A circular maze puzzle visualization featuring concentric rings connected by radial passages. Unlike rectangular mazes, this design creates a unique solving experience where the player navigates inward through ring-shaped corridors. The maze has an entry point on the outer edge and a goal at the center, with algorithmically generated walls ensuring exactly one solvable path.
# anyplot.ai
# maze-circular: Circular Maze Puzzle
# Library: makie 0.21.9 | Julia 1.11.9
# Quality: 92/100 | Created: 2026-09-02
using CairoMakie
using Colors
using Random
Random.seed!(42)
# --- Theme tokens -------------------------------------------------------------
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const BRAND = colorant"#009E73" # Imprint palette position 1 — entry/goal accent
# --- Maze parameters -----------------------------------------------------------
# 8 rings keeps the puzzle within the spec's recommended 5-10 range. Sector count
# doubles every 3 rings from the hub outward (3 -> 6 -> 12) so cell width stays
# roughly consistent from the cramped center to the roomier rim, instead of a
# fixed sector count leaving the innermost rings a dense cluster of narrow wedges.
rings = 8
ring_sectors = [3, 3, 3, 6, 6, 6, 12, 12] # ring 1 = innermost (hub side)
difficulty = "medium"
entry_sector = 1 # sector (on the outer ring) hosting the opening
hub_radius = 1.0
ring_width = 1.0
n_arc = 12 # points per drawn arc segment
radii = [hub_radius + i * ring_width for i in 0:rings] # radii[1] = hub boundary
dθ = [2π / ring_sectors[i] for i in 1:rings] # sector angle, per ring
# Node ids: 1 = center hub, then each ring's sectors packed consecutively.
ring_offset = vcat(0, cumsum(ring_sectors)) # ring_offset[i] = cells before ring i
node_id(ring, sector) = 1 + ring_offset[ring] + sector
polar(r, θ) = Point2f(r * cos(θ), r * sin(θ))
# --- Union-Find (disjoint set), used by the randomized-Kruskal maze carver ----
function find_root(parent, x)
while parent[x] != x
parent[x] = parent[parent[x]]
x = parent[x]
end
return x
end
function union_cells!(parent, a, b)
ra, rb = find_root(parent, a), find_root(parent, b)
ra == rb && return false
parent[ra] = rb
return true
end
# --- Candidate connections between adjacent cells -----------------------------
# Each entry is a wall between two cells; shape encodes how to draw it if the
# connection stays closed: an :arc (fixed radius, spans an angle range) for
# ring-to-ring boundaries, or a :line (fixed angle, spans a radius range) for
# sector-to-sector boundaries.
edges = NamedTuple{(:a, :b, :shape, :p1, :p2, :p3),Tuple{Int,Int,Symbol,Float64,Float64,Float64}}[]
# Hub <-> innermost ring.
for s in 1:ring_sectors[1]
θ1, θ2 = (s - 1) * dθ[1], s * dθ[1]
push!(edges, (a = 1, b = node_id(1, s), shape = :arc, p1 = radii[1], p2 = θ1, p3 = θ2))
end
# Ring i <-> ring i+1. `ratio` is 1 when sector count stays flat, or 2 where it
# doubles outward — each inner cell then borders exactly `ratio` outer cells.
for i in 1:(rings - 1)
ratio = ring_sectors[i + 1] ÷ ring_sectors[i]
for s in 1:ring_sectors[i], k in 1:ratio
s_out = (s - 1) * ratio + k
θ1, θ2 = (s_out - 1) * dθ[i + 1], s_out * dθ[i + 1]
push!(edges, (a = node_id(i, s), b = node_id(i + 1, s_out), shape = :arc, p1 = radii[i + 1], p2 = θ1, p3 = θ2))
end
end
# Sector <-> next sector within the same ring.
for i in 1:rings, s in 1:ring_sectors[i]
s2 = s % ring_sectors[i] + 1
θ = s * dθ[i]
push!(edges, (a = node_id(i, s), b = node_id(i, s2), shape = :line, p1 = θ, p2 = radii[i], p3 = radii[i + 1]))
end
# --- Carve the maze: randomized Kruskal spanning tree over the cell graph ----
# A spanning tree connects every cell with exactly one path between any two —
# guaranteeing exactly one solvable path from the entry to the center goal.
n_nodes = 1 + sum(ring_sectors)
parent = collect(1:n_nodes)
walls = similar(edges, 0)
for e in shuffle(edges)
union_cells!(parent, e.a, e.b) || push!(walls, e)
end
# --- Wall geometry: one polyline per closed connection, NaN-separated -------
wall_pts = Point2f[]
for e in walls
if e.shape == :arc
for θ in range(e.p2, e.p3; length = n_arc)
push!(wall_pts, polar(e.p1, θ))
end
else
push!(wall_pts, polar(e.p2, e.p1))
push!(wall_pts, polar(e.p3, e.p1))
end
push!(wall_pts, Point2f(NaN, NaN))
end
outer_r = radii[end]
outer_sectors = ring_sectors[rings]
for s in 1:outer_sectors
if s != entry_sector
for θ in range((s - 1) * dθ[rings], s * dθ[rings]; length = n_arc)
push!(wall_pts, polar(outer_r, θ))
end
push!(wall_pts, Point2f(NaN, NaN))
end
end
# --- Figure --------------------------------------------------------------------
fig = Figure(
size = (1200, 1200),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
title_str = "maze-circular · julia · makie · anyplot.ai"
ax = Axis(
fig[1, 1];
title = title_str,
titlesize = 24,
titlecolor = INK,
subtitle = "$(rings) rings · $(difficulty) difficulty · single solution",
subtitlesize = 15,
subtitlecolor = INK_SOFT,
aspect = DataAspect(),
backgroundcolor = PAGE_BG,
)
hidedecorations!(ax)
hidespines!(ax)
lines!(ax, wall_pts; color = INK, linewidth = 4.5)
# --- Goal marker at the center --------------------------------------------------
poly!(ax, Circle(Point2f(0, 0), hub_radius * 0.82); color = (BRAND, 0.12), strokewidth = 0)
scatter!(ax, [Point2f(0, 0)]; marker = :star5, markersize = 30, color = BRAND, strokewidth = 0)
text!(ax, 0.0, -hub_radius * 0.55; text = "GOAL", align = (:center, :center), color = INK, fontsize = 14)
# --- Entry marker on the outer boundary ----------------------------------------
entry_angle = (entry_sector - 0.5) * dθ[rings]
r_tail, r_tip = outer_r + 1.0, outer_r + 0.15
x0, y0 = r_tail * cos(entry_angle), r_tail * sin(entry_angle)
x1, y1 = r_tip * cos(entry_angle), r_tip * sin(entry_angle)
arrows!(ax, [x0], [y0], [x1 - x0], [y1 - y0]; color = BRAND, linewidth = 4.5, arrowsize = 22)
label_x, label_y = (outer_r + 1.55) * cos(entry_angle), (outer_r + 1.55) * sin(entry_angle)
text!(ax, label_x, label_y; text = "START", align = (:center, :center), color = INK, fontsize = 14)
# --- Content-hugging canvas limits ---------------------------------------------
# Fit the view snugly around everything actually drawn (walls + entry marker +
# labels) instead of padding every side uniformly — a uniform pad leaves extra
# empty space opposite the one-sided START arrow, since that side needs less.
content_x = Float64[x0, x1, label_x]
content_y = Float64[y0, y1, label_y]
for p in wall_pts
isfinite(p[1]) || continue
push!(content_x, p[1])
push!(content_y, p[2])
end
label_margin = 0.55 # room for the START / GOAL glyphs beyond their anchor point
xmin, xmax = minimum(content_x) - label_margin, maximum(content_x) + label_margin
ymin, ymax = minimum(content_y) - label_margin, maximum(content_y) + label_margin
half = max(xmax - xmin, ymax - ymin) / 2
cx, cy = (xmin + xmax) / 2, (ymin + ymax) / 2
xlims!(ax, cx - half, cx + half)
ylims!(ax, cy - half, cy + half)
# --- Save ------------------------------------------------------------------
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/maze-circular/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "maze-circular",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/maze-circular/julia/makie",
"hub": "https://anyplot.ai/maze-circular",
"code_json": "https://api.anyplot.ai/specs/maze-circular/makie/code",
"spec_json": "https://api.anyplot.ai/specs/maze-circular",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/maze-circular/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/maze-circular/julia/makie/plot-dark.png",
"quality_score": 92.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Circular Maze Puzzle on anyplot.ai.