Does anyone happen to know which of those algorithms are equivalent, under the following definition of equivalent?

• Maze generation algorithms A and B are equivalent if for any maze that A can generate, it is possible for B to generate that maze too, and vice versa.

For those pairs of algorithms that are equivalent, what pairs are equivalent under this stronger definition?

• Maze generation algorithms A and B are equivalent if for any maze that A generates, B can generate it too, and vice versa, and the probability that A generates that maze on any given run is the same as the probability that B does so.

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

Jamis Buck's Mazes for Programmers is a really fun book to work through. Helped me break out of some doldrums when web development really got me down.

It lets you bias the maze to make interesting designs at least: https://jsbin.com/betediceyu/edit?html,output (you might have to click "Run with JS" to make it work properly)

Eller's algorithm can be tweaked in real time and this can be useful. Nintendo MG-61 game and watch seems to be based on this algorithm.

Ellers algorithm is quite efficient though not the most beautiful to watch being created. Thanks for the links. I like the Prim’s and binary tree algorithms. The recursive division is quite interesting as well, the paterns it generates are peculiar.

The Aldous-Broder algorithm would be my choice. The large one on the page is still going strong! Amazing perseverance.

Yeah, the mazes Eller’s algorithm makes are often simplistic. Recursive backtracking give you nice, long mazes.