it’s facing.

Breaking that into code, the first thing we need to do is get the current cell that the ant is on. We can do that because an Ant has a position key that is a coordinate pair, so we can write a function that gets the cell for the ant:

getCell : Board -> Coord -> Cell
getCell board coord =
    Dict.get coord board |> Maybe.withDefault (Cell coord White)

We try to get the cell for the given coordinates, and if it doesn’t exist, we’ll just default to a White cell at those coordinates.

Once we have that cell, we need to flip it’s colour:

tick : Model -> Model
tick { ant, board } =
    let
        currentCell =
            getCell board ant.position

        newCell =
            { currentCell | colour = flipColour currentCell.colour }
    ...

Where flipColour just swaps Black to White and vice-versa:

flipColour : Colour -> Colour
flipColour colour =
    case colour of
        Black ->
            White

        White ->
            Black

Once we have the new cell we use Dict.insert to insert it back onto our board. Dict.insert will overwrite a cell if one already exists, so it’s perfect because we don’t need any custom logic depending on if the cell exists or not.

newCell =
    { currentCell | colour = flipColour currentCell.colour }

newBoard =
    Dict.insert ant.position newCell board

Next, we need to deal with the ant. Depending on the colour of the cell when the ant arrived on it, it needs to either flip itself 90 degrees left or right, so we can update the ant and change its direction:

newAnt1 =
    { ant | direction = getNextDirection ant currentCell }

Where getNextDirection looks like so:

getNextDirection : Ant -> Cell -> Direction
getNextDirection { direction } { colour } =
    case ( colour, direction ) of
        ( White, Up ) ->
            Right

        ( White, Right ) ->
            Down

        ( White, Down ) ->
            Left

        ( White, Left ) ->
            Up

        ( Black, Up ) ->
            Left

        ( Black, Right ) ->
            Up

        ( Black, Down ) ->
            Right

        ( Black, Left ) ->
            Down

In the arguments note how we destructure the ant, pulling out just the direction, and do the same with the cell to pull its direction. We then combine them into a tuple and pattern match on them, encoding the rules of the ant and how it flips based on the colour.

Finally, now we have the ant facing the right direction, we need to update its positional coordinates to move it in the right direction:

newAnt2 =
    { newAnt1 | position = getCoordInFront newAnt1 }

Where getCoordInFront maps the ant’s positional coordinates, changing either the x or y by one, positively or negatively depending on the direction:

getCoordInFront : Ant -> Coord
getCoordInFront { direction, position } =
    case direction of
        Up ->
            Tuple.mapSecond (\x -> x + 1) position

        Down ->
            Tuple.mapSecond (\x -> x - 1) position

        Left ->
            Tuple.mapFirst (\x -> x - 1) position

        Right ->
            Tuple.mapFirst (\x -> x + 1) position

Here Tuple.mapFirst and Tuple.mapSecond come in really handy to tidy this code up and keep it nice and succinct. We could have written (\x -> x + 1) as ((+) 1), but we didn’t because doing ((-1) x) ends up as -1 + x which is not what we want, so here we prefer the longer form to keep it clear.

With that, our tick function is done and we have the new model being generated. Next up, we’ll render it onto the page.

tick : Model -> Model
tick { ant, board } =
    let
        currentCell =
            getCell board ant.position

        newCell =
            { currentCell | colour = flipColour currentCell.colour }

        newBoard =
            Dict.insert ant.position newCell board

        newAnt1 =
            { ant | direction = getNextDirection ant currentCell }

        newAnt2 =
            { newAnt1 | position = getCoordInFront newAnt1 }
    in
        Model newBoard newAnt2

Rendering the board

Rather than use HTML, we chose to use elm-lang/svg for our board.

Our view function looks like so:

view : Model -> Html Msg
view { board, ant } =
    svg [ width "600", height "600", viewBox "-500 -500 1000 1000" ]
        [ renderCells board
        , renderAnt ant
        ]

By creating the SVG with a viewBox attribute of -500 -500 1000 1000 we create an SVG element that puts an element with x "0", y "0" in the middle of the box. This means when we render our first cell at (0, 0), it will go in the middle of the SVG. You can read more about scaling SVGs on CSS Tricks.

Rendering the cells

To render the cells, we map over all the values using Dict.values and render each one:

renderCell : Cell -> Svg Msg
renderCell { position, colour } =
    renderItem position (colourToSvgFill colour)


renderCells : Board -> Svg Msg
renderCells board =
    g [] (Dict.values board |> List.map renderCell)

Notice how we use the SVG element g to group elements up. g is really handy for grouping related elements without it applying any extra styling or behaviour. It’s akin to a div in HTML.

renderCell calls the generic renderItem function, passing in the position of the cell and the colour. colourToSvgFill just maps the type Black to "black", and the same with White.

renderCell produces an SVG rect element with the right width, height and positions applied:

renderItem : Coord -> String -> Svg Msg
renderItem ( xPos, yPos ) colour =
    rect
        [ stroke "black"
        , fill colour
        , x (toString (xPos * 10 - 5))
        , y (toString (yPos * 10 - 5))
        , width "10"
        , height "10"
        ]
        []

The renderAnt function also uses renderItem, just passing in a different colour depending on the ant’s direction (which you don’t need to do, we just did it so we could see the direction the ant was heading). colourForAnt just maps the ant’s colour to a direction.

renderAnt : Ant -> Svg Msg
renderAnt { position, direction } =
    renderItem position (colourForAnt direction)

Fin

And with that, we have our ant!

If you’d like to find the full code, you can find it on Github. I’d encourage you to have a try at building Langton’s Ant, it’s a well defined, contained challenge that has some really interesting parts. Elm’s type system makes it a perfect fit for a challenge like this, and it was a neat way to explore and learn more about the language.