Figure 8.3 The game of life CA

The example in the book was made using a NetLogo model based on this model from Spatial Simulation, but this page provides R code instead.

library(dplyr)
library(tidyr)
library(gsignal)
library(pracma)
library(data.table)
library(ggplot2)

Model code

The model code is in the cell below. It returns a 3D array of cell states, with each ‘layer’ a new 2D array of cell states.

# random neighbour offset
k <- matrix(c(1, 1, 1,
              1, 0, 1,
              1, 1, 1), 3, 3)

wrap_matrix <- function(m) {
  nr <- nrow(m)
  nc <- ncol(m)
  m2 <- pracma::repmat(m, 3, 3)
  m2[0:(nr + 1) + nr, 0:(nc + 1) + nc]
}

generation <- function(m) {
  nr <- nrow(m)
  nc <- ncol(m)
  live <- wconv("2d", wrap_matrix(m), k, "same")[1:nr + 1, 1:nc + 1]
  next_m <- zeros(nr, nc)
  next_m[which(m == 1 & live %in% 2:3 | m == 0 & live == 3)] <- 1
  next_m
}

init_state <- function(density = 0.35, nr, nc) {
  matrix(as.numeric(runif(nr * nc) < density),
         ncol = nc, nrow = nr)
}

life <- function(nc = 20, nr = 20, tmax = 20, 
                 density = 0.35, seed = NULL) {
  set.seed(seed)
  result <- array(0, dim = c(nr, nc, tmax))
  result[, , 1] <- init_state(density = density, 
                              nr = nr, nc = nc)
  for (gen in 2:tmax) {
    result[, , gen] <- generation(result[, , gen - 1])
  }
  result
}

Run the model

We run the model and convert it into a dataframe to make it easier to plot.

initial_density <- 0.35
width <- 50
height <- 50
time_steps <- 200

life_df <- life(nr = height, nc = width, tmax = time_steps, 
                density = initial_density) %>%
  as.data.table() %>%
  as_tibble() %>%
  rename(x = V1, y = V2, t = V3, num = value)

Plotting

The dataframe has attributes x, y, t, and state, which are most easily plotted as a sequence of model snapshots using ggplot2::facet_wrap.

ggplot(life_df %>% dplyr::filter(t >= 30, t <= 49)) + 
  geom_raster(aes(x = x, y = y, fill = num), show.legend = FALSE) + 
  coord_equal() +
  facet_wrap( ~ t, ncol = 5) +
  theme_void() + 
  theme(strip.background = element_blank(),
        strip.text.x = element_blank())

An animation

We can also make a movie…

library(gganimate)

anim <- ggplot(life_df) + 
  geom_raster(aes(x = x, y = y, fill = num), show.legend = FALSE) + 
  coord_equal() +
  transition_manual(t) + 
  labs(title = "Step: {frame}") +
  theme_void()
        
anim <- animate(anim, nframes = 100, fps = 5)
anim_save("life.gif", anim)

# License (MIT)
#
# Copyright (c) 2023 David O'Sullivan
#
# Permission is hereby granted, free of charge, to any person
# obtaining a copy of this software and associated documentation
# files (the "Software"), to deal in the Software without restriction,
# including without limitation the rights to use, copy, modify, merge,
# publish, distribute, sublicense, and/or sell copies of the Software,
# and to  permit persons to whom the Software is furnished to do so,
# subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.

© 2023 David O’Sullivan