Conway's game of life

Game of life on wikipedia.

It is also available from the Models module as Models.game_of_life.

using Agents, AgentsPlots

1. Define the rules

Rules of Conway's game of life: DSRO (Death, Survival, Reproduction, Overpopulation). Cells die if the number of their living neighbors is <D or >O, survive if the number of their living neighbors is ≤S, come to life if their living neighbors are ≥R and ≤O.

rules = (2, 3, 3, 3)

2. Build the model

First, define an agent type. It needs to have the compulsary id and pos fields, as well as an status field that is true for cells that are alive and false otherwise.

mutable struct Cell <: AbstractAgent

The following function builds a 2D cellular automaton. rules is of type Tuple{Int,Int,Int, Int} representing DSRO.

dims is a tuple of integers determining the width and height of the grid environment. Moore specifies whether cells connect to their diagonal neighbors.

This function creates a model where all cells are "off".

function build_model(; rules::Tuple, dims = (100, 100), Moore = true)
    space = GridSpace(dims, moore = Moore)
    properties = Dict(:rules => rules)
    model = ABM(Cell, space; properties = properties)
    node_idx = 1
    for x in 1:dims[1]
        for y in 1:dims[2]
            add_agent_pos!(Cell(node_idx, (x, y), false), model)
            node_idx += 1
    return model

Now we define a stepping function for the model to apply the rules to agents.

function ca_step!(model)
    new_status = fill(false, nagents(model))
    for (agid, ag) in model.agents
        nlive = nlive_neighbors(ag, model)
        if ag.status == true && (nlive ≤ model.rules[4] && nlive ≥ model.rules[1])
            new_status[agid] = true
        elseif ag.status == false && (nlive ≥ model.rules[3] && nlive ≤ model.rules[4])
            new_status[agid] = true

    for k in keys(model.agents)
        model.agents[k].status = new_status[k]

function nlive_neighbors(ag, model)
    neighbors_coords = node_neighbors(ag, model)
    nlive = 0
    for nc in neighbors_coords
        nag = model.agents[Agents.coord2vertex((nc[2], nc[1]), model)]
        if nag.status == true
            nlive += 1
    return nlive

now we can instantiate the model:

model = build_model(rules = rules, dims = (50, 50), Moore = true)
AgentBasedModel with 2500 agents of type Cell
 space: GridSpace with 2500 nodes and 9702 edges
 scheduler: fastest
 properties: Dict(:rules => (2, 3, 3, 3))

Let's make some random cells on

for i in 1:nv(model)
    if rand() < 0.2
        model.agents[i].status = true

3. Animate the model

We use the plotabm function from AgentsPlots.jl package for creating an animation.

ac(x) = x.status == true ? :black : :white
anim = @animate for i in 0:100
    i > 0 && step!(model, dummystep, ca_step!, 1)
    p1 = plotabm(model; ac = ac, as = 3, am = :square, showaxis = false)

We can now save the animation to a gif.

gif(anim, "game_of_life.gif", fps = 5)