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, Random

1. Define the rules

Conway's game of life is a cellular automaton, where each cell of the discrete space contains one agent only.

The rules of Conway's game of life are defined based on four numbers: Death, Survival, Reproduction, Overpopulation, grouped as (D, S, R, O) 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) # (D, S, R, O)

2. Build the model

First, define an agent type. It needs to have the compulsary id and pos fields, as well as a 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 given some rules. dims is a tuple of integers determining the width and height of the grid environment. metric specifies how to measure distances in the space, and in our example it actually decides whether cells connect to their diagonal neighbors.

This function creates a model where all cells are dead.

function build_model(; rules::Tuple, dims = (100, 100), metric = :chebyshev, seed = 120)
    space = GridSpace(dims; metric)
    properties = Dict(:rules => rules)
    model = ABM(Cell, space; properties, rng = MersenneTwister(seed))
    idx = 1
    for x in 1:dims[1]
        for y in 1:dims[2]
            add_agent_pos!(Cell(idx, (x, y), false), model)
            idx += 1
    return model

Now we define a stepping function for the model to apply the rules to agents. We will also perform a synchronous agent update (meaning that the value of all agents changes after we have decided the new value for each agent individually).

function ca_step!(model)
    new_status = fill(false, nagents(model))
    for agent in allagents(model)
        n = alive_neighbors(agent, model)
        if agent.status == true && (n ≤ model.rules[4] && n ≥ model.rules[1])
            new_status[] = true
        elseif agent.status == false && (n ≥ model.rules[3] && n ≤ model.rules[4])
            new_status[] = true

    for id in allids(model)
        model[id].status = new_status[id]

function alive_neighbors(agent, model) # count alive neighboring cells
    c = 0
    for n in nearby_agents(agent, model)
        if n.status == true
            c += 1
    return c

now we can instantiate the model:

model = build_model(rules = rules, dims = (50, 50))
AgentBasedModel with 2500 agents of type Cell
 space: GridSpace with size (50, 50), metric=chebyshev, periodic=true
 scheduler: fastest
 properties: rules

Let's make some random cells on

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

3. Animate the model

We use the InteractiveDynamics.abm_video for creating an animation and saving it to an mp4

using InteractiveDynamics
import CairoMakie

ac(x) = x.status == true ? :black : :white
am(x) = x.status == true ? '■' : '□'
    "game of life.mp4",
    title = "Game of Life",
    ac = :black,
    as = 12,
    framerate = 5,
    scatterkwargs = (strokewidth = 0,),