Compute the hilbert curve using R

hilbert.R

# compute hilbert curve
# inspired by https://logicgrimoire.wordpress.com/2020/06/19/how-to-draw-the-hilbert-curve-using-a-computer-program/

library(ggplot2)
library(dplyr)
library(magrittr)

# rotate matrix                
rotate <- function(x, th = pi/2) {
  x %*% matrix(c(cos(th), -sin(th), sin(th), cos(th)), ncol = 2, byrow = TRUE)
}

# reflect matrix
reflect <- function(x) {
  x[, 1] <- -x[, 1] 
  x
}

# translate matrix
translate <- function(x, v) {
  sweep(x, 2, v, `+`)
}

# compute hilbert curve
hilbert <- function(h, depth = 1) {
  if (depth == 0) return(h)
  h <- h * 0.5
  h <- rbind(
    translate(reflect(rotate(h, -pi/2)) , c(-0.5, -0.5)),
    translate(               h          , c(-0.5,  0.5)),
    translate(               h          , c( 0.5,  0.5)),
    translate(reflect(rotate(h,  pi/2)) , c( 0.5, -0.5))
    
  )
  hilbert(h, depth - 1)
}

# initialise matrix
h <- matrix(c(0, 0), ncol = 2, dimnames = list(NULL, c("x", "y")))

# compute and plot
hilbert(h, 3) %>% 
  as_tibble() %>% 
  mutate(n = seq(nrow(.))) %>%
  ggplot(aes(x, y, aes(colour = n))) + 
  geom_path(aes(colour = n)) +
  scale_colour_gradient(low = "red", high = "blue")