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Maze Algorithms (2017) (jamisbuck.org)
tromp 17 hours ago [-]
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,"_.":" |"];}
Generates a maze on the fly after entering the desired height of the maze. This compiled fine back in 1988 when I submitted it to the IOCCC (having rediscovered Eller's algorithm). Modern C compilers don't allow constant strings to be overwritten, which can be avoided by changing the first line to

    char M[3],A,Z,E=40,J[40],T[40];main(C){for(*J=A=scanf("%d",&C);
The code is explained in detail at https://tromp.github.io/maze.html
munificent 13 hours ago [-]
Neat!

Related: Here's a C program that draws random dungeons sort of like you use in a roguelike dungeon crawler:

    #include <time.h> //  Robert Nystrom
    #include <stdio.h> // @munificentbob
    #include <stdlib.h> //     for Ginny
    #define  r return    //    2008-2019
    #define  l(a, b, c, d) for (i y=a;y\
    <b; y++) for (int x = c; x < d; x++)
    typedef int i;const i H=40;const i W
    =80;i m[40][80];i g(i x){r rand()%x;
    }void cave(i s){i w=g(10)+5;i h=g(6)
    +3;i t=g(W-w-2)+1;i u=g(H-h-2)+1;l(u
    -1,u+h+2,t-1            ,t+w+2)if(m[
    y][x]=='.'                  )r;i d=0
    ;i e,f        ;if(!s){l(      u-1,u+
    h+2,t-    1,t+w+2){i s=x<t     ||x>t
    +w;i    t=y<u||           y>    u+h;
    if(s    ^t&&              m[      y]
    [x    ]=='#'    ){d++;    if(g    (d
    )     ==0)    e=x,f=y;    }}if    (d
    ==    0)r;    }l(u-1,u    +h+2    ,t
    -1    ,t+w    +2){i s=    x< t    ||
    x>    t+w;    i t= y<u    ||y>    u+
    h;    m[y]      [x]= s    &&t?   '!'
    :s^t    ?'#'                    :'.'
    ;}if    (d>0)m                  [f][
    e]=g(2    )?'\'':'+';for(i j=0;j<(s?
    1:g(6)        +1);j++)m[g(h)+u][g(w)
    +t]=s?'@'                 :g(4) ==0?
    '$':65+g(62)              ;}i main(i
    argc, const char* argv[]) {srand((i)
    time(NULL));l(0, H, 0,W)m[y][x]=' ';
    for(i j=0;j<1000;j++)cave(j==0);l(0,
    H,0,W) {i c=m[y][x]; putchar(c=='!'?
    '#':c);if(x==W-1)printf("\n");}r 0;}
binaryturtle 17 hours ago [-]
If I squeeze the eyes I can read the "MAZE". :)

Sadly neither version works here with an older clang on OS X. Both variants build fine with 9 warnings each. But the old variant dies with a "Bus Error: 10", and the new variant with "Segmentation fault: 11". Same with gcc (albeit only 8 warnings.)

/edit

OK, just wrong user input. You gotta feed it a number, and not a "foobar" or another random string.

MaskRay 16 hours ago [-]
Amazing! I read you article in 2012 when the link was https://homepages.cwi.nl/~tromp/maze.html I was learning Haskell and Ocaml and wrote my own article in Chinese then https://maskray.me/blog/2012-11-02-perfect-maze-generation

Now I should fix the link.

nickevante 16 hours ago [-]
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.

bricks96 46 minutes ago [-]
Here's a Google Sheets Maze Generator that's pure formula and no script. This post has got me thinking how I might format the formula to be shaped like a maze. https://tinyurl.com/SheetsMazeGenerator
bonsai_spool 17 hours ago [-]
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
dang 16 hours ago [-]
kamens 15 hours ago [-]
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
kamens 15 hours ago [-]
The main difference between the above tool and most custom shaped maze generators out there is breaking the assumption that the maze's outer shape must be defined by adding or removing regularly-shaped cells along the edge.

To have mazes look more human drawn, cells need to be irregular and the inner walls need naturally follow the contours of the outer shape.

ogogmad 2 hours ago [-]
Have you considered finding a conformal transformation† that maps a square to any other possible shape, as long as the shape doesn't have any holes? Such a transformation always exists by the Riemann Mapping Theorem, and is unique as long as you specify in addition (1.) which point the square's centre maps to, and (2.) the angle of rotation around that point. Not sure if anyone's ever tried that.

If you actually want more aesthetic freedom, you can compose with an arbitrary diffeomorphism of the square to itself. But I think that might usually look worse.

† - That is, preserving all angles, including right angles. The terminology stems from the output angles conforming (???) to the input angles.

jcynix 14 hours ago [-]
You show an impressive variation of mazes, cool!
jtolmar 14 hours ago [-]
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).

snorbleck 9 hours ago [-]
Awesome resource. I recently (in the past week) created a maze game. I used Claude (sonnet 4.5) for the most part, but some things, like images, were created with ChatGPT. I may do a blog about it if anyone is interested in the inner-workings and my thought process from concept to vibecoded. I am by no means a game dev, was just curious about what it would take to create unique single solution mazes with some game-like components thrown in, and trying it with the assistance of AI. It turned out somewhat retro. Now go get lost!

https://lorelabyrinth.entropicsystems.net/weekly

PacificSpecific 5 hours ago [-]
Hey thanks for sharing. I gave it a try but ran into some issues.

Is this intended to be able to be used on a phone? I saw the instructions about guiding a yellow ball but what I experienced was about 10 seconds of chiptune music with a maze that had some icons I couldn't interact with.

After the 10 seconds a series of green spheres and vertical lines washed across the screen but I wasn't able to control them.

I'm using the duck duck go browser on Android if that helps.

dang 16 hours ago [-]
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?

indigoabstract 14 hours ago [-]
I especially like this one:

https://news.ycombinator.com/item?id=45549017

Wilson’s Algorithm gives the most pleasing visual results for me.

dang 14 hours ago [-]
Added above - thanks!
y42 15 hours ago [-]
of course! :D (how to approach the development of a maze algorithm)

https://news.ycombinator.com/item?id=23131983

dang 14 hours ago [-]
That's not a good link for a list of past threads since the idea for the latter is to include only the ones with interesting comments.

However, it looks like a good article that could use a repost! Just not soon, since we want to give enough time for the hivemind caches to clear :) - if you want to repost it in (say) a month or two, email us at hn@ycombinator.com and we'll put it in the SCP (https://news.ycombinator.com/item?id=26998308).

89netraM 12 hours ago [-]
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.
racecar789 8 hours ago [-]
Pretty good! It would be nice to have a little icon showing at the preferred ending location.
89netraM 2 hours ago [-]
Thanks! Yeah, you're right, the point is to get to the center, and it's a lot easier to know where that is on my original "Polar" maze https://xn--sberg-lra.net/maze/polar?size=5&entryCount=1 I should update them to have a goal icon like you say, maybe antoher time.
dfajgljsldkjag 17 hours ago [-]
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.
amelius 11 hours ago [-]
The main insight in many of these algorithms is that if you have a tree, there's exactly one path between any two leaves (assuming you don't pass over a branch twice). So if you just draw a random tree-like structure and make the entry and exit points of the maze leaves in the tree, then you have a valid maze with exactly one solution.
richard_chase 15 hours ago [-]
This is the kind of stuff I come here for.
OscarCunningham 16 hours ago [-]
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.
1313ed01 16 hours ago [-]
There is another old site ("since September 23, 1996"), my second favorite maze site, that has some articles about things like that. Like on the page below ("Tips on how to create difficult and fun Mazes, and how to solve and analyze them").

https://www.astrolog.org/labyrnth/psych.htm

I think there is a difference if you want to make it only expensive to solve using popular maze solver algorithms, vs to make it difficult for a human to solve. Many of the recommendations on that page are for how to do things that can make a maze more difficult for humans to solve, but will not always matter to an algorithm that just mechanically tries solutions in some order.

jaberjaber23 16 hours ago [-]
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
ginko 16 hours ago [-]
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.
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