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logistic_map.R
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# 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) |
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