Astrolog

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).

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.

Think Labyrinth is an amazing resource here [1]. Specifically, look for the table in the "Perfect Maze Creation Algorithms" that breaks down a bunch of different maze generation algorithms. [1] http://www.astrolog.org/labyrnth/algrithm.htm

Another good resource for maze algorithms is Walter D. Pullen's website: https://www.astrolog.org/labyrnth/algrithm.htm . The page showing his maze generations is also interesting: https://www.astrolog.org/labyrnth/maze.htm .

For those interested in the topic, see also https://weblog.jamisbuck.org/2011/2/7/maze-generation-algorithm-recap and https://www.astrolog.org/labyrnth/algrithm.htm .

Looking at the output of Eller's algorithm, I have to say that it's not the one I'd go with. Here's a visualisation of many maze algorithms: https://www.jamisbuck.org/mazes/ - the "recursive backtracker" algorithm featured at the top of the list (comes in a parallelizable variant) is the most popular answer for this StackOverflow Q&A: https://stackoverflow.com/questions/38502/whats-a-good-algorithm-to-ge… To get a sense of what are some good properties of a maze, this blog post does a pretty comprehensive and exhaustive job: http://datagenetics.com/blog/november22015/index.html Just in case we're not doing perfect 2D mazes but some variation, the following two pages cover different kinds of mazes: http://www.astrolog.org/labyrnth/algrithm.htm http://mazesforprogrammers.com/#mazes $.02

You might also find this to be of some use: https://www.astrolog.org/astrolog.htm

There's a very good star-chart program that's been around for many years, called Astrolog [0]. Although it's obviously intended for astrologers, you don't have to believe in astrology to find it useful. Maybe you just want to know whether that bright light near the moon is Venus or Jupiter, or when is the next time Mars will be easily visible. [0] http://www.astrolog.org/astrolog.htm

I actually had some fun reading about maze algorithms some time ago. Here are two good links: http://www.astrolog.org/labyrnth/algrithm.htm http://weblog.jamisbuck.org/2011/2/7/maze-generation-algorithm-recap The first link is interesting because it describes some maze toponomy (types and characteristics of mazes) The second has a lot of algorithm implementations with nice demos. Fun stuff :)

http://www.astrolog.org/labyrnth/algrithm.htm#perfect says that both the Aldous-Broder and Wilson's algorithms will generate "all possible Mazes of a given size with equal probability". But neither meets your criteria of "efficient", since neither is even guaranteed to finish. I'm curious, too, whether there is an efficient algorithm with the same property (generate any valid maze with equal probability).

> I have to say I've never really found a maze that was challenging enough to take more than a minute or so to solve. http://www.astrolog.org/labyrnth/maze/larger.gif Enjoy! Note: This is from the "Think Labyrinth!" site mentioned on the Maze Design site: http://www.astrolog.org/labyrnth/maze.htm It is also not the "largest maze" on that page by far; there are a couple of larger ones (as zip'd files), and likely those aren't the largest today. I'm pretty certain they are just meant as "art" - and not to actually challenge someone to solve them; but if you are so inclined, go for it! EDIT: I just wanted to add a bit more about the "dense maze" - the start/end is at the upper-left/lower-right of the maze; the white line is the "path" of the maze (black being the walls). Note how the image "changes" depending on the level of "zoom" - if you fit it to a smaller size, the "white" of the image will take a "cross shape", while other areas are "darker" - zoom in on those various areas, and notice how the path changes; it's a very complex construct!