Voronoi Puzzles

Organic, natural-looking tessellations

Overview

Voronoi puzzles create organic, natural-looking pieces based on Voronoi tessellation. Each piece is a convex polygon formed by the regions closest to a set of seed points. The result resembles patterns found in nature, like honeycomb cells, giraffe spots, or cracked mud.

Cell Count Variations

make_vor_cells <- function(n) {
  ggplot() +
    geom_puzzle_voronoi(
      aes(fill = after_stat(piece_id)),
      n_cells = n,
      seed = 42
    ) +
    scale_fill_viridis_c(option = "turbo", guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = paste0(n, " cells"))
}

print(make_vor_cells(10) + make_vor_cells(25) + make_vor_cells(50))

# Generate cell count previews in a grid
cells <- c(10, 25, 50)
items <- lapply(cells, function(n) {
  generate_puzzle(type = "voronoi", grid = c(n), size = c(200, 200), seed = 42, fill_palette = "turbo")
})
render_puzzle_grid(items, ncol = 3, labels = paste(cells, "cells"))

10 cells

25 cells

50 cells

Figure 2

Aspect Ratios

Voronoi puzzles adapt to any aspect ratio - wide, square, or tall. See the Aspect Ratios Tutorial for examples comparing all puzzle types.

Color Palettes

make_vor_palette <- function(pal) {
  ggplot() +
    geom_puzzle_voronoi(
      aes(fill = after_stat(piece_id)),
      n_cells = 20,
      seed = 42
    ) +
    scale_fill_viridis_c(option = pal, guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = pal)
}

print((make_vor_palette("viridis") + make_vor_palette("magma") + make_vor_palette("plasma")) /
(make_vor_palette("inferno") + make_vor_palette("cividis") + make_vor_palette("turbo")))

# Generate all palette previews and combine into a grid
palettes <- c("viridis", "magma", "plasma", "inferno", "cividis", "turbo")
items <- lapply(palettes, function(pal) {
  generate_puzzle(type = "voronoi", grid = c(20), size = c(200, 200), seed = 42, fill_palette = pal)
})
render_puzzle_grid(items, ncol = 3, labels = palettes)

viridis

magma

plasma

inferno

cividis

turbo

Figure 4

Fill Direction

Control the spatial order of color assignment. This is distinct from palette_invert which reverses the dark↔︎light ends of the palette.

make_direction_plot <- function(dir) {
  ggplot() +
    geom_puzzle_voronoi(
      aes(fill = after_stat(fill_order)),
      n_cells = 20,
      fill_direction = dir,
      seed = 42
    ) +
    scale_fill_viridis_c(option = "viridis", guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = paste0("fill_direction = \"", dir, "\""))
}

print(make_direction_plot("forward") + make_direction_plot("reverse"))

directions <- c("forward", "reverse")
items <- lapply(directions, function(dir) {
  generate_puzzle(type = "voronoi", grid = c(20), size = c(200, 200), seed = 42, fill_palette = "viridis", fill_direction = dir)
})
render_puzzle_grid(items, ncol = 2, labels = paste0("fill_direction = \"", directions, "\""))

fill_direction = "forward"

fill_direction = "reverse"

Figure 6

Offset (Separation)

make_vor_offset <- function(off) {
  ggplot() +
    geom_puzzle_voronoi(
      aes(fill = after_stat(piece_id)),
      n_cells = 20,
      offset = off, seed = 42
    ) +
    scale_fill_viridis_c(option = "viridis", guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = paste0("offset = ", off))
}

print(make_vor_offset(0) + make_vor_offset(5) + make_vor_offset(10) + make_vor_offset(20))

# Generate offset previews in a grid
offsets <- c(0, 5, 10, 20)
items <- lapply(offsets, function(off) {
  generate_puzzle(type = "voronoi", grid = c(20), size = c(200, 200), seed = 42, offset = off, fill_palette = "viridis")
})
render_puzzle_grid(items, ncol = 4, labels = paste("offset =", offsets))

offset = 0

offset = 5

offset = 10

offset = 20

Figure 8

Seed Variations

Different seeds create completely different tessellations:

make_vor_seed <- function(s) {
  ggplot() +
    geom_puzzle_voronoi(
      aes(fill = after_stat(piece_id)),
      n_cells = 15,
      seed = s
    ) +
    scale_fill_viridis_c(option = "magma", guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = paste0("seed = ", s))
}

print(make_vor_seed(1) + make_vor_seed(42) + make_vor_seed(123) + make_vor_seed(999))

# Generate seed variation previews in a grid
seeds <- c(1, 42, 123, 999)
items <- lapply(seeds, function(s) {
  generate_puzzle(type = "voronoi", grid = c(15), size = c(200, 200), seed = s, fill_palette = "magma")
})
render_puzzle_grid(items, ncol = 4, labels = paste("seed =", seeds))

seed = 1

seed = 42

seed = 123

seed = 999

Figure 10

Fusion Groups

Merge pieces together using PILES notation:

# Standard
print(ggplot() +
  geom_puzzle_voronoi(
    aes(fill = after_stat(piece_id)),
    n_cells = 12,
    seed = 42
  ) +
  scale_fill_viridis_c(option = "magma", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "Standard"))

# Adjacent pieces fused
print(ggplot() +
  geom_puzzle_voronoi(
    aes(fill = after_stat(piece_id)),
    n_cells = 12,
    seed = 42,
    fusion_groups = "1-2-3,5-6"
  ) +
  scale_fill_viridis_c(option = "magma", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "Pieces fused"))

# Standard
result_standard <- generate_puzzle(
  type = "voronoi",
  grid = c(12),
  size = c(200, 200),
  seed = 42,
  fill_palette = "magma"
)
render_puzzle_preview(result_standard, title = "Standard")

# Adjacent pieces fused
result_fused <- generate_puzzle(
  type = "voronoi",
  grid = c(12),
  size = c(200, 200),
  seed = 42,
  fill_palette = "magma",
  fusion_groups = "1-2-3,5-6"
)
render_puzzle_preview(result_fused, title = "Pieces fused")

Figure 13: Standard 12-cell

Figure 14: Standard 12-cell

Large Voronoi Puzzle

ggplot() +
  geom_puzzle_voronoi(
    aes(fill = after_stat(piece_id)),
    n_cells = 80,
    width = 400, height = 300,
    seed = 789
  ) +
  scale_fill_viridis_c(option = "turbo", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "80-Cell Voronoi Puzzle")

result <- generate_puzzle(
  type = "voronoi",
  grid = c(80),
  size = c(300, 400),
  seed = 789,
  fill_palette = "turbo"
)
render_puzzle_preview(result, max_width = "600px")

Figure 16

Parameters Reference

Parameter	Type	Default	Description
`n_cells`	integer	12	Number of Voronoi cells (pieces)
`seed`	integer	random	Random seed for reproducibility
`offset`	numeric	0 (mm)	Piece separation distance
`tabsize`	numeric	6 (%)	Tab size as percentage of edge length
`jitter`	numeric	2 (%)	Randomness in tab shape as percentage
`min_tab_size`	numeric	0 (mm)	Minimum tab size in millimeters
`max_tab_size`	numeric	Inf (mm)	Maximum tab size in millimeters
`point_distribution`	string	“fermat”	Seed point distribution method
`fusion_groups`	string	NULL	PILES notation for fusing pieces

About Voronoi Tessellation

Voronoi tessellation divides a plane into regions based on distance to seed points. Each region consists of all points closer to its seed than to any other seed. This creates:

Convex polygons: Each piece is a convex polygon
Natural appearance: Resembles patterns in nature
Variable sizes: Piece sizes depend on seed point distribution

Code Example

ggplot() +
  geom_puzzle_voronoi(
    aes(fill = after_stat(piece_id)),
    n_cells = 35,
    width = 400, height = 300,
    seed = 42,
    offset = 5
  ) +
  scale_fill_viridis_c(option = "turbo", guide = "none") +
  coord_fixed() +
  theme_puzzle()

# Generate puzzle
result <- generate_puzzle(
  type = "voronoi",
  grid = c(35),          # 35 cells
  size = c(300, 400),    # height=300mm, width=400mm
  seed = 42,
  offset = 5
)

# writeLines(result$svg_content, "voronoi_puzzle.svg")

# Preview
render_puzzle_preview(result)

When to Use Voronoi

Voronoi puzzles are ideal for:

Organic themes: Nature, landscapes, biological subjects
Artistic effects: Modern art, abstract designs
Variable difficulty: More cells = harder puzzle
Unique designs: Every seed creates a different pattern