results <- c()
for(i in c(1:20)) {
  r <- 1
  limit <- 2^i
  points <- data.frame(
    x = runif(limit, -r, r),
    y = runif(limit, -r, r))
  points$d <- sqrt(points$x^2 + points$y^2)
  points$type <- ifelse(points$d < r, "c", "s")
  picalc <- 4 * length(points$type[points$type=="c"]) / limit
  error <- pi - picalc
  label <- paste0('Pi calc : ', round(picalc, 6), 'nError : ', round(error, 6))
  iter <- data.frame(n = limit, picalc = picalc, error = error, label = label)
  results <- rbind(results, iter)
}

# GGANIMATE
library(ggplot2)
library(gganimate)
p <- ggplot(results, aes(x = runif(n, -1, 1), y = runif(n, -1, 1))) +
  geom_point(lwd = 2, alpha = 0.3) +
  theme_minimal() +
  geom_text(aes(x = 0, y = 0, label = label), size = 5) +
  labs(caption = 'Number of random points : {frame_time}') +
  transition_time(n)
animate(p, nframes =  nrow(results), fps = 5)

library(ggplot2)
library(gganimate)
p <- ggplot(results, aes(x = n, y = error)) +
  geom_point(lwd = 2, alpha = 0.3) +
  theme_minimal() +
  geom_text(aes(x = 0, y = 0, label = label), size = 5, hjust = 0) +
  scale_x_log10(breaks = c(2^(1:4), 4^(2:10)), minor_breaks = NULL) +
  labs(caption = 'Number of random points : {frame}') +
  transition_manual(n) +
  shadow_trail(exclude_layer = 2)
animate(p, nframes =  nrow(results), fps = 5)