# Conway's 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, 3, 3, 3)`

## 2. Build the model

Like in the Forest fire example, we have a cellular automaton in our hands. This is a model that does not require any agents. Just a matrix whose "color" or "status" is the only thing necessary for the simulation.

We still need to define a dummy agent type though for `ABM`

:

`@agent Automaton GridAgent{2} begin end`

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 or not. `:chebyshev`

includes diagonal, `:manhattan`

does not.

This function creates a model where all cells are dead.

```
function build_model(rules::Tuple;
alive_probability = 0.2,
dims = (100, 100), metric = :chebyshev, seed = 42
)
space = GridSpaceSingle(dims; metric)
properties = Dict(:rules => rules)
status = zeros(Bool, dims)
# We use a second copy so that we can do a "synchronous" update of the status
new_status = zeros(Bool, dims)
# We use a `NamedTuple` for the parameter container to avoid type instabilities
properties = (; rules, status, new_status)
model = ABM(Automaton, space; properties, rng = MersenneTwister(seed))
# Turn some of the cells on
for pos in positions(model)
if rand(model.rng) < alive_probability
status[pos...] = true
end
end
return model
end
model = build_model(rules)
```

```
AgentBasedModel with 0 agents of type Automaton
space: GridSpaceSingle with size (100, 100), metric=chebyshev, periodic=true
scheduler: fastest
properties: rules, status, new_status
```

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 game_of_life_step!(model)
# First, get the new statuses
new_status = model.new_status
status = model.status
@inbounds for pos in positions(model)
# Convenience function that counts how many nearby cells are "alive"
n = alive_neighbors(pos, model)
if status[pos...] == true && (n ≤ model.rules[4] && n ≥ model.rules[1])
new_status[pos...] = true
elseif status[pos...] == false && (n ≥ model.rules[3] && n ≤ model.rules[4])
new_status[pos...] = true
else
new_status[pos...] = false
end
end
# Then, update the new statuses into the old
status .= new_status
return
end
function alive_neighbors(pos, model) # count alive neighboring cells
c = 0
@inbounds for near_pos in nearby_positions(pos, model)
if model.status[near_pos...] == true
c += 1
end
end
return c
end
```

`alive_neighbors (generic function with 1 method)`

now we can instantiate the model:

`model = build_model(rules)`

```
AgentBasedModel with 0 agents of type Automaton
space: GridSpaceSingle with size (100, 100), metric=chebyshev, periodic=true
scheduler: fastest
properties: rules, status, new_status
```

## 3. Animate the model

We use the `InteractiveDynamics.abmvideo`

for creating an animation and saving it to an mp4

```
using InteractiveDynamics
using CairoMakie
plotkwargs = (
add_colorbar = false,
heatarray = :status,
heatkwargs = (
colorrange = (0, 1),
colormap = cgrad([:white, :black]; categorical = true),
),
)
abmvideo(
"game_of_life.mp4",
model,
dummystep,
game_of_life_step!;
title = "Game of Life",
framerate = 10,
frames = 60,
plotkwargs...,
)
```

```
┌ Warning: Unknown agent position type: Vector{Any}. Skipping plotting agents.
└ @ InteractiveDynamics ~/.julia/packages/InteractiveDynamics/EThtU/src/agents/abmplot.jl:253
```