# Set Seed
set.seed(184)

# Library
library(tidyverse)

# Data
a <- data.frame(x = rnorm(20000, 12,   2),   y = rnorm(20000, 10,   0.5))
b <- data.frame(x = rnorm(20000, 15,   1.5), y = rnorm(20000, 11,   0.5))
c <- data.frame(x = rnorm(20000, 10,   1.1), y = rnorm(20000, 11.5, 0.7))
data <- rbind(a, b, c)

# Area + contour
ggplot(data, aes(x = x, y = y)) +
  stat_density_2d(aes(fill = after_stat(level)),
                  geom = "polygon", colour = "white") +
  theme_light() +
  scale_fill_viridis_c(option = "magma")

# Color palette
bg_color    <- "#FFFFFF"
light_blue  <- "#DDEAF5"
mid_blue    <- "#9BB8DC"
edge_color  <- "#001E44"   # Penn State Navy

# Draw a single unit cube at grid position (gx, gy, gz)
# Uses simple axonometric projection: x' = gx + 0.4*gz, y' = gy + 0.4*gz
draw_cube <- function(gx, gy, gz, fill = light_blue) {
  s  <- 1
  dx <- 0.4 * s
  dy <- 0.4 * s

  px <- gx + dx * gz
  py <- gy + dy * gz

  # Front face
  polygon(c(px, px + s, px + s, px),
          c(py, py,     py + s, py + s),
          col = fill, border = edge_color, lwd = 1.2)
  # Top face
  polygon(c(px,        px + s,        px + s + dx, px + dx),
          c(py + s,    py + s,        py + s + dy, py + s + dy),
          col = fill, border = edge_color, lwd = 1.2)
  # Right face (slightly darker for shading)
  shade <- adjustcolor(fill, red.f = 0.92, green.f = 0.92, blue.f = 0.95)
  polygon(c(px + s,    px + s + dx,   px + s + dx, px + s),
          c(py,        py + dy,       py + s + dy, py + s),
          col = shade, border = edge_color, lwd = 1.2)
}

# Alternating fill in 3D (checkerboard)
checker_fill <- function(i, j, k = 0) {
  if ((i + j + k) %% 2 == 0) light_blue else mid_blue
}

par(mar = c(0, 0, 0, 0), bg = bg_color)
plot.new()
plot.window(xlim = c(0, 18), ylim = c(0, 6), asp = 1)

# 1. Vector: 1 x 3 row
ox <- 1; oy <- 2.2
for (i in 0:2) {
  draw_cube(ox + i, oy, 0, fill = checker_fill(i, 0))
}
text(ox + 1.7, oy - 1, "Vector",
     cex = 1.4, col = edge_color, font = 2)

# 2. Matrix: 3 x 3 grid
ox <- 7; oy <- 1
for (j in 0:2) {
  for (i in 0:2) {
    draw_cube(ox + i, oy + j, 0, fill = checker_fill(i, j))
  }
}
text(ox + 1.7, oy - 1, "Matrix",
     cex = 1.4, col = edge_color, font = 2)

# 3. Array: 3 x 3 x 3 cube — draw back-to-front, bottom-up, left-right
ox <- 13; oy <- 1
for (k in 2:0) {
  for (j in 0:2) {
    for (i in 0:2) {
      draw_cube(ox + i, oy + j, k, fill = checker_fill(i, j, k))
    }
  }
}
text(ox + 2.3, oy - 1, "Array",
     cex = 1.4, col = edge_color, font = 2)