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+---
+id: wiki-2026-0508-procedural-level-geometry
+title: Procedural Level Geometry
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [PCG, Procedural Generation, Level PCG, Roguelike Generation]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [game-design, level-design, pcg, procedural-generation]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: python
+  framework: roguelike / 3d-engine
+---
+
+# Procedural Level Geometry
+
+## 매 한 줄
+> **"매 grammar + constraint = playable layout"**. Procedural level geometry 는 매 1980s Rogue 의 BSP 부터 매 2010s Spelunky 의 room template, 매 2020s Minecraft / No Man's Sky / Townscaper 의 WFC, 매 2026 ML-assisted hybrid (Pixar's RayBend, Nvidia GANverse) 까지 매 evolution. 매 핵심 trade-off: **매 controllability ↔ matrix variety**.
+
+## 매 핵심
+
+### 매 algorithm families
+1. **BSP / partition**: Rogue, NetHack — 매 simple, 매 grid-only.
+2. **Cellular automata**: Cave generation — 매 organic shape.
+3. **Random walk / drunkard**: 매 cave / path.
+4. **Template + stitching**: Spelunky, Enter the Gungeon — 매 controllable.
+5. **Wave Function Collapse (WFC)**: Townscaper, Bad North — 매 high constraint.
+6. **Grammar / L-system**: Vegetation, dungeons (Lindenmayer).
+7. **ML-assisted**: 2026 — diffusion-based heightmap, GAN tile generation.
+
+### 매 pipeline
+```
+Seed → Macro layout (zones) → Meso (rooms / chunks)
+     → Micro (geometry, props) → Validation → Polish
+```
+
+### 매 응용
+1. Roguelike dungeons (Caves of Qud, Brogue, Cogmind).
+2. Open-world terrain (Minecraft, Valheim, NMS).
+3. City generation (Cities Skylines mods, Townscaper).
+4. Mission layouts (Hitman freelancer mode, XCOM).
+
+## 💻 패턴
+
+### BSP dungeon
+```python
+def bsp_split(rect, depth=0, max_depth=4):
+    if depth >= max_depth or rect.too_small():
+        return [rect.shrink(margin=1)]   # leaf = room
+    axis = "h" if rect.w < rect.h else "v"
+    cut = random.uniform(0.4, 0.6)
+    a, b = rect.split(axis, cut)
+    return bsp_split(a, depth+1, max_depth) + bsp_split(b, depth+1, max_depth)
+
+def connect_rooms(rooms, grid):
+    for r1, r2 in zip(rooms, rooms[1:]):
+        carve_corridor(grid, r1.center, r2.center)
+```
+
+### Cellular automata cave
+```python
+def cave(w, h, fill=0.45, iters=5):
+    g = [[1 if random.random() < fill else 0 for _ in range(w)] for _ in range(h)]
+    for _ in range(iters):
+        g = [
+            [smooth(g, x, y) for x in range(w)]
+            for y in range(h)
+        ]
+    return g
+
+def smooth(g, x, y):
+    walls = sum(g[y+dy][x+dx]
+                for dy in (-1,0,1) for dx in (-1,0,1)
+                if 0 <= x+dx < len(g[0]) and 0 <= y+dy < len(g))
+    return 1 if walls >= 5 else 0
+```
+
+### Wave Function Collapse (sketch)
+```python
+def wfc(tiles, w, h, adjacency):
+    grid = [[set(tiles) for _ in range(w)] for _ in range(h)]
+    while not all_collapsed(grid):
+        x, y = lowest_entropy(grid)
+        choice = random.choice(list(grid[y][x]))
+        grid[y][x] = {choice}
+        propagate(grid, x, y, adjacency)
+    return grid
+```
+
+### Spelunky-style template stitching
+```python
+ROOM_TEMPLATES = {
+    "side": ["....", "..S.", "....", ".###"],
+    "drop": [".S..", "....", "###.", "...."],
+    "trap": [["X" if random.random()<.1 else "." for _ in range(4)] for _ in range(4)],
+}
+def build_level(plan):
+    """plan: 4×4 grid of (template_kind)."""
+    return [
+        ROOM_TEMPLATES[kind] for row in plan for kind in row
+    ]
+```
+
+### Validation — solvability check
+```python
+def is_solvable(grid, start, goal):
+    return bfs_reachable(grid, start, goal)
+
+def regenerate_until_valid(generator, validate, max_tries=100):
+    for _ in range(max_tries):
+        level = generator()
+        if validate(level):
+            return level
+    raise GenerationFailure()
+```
+
+### L-system dungeon grammar
+```
+Axiom: ROOM
+Rules:
+  ROOM     → ROOM CORRIDOR ROOM
+  ROOM     → ROOM CORRIDOR JUNCTION
+  JUNCTION → ROOM | LOOP_BACK
+Iterations: 4
+→ post-process: place geometry, add doors
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Tight authored feel needed | Template stitching (Spelunky) |
+| Organic cave / terrain | Cellular automata + erosion |
+| Strict constraint (city, building) | **WFC** |
+| Branching dungeon | BSP + grammar |
+| Open world heightmap | Perlin / Simplex + erosion + biome mask |
+| Fully ML-driven (2026) | Diffusion + WFC fallback |
+
+**기본값**: Template + WFC hybrid + validation regen-loop.
+
+## 🔗 Graph
+- 부모: [[Level_Design]] · [[Procedural_Content_Generation]]
+- 변형: [[Cellular Automata]]
+- Adjacent: [[Base-Layouts-and-Kill-Zones]] · [[Immersive-Sims-Deus-Ex-Thief]]
+
+## 🤖 LLM 활용
+**언제**: 매 roguelike / sandbox / open-world 의 generation system, 매 designer 의 매 toolkit, 매 controllability ↔ variety trade-off discussion.
+**언제 X**: 매 highly-authored linear narrative — 매 PCG 의 cost > benefit.
+
+## ❌ 안티패턴
+- **No validation**: 매 unreachable goal / 매 closed-off key item.
+- **Over-randomization**: 매 every tile random = 매 chaos, 매 design intent X.
+- **No reproducibility**: 매 seed 의 expose 의 X — 매 bug repro / 매 speedrun 의 X.
+
+## 🧪 검증 / 중복
+- Verified (Shaker / Togelius "Procedural Content Generation in Games" 2016; WFC paper Gumin 2016; Spelunky postmortem GDC 2014).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — algorithm taxonomy, BSP / CA / WFC / template code, validation pattern |