One Million Digits of Pi

tidytuesday

Published

March 24, 2026

The Data

This week’s dataset comes from the TidyTuesday repository and contains the digits of pi. As Eve Andersson notes:

“Pi is an irrational number, meaning its decimal representation never ends and never settles into a permanent repeating pattern.”

Since pi’s digits are essentially random, I thought it would be fun to treat them as directions on a compass and create a visualization showing the “walking path” that pi traces out. I saw a great post by Steven Ponce on Bluesky where he created a random walk using digits as compass directions, and I wanted to recreate his visualization for myself.

Loading the Data

Code

# Packages
library(tidyverse)

# Load data
tuesdata <- tidytuesdayR::tt_load('2026-03-24')

# Extract data
pi_digits <- tuesdata$pi_digits

# Show the first few values
head(pi_digits)

# A tibble: 6 × 2
  digit_position digit
           <dbl> <dbl>
1              1     3
2              2     1
3              3     4
4              4     1
5              5     5
6              6     9

Creating the Visualization

Here’s the concept: A compass has 360 degrees, so we can divide it into 10 equal sections—one for each digit 0-9. Each digit gets 36 degrees (digit 0 = 0°, digit 1 = 36°, and so on).

Using basic trigonometry, for a unit circle centered at (0,0), moving one unit at angle \(\theta\) gives us the coordinates \((\cos(\theta), \sin(\theta))\). By taking the cumulative sum of all these displacements in the x and y directions, we can plot the path that pi traces out:

Code

# Define the direction in degrees and radians
step_directions <- data.frame(
  digit = 0:9,
  degree = seq(0, 360-36, l = 10)
) %>% 
  mutate(
    radian = degree*pi/180
  )

# Set end point to set the number of digits
end_spot <- 10000

# Create the walking path
p_walk <- pi_digits %>% 
  left_join(step_directions, by = 'digit') %>% 
  mutate(displacement_x = cos(radian),
         displacement_y = sin(radian),
         pos_x = cumsum(displacement_x),
         pos_y = cumsum(displacement_y)) %>% 
  filter(digit_position <= end_spot) %>%
  ggplot(mapping = aes(x = pos_x, y = pos_y)) + 
  geom_path(alpha = 1/3, color = '#63B3ED') + 
  labs(title = "Where did my π go?",
       subtitle = 'The walking path of π. Digit values are used to\nmark the direction of travel (0=0°, 1=36°, ..., 9=324°)',
       caption = '') + 
  theme_void() + 
  theme(aspect.ratio = 1,
        plot.background =  element_rect(fill = '#151D28', color = 'black'),
        plot.margin = margin(1/2, 1, 0, 1/2, "cm"),
        plot.title = element_text(color = 'grey99', face = 'bold', size = 24),
        plot.subtitle = element_text(color = 'grey99', size = 10))
p_walk

Adding Animation

The static chart above shows the complete path, but we can make it more engaging by animating it with the gganimate package. I also included a point to clearly show the current position of the walking path:

Code

library(gganimate)
p_animate <- p_walk + 
  geom_point(color = 'gold', size = 2) + 
  transition_reveal(digit_position) +
  ease_aes('linear')

animate(p_animate, nframes = 100, end_pause = 10, rewind = TRUE)