i^i^i

i^i^i.R

pacman::p_load(tidyverse, extrafont)

i <- complex(real = 0, imaginary = 1)
count <- 1
point <- complex(real = 0.5, imaginary = 0.5)
x <- c(0.5)
y <- c(0.5)

while (count <= 25) {
    z <- i^point
    x <- c(x, Re(z))
    y <- c(y, Im(z))
    count <- count + 1
    point <- complex(real = Re(z), imaginary = Im(z))
}

dat <- as_tibble(bind_cols(x=x, y=y))
p <- ggplot(dat, aes(x=x, y=y)) +
    geom_point(aes(alpha=0.8)) +
    geom_path(alpha = 0.75, color = "#112987") +
    labs(title = "i^i^i ...",
         caption = "Inspired by John Cook's blog post
         https://www.johndcook.com/blog/2021/03/10/iii/
         By: @rexarski",
         x = "Real part of z",
         y = "Imaginary part of z") +
    theme_bw() +
    theme(text = element_text(family = "Roboto Condensed"),
          title = element_text(size = 18),
          plot.caption = element_text(size = 10),
          axis.title = element_text(size = 14),
          axis.text = element_text(size = 10),
          axis.title.y = element_text(angle = 0, vjust = 0.5),
          panel.grid.minor.x = element_blank(),
          legend.position = "none")
ggsave(plot = p, "i^i^i.png", height = 9, width = 12)