Inspired by @coolbutuseless's rgl menger sponge post: https://coolbutuseless.github.io/2020/09/27/a-level-3-menger-sponge-in-r/

rgl_menger_sponge.R

library(rgl)

sl  <- shapelist3d(cube3d(alpha = 1, 
                          color = 'grey90', 
                          specular = 'black', 
                          lit = TRUE), 
                   plot = FALSE)

create_next_level <- function(sl, level) {
  
  scale <- 0.5
  sla <- scale3d(sl, scale, scale, scale)
  x <- 1.5^(level - 1)
  
  multipliers <- rep(list(c(-1, 0, 1)), 3)
  permutations <- expand.grid(multipliers)
  
  too_many_zeros <- rowSums(permutations == 0) > 1
  permutations <- permutations[!too_many_zeros,]
  
  translation_list <- lapply(
    1:nrow(permutations),
    function(perm_row) {
      translate3d(sla, 
                  x*permutations[perm_row,1], 
                  x*permutations[perm_row,2], 
                  x*permutations[perm_row,3])
    })
  
  shapelist3d(translation_list,
              plot = FALSE)
  
}

rgl::clear3d()
sl <- create_next_level(sl, level = 1)
sl <- create_next_level(sl, level = 2)
sl <- create_next_level(sl, level = 3)

shade3d(sl)

Trying to make a version of @coolbutuseless's Menger Sponge that doesn't explicitly list every combination.

Not sure it really ended up being more succinct, but I tried :)

Original tweet:
https://twitter.com/coolbutuseless/status/1310135325633777664

Blog post with code:
https://coolbutuseless.github.io/2020/09/27/a-level-3-menger-sponge-in-r/