Estimating pi value with Monte Carlo simulation

# Load of libraries
library(tidyverse)
library(sp)
library(gganimate)

n_simulations <- 3000
df <- tibble(
  
  values_x = runif(n_simulations,0,1),
  values_y = runif(n_simulations,0,1)
)
circleFun <- function(center=c(0,0), diameter=1, npoints=100, start=0, end=2)
{
  tt <- seq(start*pi, end*pi, length.out=npoints)
  data.frame(x = center[1] + diameter / 2 * cos(tt), 
             y = center[2] + diameter / 2 * sin(tt))
}
dat <- circleFun(c(0,0), 2, start=1.5, end=2.5)
df <- df %>%
  rowwise() %>%
  mutate(label = point.in.polygon(values_x, values_y, dat$x, dat$y, mode.checked=FALSE)) %>%
  ungroup() %>%
  mutate(count_in = cumsum(label),
         id = row_number(),
         pi_value = 4*(count_in / id))

ggplot(df) +
  geom_rect(aes(xmin = -1, xmax = 1, ymin = -1, ymax = 1), 
            colour = "black", show.legend = FALSE) +
  geom_polygon(aes(x, y), data = dat, alpha = 0.4) +
  geom_point(aes(x = values_x, y = values_y, fill = factor(label), group=id), 
             color = 'black', shape = 21, show.legend = FALSE) +
  theme_minimal() +
  coord_cartesian(ylim=c(0, 1), xlim = c(0,1)) +
  transition_reveal(id)  +
  labs(title = 'Nº of observations: {frame_along} of {n_simulations}',
       subtitle = 'Estimated value of pi: {df$pi_value[as.integer(frame_along)]}')

ggplot(df, aes(id, pi_value)) +
  geom_line() +
  geom_point(colour = 'red', size = 3) +
  transition_reveal(id) +
  geom_hline(yintercept = pi, color = 'red', linetype= 'dashed') +
  theme_bw() +
  labs(title = 'Nº of observations: {frame_along} of {n_simulations}',
       subtitle = 'Estimated value of pi: {df$pi_value[as.integer(frame_along)]}',
       x = 'Sample size',
       y = 'Pi value') +
    coord_cartesian(ylim=c(0, 4))