Maze Algorithms (2017)

A maze generator in the shape of a maze whose corridors spell a 4-letter word:

    char*M,A,Z,E=40,J[40],T[40];main(C){for(*J=A=scanf(M="%d",&C);
    --            E;             J[              E]             =T
    [E   ]=  E)   printf("._");  for(;(A-=Z=!Z)  ||  (printf("\n|"
    )    ,   A    =              39              ,C             --
    )    ;   Z    ||    printf   (M   ))M[Z]=Z[A-(E   =A[J-Z])&&!C
    &    A   ==             T[                                  A]
    |6<<27<rand()||!C&!Z?J[T[E]=T[A]]=E,J[T[A]=A-Z]=A,"_.":" |"];}

    char M[3],A,Z,E=40,J[40],T[40];main(C){for(*J=A=scanf("%d",&C);

For anyone interested in this, Jamis Buck's book 'Mazes for Programmers' is a masterpiece of the genre.

My personal favorite distinction is between the Recursive Backtracker (which creates long, winding corridors with few dead ends which is great for tower defense games) vs. Prim's Algorithm (which creates lots of short cul-de-sacs which is better for roguelikes). The bias of the algorithm dictates the feel of the game more than the graphics do.

I've built a few maze generators based on Jamis' book. The one I'm most proud of is this one https://xn--sberg-lra.net/maze/irregular?size=5&entryCount=1 that generates SVG mazes with sort of irregular lines.

Lovely page. Reminds me of the venerable Think Labyrinth (https://www.astrolog.org/labyrnth/algrithm.htm) page, but the live demos add a lot.

My favorite maze algorithm is a variant of the growing tree algorithm - each time you carve a cell, add it to a random one of N lists. When choosing a cell to visit, pop the last cell off the first non-empty list. It's considerably faster than the standard tree algorithm, but more importantly, changing N has a dramatic impact on the texture of the maze (compare 1 2 4 8 etc on a decently large maze).

Mike Bostock had several very lovely visualizations back on the D3.js site which I can't find. Here's a cool blogpost he wrote: https://bost.ocks.org/mike/algorithms/#maze-generation

I used Jamis' book extensively to build this AI tool for generating custom mazes of any shape! https://kamens.com/blog/generating-custom-mazes-with-ai

Related:

Maze Generation: Recursive Division (2011) - https://news.ycombinator.com/item?id=42703816 - Jan 2025 (12 comments)

Maze Algorithms (2011) - https://news.ycombinator.com/item?id=23429368 - June 2020 (22 comments)

Representing a Toroidal Grid - https://news.ycombinator.com/item?id=10608476 - Nov 2015 (2 comments)

Maze Generation: Recursive Backtracking - https://news.ycombinator.com/item?id=4058525 - June 2012 (1 comment)

Maze Generation: Weave mazes - https://news.ycombinator.com/item?id=4052856 - June 2012 (3 comments)

Maze-generation algorithms, with JS demos - https://news.ycombinator.com/item?id=2190017 - Feb 2011 (9 comments)

Generating random mazes with the Growing Tree algorithm (w/ Javascript demo) - https://news.ycombinator.com/item?id=2148348 - Jan 2011 (6 comments)

Maze Generation: Wilson's algorithm - https://news.ycombinator.com/item?id=2123695 - Jan 2011 (11 comments)

Maze Generation: Kruskal's Algorithm - https://news.ycombinator.com/item?id=2062999 - Jan 2011 (9 comments)

Maze Generation: Eller's Algorithm - https://news.ycombinator.com/item?id=2048752 - Dec 2010 (9 comments)

Also:

Wilson's Algorithm - https://news.ycombinator.com/item?id=45549017 - Oct 2025 (9 comments)

Maze Tree - https://news.ycombinator.com/item?id=7746822 - May 2014 (38 comments)

Solving a Maze with D3.js - https://news.ycombinator.com/item?id=7631864 - April 2014 (19 comments)

Think Labyrinth: Maze Algorithms - https://news.ycombinator.com/item?id=10101728 - Aug 2015 (10 comments)

Practical algorithms and code optimization: maze generation - https://news.ycombinator.com/item?id=5431561 - March 2013 (10 comments)

Maze Algorithms - https://news.ycombinator.com/item?id=157266 - April 2008 (1 comment)

Others?

I've always known about algorithms that solve mazes, but never about actually making them. It's interesting seeing all these algorithms and how the mazes they generate look different.

Is it known which algorithms produce 'difficult' mazes? I'm imagining you could run all the maze solving algorithms against all the maze generating algorithms many times, and then calculate what the Nash equilibrium would be if the solver is trying to minimise expected time and the generator is trying to maximise it.

This is the kind of stuff I come here for.

seconding the jamis buck book, its one of the few programming books i actually finished. the way he explains each algorithm with visualizations makes it stick

It feels like many of the more complicated algorithms produce worse mazes (long horizontal/vertical walls, many 1-2 square dead ends next to another) than basic recursive backtracking.