Concentric Puzzles

Rings of pieces radiating from a central shape

Overview

Concentric puzzles feature rings of pieces that radiate outward from a central shape. They combine the elegance of hexagonal geometry with a distinctive radial pattern, creating puzzles that are both beautiful and satisfying to assemble.

Ring Variations

ggpuzzle

make_conc_rings <- function(r) {
  ggplot() +
    geom_puzzle_conc(
      aes(fill = after_stat(ring)),
      rings = r,
      seed = 42
    ) +
    scale_fill_viridis_c(option = "plasma", guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = paste0(r, " rings"))
}

print(make_conc_rings(2) + make_conc_rings(3) + make_conc_rings(4))

Figure 1

API

# Generate ring previews in a grid
rings <- c(2, 3, 4)
items <- lapply(rings, function(r) {
  generate_puzzle(type = "concentric", grid = c(r), size = c(200), seed = 42, fill_palette = "plasma")
})
render_puzzle_grid(items, ncol = 3, labels = paste(rings, "rings"))

2 rings

3 rings

4 rings

Figure 2

Center Shape Options

The center piece can be either a hexagon or a circle:

ggpuzzle

# Hexagon center (default)
print(ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 3,
    center_shape = "hexagon",
    seed = 42
  ) +
  scale_fill_viridis_c(option = "magma", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "Hexagon center"))

# Circle center
print(ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 3,
    center_shape = "circle",
    seed = 42
  ) +
  scale_fill_viridis_c(option = "magma", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "Circle center"))

Figure 3: Hexagon center

Figure 4: Circle center

API

# Hexagon center (default)
result_hex <- generate_puzzle(
  type = "concentric",
  grid = c(3),
  size = c(200),
  seed = 42,
  center_shape = "hexagon",
  fill_palette = "magma"
)
render_puzzle_preview(result_hex)

# Circle center
result_circle <- generate_puzzle(
  type = "concentric",
  grid = c(3),
  size = c(200),
  seed = 42,
  center_shape = "circle",
  fill_palette = "magma"
)
render_puzzle_preview(result_circle)

Figure 5: Hexagon center

Figure 6: Hexagon center

Fill by Ring vs Piece ID

# By ring
print(ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 3, seed = 42
  ) +
  scale_fill_viridis_c(option = "viridis", name = "Ring") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "By ring") +
  theme(legend.position = "bottom"))

# By piece_id
print(ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(piece_id)),
    rings = 3, seed = 42
  ) +
  scale_fill_viridis_c(option = "viridis", name = "Piece") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "By piece_id") +
  theme(legend.position = "bottom"))

Figure 7: Fill by ring

Figure 8: Fill by piece_id

Color Palettes

ggpuzzle

make_conc_palette <- function(pal) {
  ggplot() +
    geom_puzzle_conc(
      aes(fill = after_stat(ring)),
      rings = 3, seed = 42
    ) +
    scale_fill_viridis_c(option = pal, guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = pal)
}

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

Figure 9

API

# 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 = "concentric", grid = c(3), size = c(200), seed = 42, fill_palette = pal)
})
render_puzzle_grid(items, ncol = 3, labels = palettes)

viridis

magma

plasma

inferno

cividis

turbo

Figure 10

Fill Direction

Control the spatial order of color assignment. For concentric puzzles, "reverse" reverses colors within each ring while keeping the center piece unchanged. This is distinct from palette_invert which reverses the dark↔︎light ends of the palette.

ggpuzzle

make_direction_plot <- function(dir) {
  ggplot() +
    geom_puzzle_conc(
      aes(fill = after_stat(fill_order)),
      rings = 3,
      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"))

Figure 11

API

directions <- c("forward", "reverse")
items <- lapply(directions, function(dir) {
  generate_puzzle(type = "concentric", grid = c(3), size = c(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 12

Offset (Separation)

ggpuzzle

make_conc_offset <- function(off) {
  ggplot() +
    geom_puzzle_conc(
      aes(fill = after_stat(ring)),
      rings = 3,
      offset = off, seed = 42
    ) +
    scale_fill_viridis_c(option = "cividis", guide = "none") +
    coord_fixed() +
    theme_puzzle() +
    labs(title = paste0("offset = ", off))
}

print(make_conc_offset(0) + make_conc_offset(5) + make_conc_offset(10) + make_conc_offset(15))

Figure 13

API

# Generate offset previews in a grid
offsets <- c(0, 5, 10, 15)
items <- lapply(offsets, function(off) {
  generate_puzzle(type = "concentric", grid = c(3), size = c(200), seed = 42, offset = off, fill_palette = "cividis")
})
render_puzzle_grid(items, ncol = 4, labels = paste("offset =", offsets))

offset = 0

offset = 5

offset = 10

offset = 15

Figure 14

Fusion Groups

Merge pieces together using PILES notation:

ggpuzzle

# Center merged with ring 1
print(ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 3,
    fusion_groups = "center-ring1",
    seed = 42
  ) +
  scale_fill_viridis_c(option = "plasma", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "center + ring1"))

# Ring 2 pieces merged
print(ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 3,
    fusion_groups = "ring2",
    seed = 42
  ) +
  scale_fill_viridis_c(option = "plasma", guide = "none") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "ring2"))

Figure 15: center + ring1

Figure 16: All of ring2

API

# Center merged with ring 1
result_center_ring1 <- generate_puzzle(
  type = "concentric",
  grid = c(3),
  size = c(200),
  seed = 42,
  fusion_groups = "center-ring1",
  fill_palette = "plasma"
)
render_puzzle_preview(result_center_ring1)

# Ring 2 pieces merged
result_ring2 <- generate_puzzle(
  type = "concentric",
  grid = c(3),
  size = c(200),
  seed = 42,
  fusion_groups = "ring2",
  fill_palette = "plasma"
)
render_puzzle_preview(result_ring2)

Figure 17: center + ring1

Figure 18: center + ring1

Large Concentric Puzzle

ggpuzzle

ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 5,
    center_shape = "hexagon",
    seed = 456
  ) +
  scale_fill_viridis_c(
    option = "turbo",
    name = "Ring"
  ) +
  coord_fixed() +
  theme_puzzle() +
  theme(
    legend.position = "bottom",
    plot.title = element_text(hjust = 0.5, size = 16)
  ) +
  labs(title = "5-Ring Concentric Puzzle")

Figure 19

API

result <- generate_puzzle(
  type = "concentric",
  grid = c(5),
  size = c(300),
  seed = 456,
  center_shape = "hexagon",
  fill_palette = "turbo"
)
render_puzzle_preview(result, max_width = "500px")

Figure 20

Parameters Reference

Parameter	Type	Default	Description
rings	integer	3	Number of concentric rings
center_shape	string	“hexagon”	Center shape: “hexagon” or “circle”
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
fusion_groups	string	NULL	PILES notation for fusing pieces

Fill Variables

When using ggplot2 with concentric puzzles, you can map these variables:

Variable	Description
piece_id	Unique piece identifier
ring	Which ring the piece belongs to (0 = center)
is_center	TRUE if the piece is the center piece

Code Example

ggpuzzle

# Visualize with ggplot2
ggplot() +
  geom_puzzle_conc(
    aes(fill = after_stat(ring)),
    rings = 4,
    diameter = 280,
    center_shape = "hexagon",
    seed = 42,
    offset = 5
  ) +
  scale_fill_viridis_c(option = "plasma", name = "Ring") +
  coord_fixed() +
  theme_puzzle() +
  labs(title = "4-Ring Concentric Puzzle")

API

# Generate puzzle
result <- generate_puzzle(
  type = "concentric",
  grid = c(4),           # 4 rings
  size = c(280),         # 280mm diameter
  seed = 42,
  center_shape = "hexagon",
  offset = 5
)

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

# Preview the puzzle
render_puzzle_preview(result)