library(tidyverse)
# options(gganimate.nframes = 400, scipen = 10)
## 설정 --------------
n <- 70  # number of ball bearnings 
stop_level <- 10 # number of perturbation levels 
                # make it an even number
levels <- 44 # greater than stop_levels
## 데이터셋 -----------
set.seed(2019)
ball_bearings <- crossing(unit_id = 1:n, 
                          level = 1:levels - 1) %>% 
  mutate(perturbation =     # moves
           sample(c(-1,1),  # left or right
                  n(), # each ball at each level 
                  replace = T)) %>%
  group_by(unit_id) %>% # operations on each ball
  mutate(perturbation = 
           ifelse(row_number() == 1, 
                  yes = 0, # start centered
                  no = perturbation)) %>% 
  # each ball should release one at a time
  mutate(time = # displacing them in time w/ 
           row_number() + 
           # using unit id
           unit_id * 3 - 1) %>% 
  filter(time > 0) %>% 
  mutate(x_position = # we get the x position
           # by summing the cumulative distributions
           cumsum(perturbation)) %>% 
  # if ball is beyond the perturbation levels
  mutate(x_position = # we overwrite the x position
           ifelse(level <= stop_level,
                  yes = x_position, 
                  no = NA)) %>% 
  # then fill in with the last x position
  fill(x_position) %>% 
  ungroup()
## 최종 관측점----------
ball_bearings %>% 
  filter(level == (levels - 1) ) %>% 
  rename(final_time = time) %>% 
  crossing(time = as.numeric(1:max(ball_bearings$time))) %>% 
  group_by(time, x_position) %>% 
  summarise(x_position_count = sum(time > final_time)) ->
ball_bearings_collect
## 갤톤 상자
pegs <- crossing(unit_id = -stop_level:stop_level, 
                 level = 1:stop_level) %>% 
  mutate(transparent = 
           (unit_id + level) %% 2) 
# Lets make walls
walls <- crossing(unit_id = 
           -(stop_level + 1):(stop_level + 1), 
         level = stop_level:levels) %>% 
  mutate(transparent = 
           unit_id %% 2) 
ball_bearings_size <- 2
peg_size <- 3
## 정적 그래프
galton_static <- ggplot(ball_bearings) +
  aes(y = level) +
  aes(x = x_position) +
  scale_y_reverse() +
  aes(group = unit_id) +
  geom_point(data = walls, 
             aes(x = unit_id, alpha = transparent), 
             col = "grey30", size = peg_size) +
  geom_point(data = pegs, 
             aes(x = unit_id, alpha = transparent), 
             col = "grey30", size = peg_size) +
  geom_segment(x = -sqrt(n), xend = -1.5, 
               y = 0, yend = 0) +
  geom_segment(x = sqrt(n), xend = 1.5, 
               y = 0, yend = 0) +
  geom_abline(intercept = 1.5, 
              slope = -1) +
  geom_abline(intercept = 1.5, 
              slope = 1) +
  annotate(geom = "tile", 
           height = 2, width = 2, 
           x = 0 , y = -1.5) +
  annotate(geom = "tile", 
           height = 2, width = 1.75, 
           x = 0 , y = -1.5, fill = "white") +
  geom_rect(data = ball_bearings_collect,
            mapping = aes(xmin = x_position - .35, 
                          xmax = x_position + .35,
                          ymax = max(ball_bearings$level) + 1 - x_position_count*1.5,
                          ymin = max(ball_bearings$level) + 1,
                          group = x_position, 
                          y = NULL, x = NULL),
            fill = "darkgrey") +
  geom_point(size = ball_bearings_size, 
             col = "steelblue") +
  coord_equal() +
  geom_hline(yintercept = stop_level, 
             linetype = "dotted") +
  scale_alpha_continuous(range = c(0, 1), guide = F) +
  theme_void()
# galton_static
## 애니메이션
# galton_static +  
#   gganimate::transition_time(time = time) + 
#   gganimate::shadow_wake(wake_length = .05) + 
#   gganimate::ease_aes("bounce-in-out") #BREAK