collatz.R

## https://youtu.be/094y1Z2wpJg

library(tidyverse)

collatz <- function(x){

    v = c(x)
    i = 1
   
    while (v[i] != 1){

        z = v[i]
        i = i + 1

        if (z %% 2 == 0){
            v[i] = z/2
        } else {
            v[i] = 3*z+1
        }
    }

    steps = length(v) - 1
    list(
        original = x,
        total_stopping_time = steps,
        data = tibble::tibble(
            original = x,
            hailstones = v,
            time = seq(1, steps + 1)
        )
    )
}

collatz(27)
111




r <- sample.int(1000000000, 1000)

samps <- lapply(r, collatz)



pdat = dplyr::bind_rows(lapply(samps, function(x) x$data))
mean(sapply(samps, function(x) x$total_stopping_time))

pdat %>%
    ggplot(aes(x = time, y = hailstones, group = original)) +
        geom_line(show.legend = FALSE, alpha = .025, color = 'black')+
        coord_cartesian(ylim = c(0, 5000))