Maze Generation Algorithms

Discover the fascinating algorithms behind maze generation. Each algorithm creates unique patterns and characteristics.

Recursive Backtracker

Also known as: Depth-First Search (DFS)

Difficulty: Medium

The classic maze generation algorithm that creates long, winding corridors with relatively few dead ends.

How It Works

  1. 1 Start at a random cell and mark it as visited
  2. 2 While there are unvisited cells, pick a random unvisited neighbor
  3. 3 Remove the wall between the current cell and chosen neighbor
  4. 4 Move to the neighbor and repeat
  5. 5 If no unvisited neighbors exist, backtrack to find one

Characteristics

  • Creates mazes with long, twisting passages
  • Relatively few dead ends compared to other algorithms
  • Good for beginners due to predictable paths
  • Memory efficient with iterative implementation

Best for: Traditional mazes with single solution paths

Prim's Algorithm

Also known as: Randomized Prim's

Difficulty: Hard

A minimum spanning tree algorithm adapted for maze generation, creating mazes with many short dead ends.

How It Works

  1. 1 Start with a grid full of walls
  2. 2 Pick a random starting cell and add its walls to a list
  3. 3 While the wall list is not empty, pick a random wall
  4. 4 If the cell on the opposite side hasn't been visited, remove the wall
  5. 5 Add the neighboring walls of the new cell to the list

Characteristics

  • Creates many short dead ends
  • More branching than recursive backtracker
  • Mazes appear more "bushy" and complex
  • Harder to solve due to frequent decision points

Best for: Challenging mazes with many dead ends

Kruskal's Algorithm

Also known as: Randomized Kruskal's

Difficulty: Medium-Hard

Another spanning tree algorithm that randomly removes walls while ensuring all cells remain connected.

How It Works

  1. 1 Create a list of all interior walls
  2. 2 Assign each cell to its own unique set
  3. 3 Randomly select a wall from the list
  4. 4 If the cells on either side belong to different sets, remove the wall
  5. 5 Merge the two sets and repeat until one set remains

Characteristics

  • Creates uniform, unbiased mazes
  • No visible patterns or directional bias
  • Good distribution of dead ends
  • Each maze is truly random

Best for: Unbiased mazes with uniform texture

Recursive Division

Also known as: Chamber Algorithm

Difficulty: Easy-Medium

A wall-adding algorithm that recursively divides the space into smaller chambers with passages between them.

How It Works

  1. 1 Start with an empty room
  2. 2 Add a wall that divides the room in two
  3. 3 Add a passage through the wall at a random point
  4. 4 Recursively apply to both sub-rooms
  5. 5 Stop when rooms are too small to divide

Characteristics

  • Creates rectangular, room-like chambers
  • Long straight corridors are common
  • Recognizable geometric pattern
  • Fast generation even for large mazes

Best for: Mazes with distinct rectangular rooms

Binary Tree

Also known as: Binary Tree Algorithm

Difficulty: Easy

The simplest maze algorithm with a distinctive diagonal bias in the resulting maze.

How It Works

  1. 1 Visit each cell in the grid
  2. 2 For each cell, randomly carve a passage either north or east
  3. 3 If on the north edge, always go east
  4. 4 If on the east edge, always go north
  5. 5 Results in a perfect maze with diagonal flow

Characteristics

  • Very fast and simple to implement
  • Strong diagonal bias (NE corner is always open)
  • Two edges of the maze are always open corridors
  • Easier to solve when going NE, harder going SW

Best for: Quick generation, educational purposes

Wilson's Algorithm

Also known as: Loop-Erased Random Walk

Difficulty: Medium

Uses loop-erased random walks to generate unbiased mazes where every possible maze is equally likely.

How It Works

  1. 1 Mark one cell as part of the maze
  2. 2 Start a random walk from an unvisited cell
  3. 3 If the walk loops back on itself, erase the loop
  4. 4 When the walk reaches the maze, add the path to the maze
  5. 5 Repeat until all cells are in the maze

Characteristics

  • Generates perfectly unbiased mazes
  • Every possible maze has equal probability
  • Can be slow for large mazes (random walks)
  • Mathematically beautiful algorithm

Best for: Unbiased, mathematically perfect mazes

Cellular Automaton

Also known as: Cave Generation

Difficulty: Variable

Uses cellular automaton rules to create organic, cave-like structures rather than traditional corridors.

How It Works

  1. 1 Start with random noise (cells randomly open or closed)
  2. 2 Apply smoothing rules based on neighbor count
  3. 3 If a cell has many wall neighbors, it becomes a wall
  4. 4 If a cell has many open neighbors, it becomes open
  5. 5 Repeat smoothing several times

Characteristics

  • Creates organic, natural-looking caves
  • May produce disconnected regions
  • Non-traditional maze appearance
  • Good for game level generation

Best for: Organic, cave-like structures

Sidewinder

Also known as: Sidewinder Algorithm

Difficulty: Easy

A row-by-row algorithm similar to Binary Tree but with horizontal bias instead of diagonal.

How It Works

  1. 1 Process each row from left to right
  2. 2 For each cell, randomly decide to continue East or close the "run"
  3. 3 When closing a run, pick a random cell from the run and carve North
  4. 4 The first row is always a single corridor (all East)
  5. 5 Results in maze with horizontal passages and vertical connections

Characteristics

  • Creates long horizontal corridors
  • Top row is always completely open
  • No diagonal bias (unlike Binary Tree)
  • Very fast - processes row by row

Best for: Mazes with horizontal emphasis

Hunt and Kill

Also known as: Hunt-and-Kill Algorithm

Difficulty: Medium

Similar to Recursive Backtracker but uses a "hunt" phase instead of backtracking when stuck.

How It Works

  1. 1 Start at a random cell, perform random walk (Kill phase)
  2. 2 When stuck (no unvisited neighbors), scan grid for unvisited cell next to visited cell (Hunt phase)
  3. 3 Connect the found cell to a visited neighbor
  4. 4 Continue random walk from there
  5. 5 Repeat until all cells are visited

Characteristics

  • Creates long, winding passages like DFS
  • No stack needed - memory efficient
  • Slightly more uniform than Recursive Backtracker
  • Hunt phase can be slow on large mazes

Best for: Long corridors without stack overhead

Growing Tree

Also known as: Configurable Growing Tree

Difficulty: Variable

The most flexible algorithm - behavior changes based on how cells are selected from the active list.

How It Works

  1. 1 Start with a random cell in the active list
  2. 2 Select a cell from the list (newest, oldest, or random)
  3. 3 If it has unvisited neighbors, connect to one and add it to list
  4. 4 If no neighbors, remove cell from list
  5. 5 Selection method determines maze style

Characteristics

  • Newest selection = Recursive Backtracker style
  • Random selection = Prim's style
  • Mixed selection = balanced passages and dead ends
  • Most versatile algorithm

Best for: Customizable maze characteristics

Eller's Algorithm

Also known as: Row-by-row Generation

Difficulty: Medium

A memory-efficient algorithm that generates mazes row by row, using set theory to track connected cells.

How It Works

  1. 1 Initialize first row with each cell in its own set
  2. 2 Randomly merge adjacent cells in the same row
  3. 3 For each set, create at least one vertical connection
  4. 4 Move to next row, carrying set information forward
  5. 5 In the last row, merge all remaining separate sets

Characteristics

  • O(width) memory - can generate infinite mazes
  • Row-by-row generation, no backtracking
  • Creates well-balanced mazes
  • Perfect for streaming maze generation

Best for: Memory-constrained environments

Aldous-Broder

Also known as: Random Walk Algorithm

Difficulty: Easy

The simplest unbiased maze algorithm using a random walk that continues until every cell has been visited.

How It Works

  1. 1 Start at a random cell
  2. 2 Randomly move to any neighbor
  3. 3 If the neighbor is unvisited, carve a passage
  4. 4 Continue random walking regardless of visited state
  5. 5 Stop when all cells have been visited

Characteristics

  • Perfectly unbiased - all mazes equally likely
  • Very simple to implement
  • Can be slow on large mazes (random walk)
  • No visible patterns or directional bias

Best for: Uniform random maze selection

Braid Maze

Also known as: No Dead Ends Maze

Difficulty: Easy

A maze with no dead ends - every path either leads somewhere or loops back, creating multiple routes.

How It Works

  1. 1 Generate a standard maze first
  2. 2 Find all dead ends (cells with 3 walls)
  3. 3 Remove walls from dead ends to create loops
  4. 4 Repeat until no dead ends remain
  5. 5 Result has multiple valid solution paths

Characteristics

  • No dead ends anywhere
  • Multiple valid solutions exist
  • Less frustrating for beginners
  • Good for chase/race games

Best for: Games and beginner-friendly puzzles

Fractal Maze

Also known as: Self-Similar Pattern Maze

Difficulty: Medium

Creates mazes with fractal-like structure where similar patterns appear at different scales through recursive subdivision.

How It Works

  1. 1 Choose a fractal pattern (cross, spiral, tree, serpent)
  2. 2 Recursively divide space into regions
  3. 3 Create passages between divided regions
  4. 4 Apply same pattern at smaller scales
  5. 5 Ensure full connectivity across all regions

Characteristics

  • Self-similar patterns at different scales
  • Mathematical, organized appearance
  • Multiple pattern variations available
  • Unique aesthetic quality

Best for: Mathematical art and education

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