logistic_map.R

logistic_map.R

# See gif at https://twitter.com/_Axeman_/status/1223037685704474624
library(tidyverse)
library(gganimate)

logistic_map <- function(r, steps = 500, init = .5) {
  x <- vector('numeric', steps)
  x[1] <- init
  for (n in 2:steps) x[n] <- r * x[n-1] * (1 - x[n-1])
  return(unique(round(tail(x, -100), 4)))
}

outcomes <- tibble(
  r = seq(0.01, 4, by = 0.001),
  population = map(r, logistic_map)
) %>% 
  unnest(population)

p <- ggplot(outcomes, aes(r, population)) + 
  geom_point(shape = 16, col = 'lightblue', alpha = 0.1, size = 1e-5) +
  annotate(geom = 'text', label = "x[n+1] == rx[n](1 - x[n])", x = .7, y = .4, parse = TRUE) +
  transition_time(r ^ 3) +
  shadow_mark() +
  view_zoom_manual(
    xmin = c(0, 3), xmax = c(3, 4), ymin = c(0, 0.3), ymax = c(0.75, 1), 
    wrap = FALSE, ease = 'quadratic-in-out'
  ) +
  labs(x = expression('growth rate' ~ italic(r)), y = expression('population size' ~ italic(x))) + 
  ggdark::dark_theme_linedraw()

anim_save('logistic_map.gif', p, fps = 20, duration = 10, end_pause = 20, width = 1000, height = 800, res = 300)