How to recursively create squares, based on previous squares?

Question

I have a df that contains coordinates to create a square:

library(ggplot2)

df = data.frame(xmin = 1, xmax = 3, ymin = 10, ymax = 15)

ggplot(df) +
        geom_rect(aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax), fill = "green")

Now, I want to have a function, when it is given df, it adds new rows to the df, with 5 scaled versions of the original square, showing like this:

This means, the area of the green coloured squares in the new square(s) corresponds to the 5/9 of the original square.

I also want to make it recursively, so that, given the df with scaled version (5 squares, like in the second image) it gives:

and so on.

Answer 1

Using a recursive approach you could do:

square5 <- function(xmin, xmax, ymin, ymax) {
  x <- data.frame(
    xmin = c(0, rep(1/3, 3), 2/3),
    xmax = c(0, rep(1/3, 3), 2/3) + 1/ 3,
    ymin = c(1/3, 0, 1/3, 2/3, 1/3),
    ymax = c(1/3, 0, 1/3, 2/3, 1/3) + 1/ 3
  )
  
  x[c("xmin", "xmax")] <- lapply(x[c("xmin", "xmax")], scales::rescale, to = c(xmin, xmax), from = c(0, 1))
  x[c("ymin", "ymax")] <- lapply(x[c("ymin", "ymax")], scales::rescale, to = c(ymin, ymax), from = c(0, 1))
  
  return(x)
}

df = data.frame(xmin = 1, xmax = 3, ymin = 10, ymax = 15)

df1 <- purrr::reduce(seq(5), function(x, n) purrr::pmap_df(x, square5), .init = df)

library(ggplot2)

ggplot(df1) +
  geom_rect(aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax), fill = "green", color = "darkgreen", size = .5)