Maze Generation: How Computers Build Labyrinths

Watch algorithms carve paths through grids

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What is a Maze?

A maze is a grid of cells connected by passages. Each cell can have walls on its four sides. Click cells to toggle walls and see how mazes are structured!

Wall
Path
Start
End

Grid Structure

Mazes are built on a grid. Each cell is either a wall or a passage. The challenge is creating paths without dead ends (except intentional ones!).

Perfect Mazes

A "perfect" maze has exactly one path between any two points. No loops, no isolated areas - every cell is reachable!

Fun Fact
The oldest known labyrinth was found in Egypt, dating back to 1800 BCE. Computer-generated mazes have been around since the 1950s!
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Recursive Backtracking

The most popular maze algorithm! It explores as deep as possible, then backtracks when it hits a dead end. Watch the purple cell carve paths through the grid.

Steps: 0

How It Works

1. Pick a starting cell
2. Choose a random unvisited neighbor
3. Remove the wall between them
4. Repeat until no unvisited neighbors
5. Backtrack to find new paths

Characteristics

Creates long, winding corridors with few branches. High "river" factor - paths flow like rivers. Great for adventure games!

Algorithm Insight
This uses a "stack" data structure - the last cell visited is the first to backtrack from. It's called LIFO: Last In, First Out.
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Prim's Algorithm

Instead of going deep, Prim's grows outward from a frontier. Watch the orange frontier cells expand like a growing organism!

Steps: 0 | Frontier: 0
Visited
Frontier
Unvisited

How It Works

1. Start with one cell in the maze
2. Add its neighbors to the frontier
3. Pick a random frontier cell
4. Connect it to the maze
5. Add its neighbors to frontier
6. Repeat!

Characteristics

Creates more "organic" looking mazes with shorter corridors. The maze grows outward evenly. Often used for cave generation in games!

4

Binary Tree Algorithm

The simplest maze algorithm! For each cell, just carve a passage either up OR left. That's it! But notice the diagonal bias...

Steps: 0

How It Works

For each cell, flip a coin:
- Heads: carve north
- Tails: carve west
(Handle edges appropriately)

That's the entire algorithm!

The Bias Problem

Notice the diagonal corridors? Binary Tree always has a bias toward one corner. The top row and left column are always open corridors!

Why "Binary Tree"?
The structure forms a tree where each cell has exactly one "parent" (north or west). It's binary because there are only 2 choices!
5

Kruskal's Algorithm

Watch separate regions merge into one! Each color is an isolated region. When walls are removed, regions combine until the whole maze is connected.

Steps: 0 | Regions: 0

How It Works

1. Each cell starts as its own region
2. Shuffle all walls randomly
3. For each wall, if it separates two regions, remove it
4. Regions merge together
5. Stop when only one region remains

Union-Find Structure

Uses a "disjoint set" to track which cells belong to which region. Merging regions is nearly instant with this clever data structure!

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Recursive Division

The opposite approach! Start with an open room and add walls to divide it. Each wall has exactly one passage. Divide and conquer!

Steps: 0

How It Works

1. Start with an open room
2. Draw a wall across the room
3. Add one passage in the wall
4. Recursively divide each side
5. Stop when regions are too small

Characteristics

Creates long straight walls and rectangular rooms. Often looks more "architectural". Great for dungeon-style games!

Pro Tip
Recursive Division is the only algorithm here that "builds walls" instead of "carving paths." It starts full and ends with a maze!
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Sidewinder Algorithm

Works row by row! For each cell, either extend the current "run" or close it by carving up. Watch the runs form and close.

Steps: 0 | Current Run: 0
Current Run
Completed

How It Works

For each row (except the first):
1. Start a "run" of cells
2. Either extend the run east
3. Or close it by carving north from a random run cell
4. First row is always open

Characteristics

Like Binary Tree, has a bias (northern corridor). But produces more varied paths. Can generate mazes row-by-row for infinite scrolling games!

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Algorithm Arena

Watch all six algorithms race to generate a maze! Which one finishes first? Spoiler: speed depends on maze size and implementation.

Recursive Backtracking
Ready
Prim's Algorithm
Ready
Binary Tree
Ready
Kruskal's
Ready
Recursive Division
Ready
Sidewinder
Ready
Key Insight
All algorithms create valid "perfect" mazes, but each has unique characteristics. The "best" algorithm depends on what patterns you want!

Maze Master!

You've explored how computers generate mazes using different algorithms. Each approach creates unique patterns and challenges!

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Mazes Generated
0
Algorithms Explored
0
Time Exploring

Grids are the Foundation

Mazes start as a grid of cells with walls between them.

Recursive Backtracking

Goes deep, hits a wall, backs up - creates long winding paths.

Prim's Algorithm

Grows outward from a point - creates more organic-looking mazes.

Different Algorithms, Different Patterns

Each algorithm has its own "signature" look and feel.

Binary Tree is Simplest

One line of logic creates a complete maze with a diagonal bias.

Recursive Division Builds Walls

The opposite approach - start open, add walls!

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