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: plotly 6.7.0 | Python 3.13.13
Quality: 88/100 | Updated: 2026-05-20
"""
import os
import sys
from collections import deque
# Remove current directory from path to avoid importing local plotly.py
sys.path = [p for p in sys.path if p not in ("", ".", os.path.dirname(__file__))]
import numpy as np
import plotly.graph_objects as go
# Theme
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
ACCENT = "#009E73" # Okabe-Ito position 1
# Maze parameters — outer rings have more sectors than inner rings
np.random.seed(42)
NUM_RINGS = 7
SECTORS = [42, 36, 30, 24, 18, 12, 6]
# Wall arrays: radial_walls[r][s] = wall clockwise from sector s in ring r
# ring_walls[r][s] = wall between ring r and ring r+1 at sector s
radial_walls = [[True] * SECTORS[r] for r in range(NUM_RINGS)]
ring_walls = [[True] * SECTORS[r] for r in range(NUM_RINGS - 1)]
# Depth-first search maze generation — guarantees exactly one solution
visited = {(0, 0)}
dfs_stack = [(0, 0)]
while dfs_stack:
cr, cs = dfs_stack[-1]
n = SECTORS[cr]
neighbors = [(cr, (cs + 1) % n, "cw"), (cr, (cs - 1) % n, "ccw")]
if cr < NUM_RINGS - 1:
neighbors.append((cr + 1, int(cs * SECTORS[cr + 1] / n), "in"))
if cr > 0:
neighbors.append((cr - 1, int(cs * SECTORS[cr - 1] / n), "out"))
unvisited = [(r, s, d) for r, s, d in neighbors if (r, s) not in visited]
if unvisited:
nr, ns, d = unvisited[np.random.randint(len(unvisited))]
if d == "cw":
radial_walls[cr][cs] = False
elif d == "ccw":
radial_walls[cr][ns] = False
elif d == "in":
ring_walls[cr][cs] = False
else:
ring_walls[nr][ns] = False
visited.add((nr, ns))
dfs_stack.append((nr, ns))
else:
dfs_stack.pop()
# Build undirected passage graph for BFS
graph = {}
for r in range(NUM_RINGS):
for s in range(SECTORS[r]):
if not radial_walls[r][s]:
a, b = (r, s), (r, (s + 1) % SECTORS[r])
graph.setdefault(a, []).append(b)
graph.setdefault(b, []).append(a)
for r in range(NUM_RINGS - 1):
for s in range(SECTORS[r]):
if not ring_walls[r][s]:
inner_s = int(s * SECTORS[r + 1] / SECTORS[r])
a, b = (r, s), (r + 1, inner_s)
graph.setdefault(a, []).append(b)
graph.setdefault(b, []).append(a)
# BFS to find the unique solution path to the innermost ring
bfs_queue = deque([((0, 0), [(0, 0)])])
bfs_seen = {(0, 0)}
solution = []
while bfs_queue:
cell, path = bfs_queue.popleft()
if cell[0] == NUM_RINGS - 1:
solution = path
break
for nb in graph.get(cell, []):
if nb not in bfs_seen:
bfs_seen.add(nb)
bfs_queue.append((nb, path + [nb]))
sol_x, sol_y = [], []
for r, s in solution:
r_mid = NUM_RINGS - r - 0.5
angle = (s + 0.5) * 2 * np.pi / SECTORS[r]
sol_x.append(r_mid * np.cos(angle))
sol_y.append(r_mid * np.sin(angle))
sol_x.append(0.0)
sol_y.append(0.0)
# Drawing constants
OUTER_R = NUM_RINGS
WALL_W = 3
fig = go.Figure()
# Ring arc walls — inner boundary arcs where wall exists
for r in range(NUM_RINGS - 1):
n = SECTORS[r]
inner_r = NUM_RINGS - r - 1
sa = 2 * np.pi / n
for s in range(n):
if ring_walls[r][s]:
theta = np.linspace(s * sa, (s + 1) * sa, 30)
fig.add_trace(
go.Scatter(
x=inner_r * np.cos(theta),
y=inner_r * np.sin(theta),
mode="lines",
line={"color": INK, "width": WALL_W},
showlegend=False,
hoverinfo="skip",
)
)
# Outer boundary circle with entry gap at sector 0
gap_start = 0.0
gap_end = 2 * np.pi / SECTORS[0]
theta_outer = np.linspace(gap_end, gap_start + 2 * np.pi, 300)
fig.add_trace(
go.Scatter(
x=OUTER_R * np.cos(theta_outer),
y=OUTER_R * np.sin(theta_outer),
mode="lines",
line={"color": INK, "width": WALL_W + 1},
showlegend=False,
hoverinfo="skip",
)
)
# Radial walls — spokes between ring boundaries
for r in range(NUM_RINGS):
r_out = NUM_RINGS - r
r_in = NUM_RINGS - r - 1
n = SECTORS[r]
for s in range(n):
if radial_walls[r][s]:
theta = (s + 1) * 2 * np.pi / n
fig.add_trace(
go.Scatter(
x=[r_in * np.cos(theta), r_out * np.cos(theta)],
y=[r_in * np.sin(theta), r_out * np.sin(theta)],
mode="lines",
line={"color": INK, "width": WALL_W},
showlegend=False,
hoverinfo="skip",
)
)
# Solution path — hidden by default; click legend entry to reveal
fig.add_trace(
go.Scatter(
x=sol_x,
y=sol_y,
mode="lines",
name="Show Solution",
line={"color": "#C475FD", "width": 4, "dash": "dot"},
opacity=0.85,
visible="legendonly",
)
)
# Center goal circle
goal_r = 0.4
theta_g = np.linspace(0, 2 * np.pi, 60)
fig.add_trace(
go.Scatter(
x=goal_r * np.cos(theta_g),
y=goal_r * np.sin(theta_g),
fill="toself",
fillcolor=ACCENT,
line={"color": ACCENT, "width": 2},
showlegend=False,
hoverinfo="skip",
)
)
fig.add_trace(
go.Scatter(
x=[0.0],
y=[0.0],
mode="markers",
marker={"symbol": "star", "size": 20, "color": "#DDCC77", "line": {"color": ACCENT, "width": 2}},
showlegend=False,
hoverinfo="skip",
)
)
# Entry arrow and labels
entry_angle = 0.5 * 2 * np.pi / SECTORS[0]
fig.add_annotation(
x=OUTER_R * np.cos(entry_angle),
y=OUTER_R * np.sin(entry_angle),
ax=(OUTER_R + 1.5) * np.cos(entry_angle),
ay=(OUTER_R + 1.5) * np.sin(entry_angle),
xref="x",
yref="y",
axref="x",
ayref="y",
showarrow=True,
arrowhead=2,
arrowsize=2,
arrowwidth=3,
arrowcolor=ACCENT,
)
fig.add_annotation(
x=(OUTER_R + 2.8) * np.cos(entry_angle),
y=(OUTER_R + 2.8) * np.sin(entry_angle),
text="START",
showarrow=False,
xref="x",
yref="y",
font={"size": 22, "color": ACCENT, "family": "Arial Black"},
)
fig.add_annotation(
x=0.0,
y=-(OUTER_R + 1.5),
text="GOAL",
showarrow=False,
xref="x",
yref="y",
font={"size": 22, "color": ACCENT, "family": "Arial Black"},
)
# Layout
fig.update_layout(
title={
"text": "maze-circular · python · plotly · anyplot.ai",
"font": {"size": 16, "color": INK},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"showgrid": False,
"zeroline": False,
"showticklabels": False,
"scaleanchor": "y",
"scaleratio": 1,
"range": [-(OUTER_R + 4.0), OUTER_R + 4.0],
},
yaxis={"showgrid": False, "zeroline": False, "showticklabels": False, "range": [-(OUTER_R + 4.0), OUTER_R + 4.0]},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
showlegend=True,
legend={
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
"font": {"color": INK_SOFT, "size": 10},
"x": 0.02,
"y": 0.98,
"xanchor": "left",
"yanchor": "top",
},
margin={"l": 50, "r": 50, "t": 100, "b": 50},
)
# Save
fig.write_image(f"plot-{THEME}.png", width=600, height=600, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Circular Maze Puzzle on anyplot.ai.