A better starting point for automatic generation of perfect mazes would be [this](http://www.mazeworks.com/mazegen/mazetut/index.htm).
Thanks for sharing this resource! Years ago, I wrote a maze game that used an unnecessarily complex algorithm (I didn't have a clue, really). The depth-first search is elegant. I'll finally be able to add mazes to my board game maker software.
I had to smile, Mitch! I also wrote a maze game once, and also had to design my own maze-generation algorithm. Mine is similar to what I saw at the site Seo posted, but not identical. In mine, the first pass only creates the "true path" from the entrance to the exit. A second pass then fills in the forks and dead ends. I found that to get really good mazes, I had to tune it a bit: if the true path wanders and curves too much, it fills the space leaving room for few false paths, making the maze too easy to solve. But if it doesn't wander enough, the solution is too short and obvious. I got the best results by having the true path favor going straight rather than turning a corner.
What else does your program offer? It sounds interesting!
Ah, the joys of reinventing the wheel. My maze game started with a grid of solid blocks, which my algorithm randomly blasted to dust. Then, it picked two random edge blocks, blasted them and tried to make a path.
Finally, my little monster was dropped into the maze and tasked with finding its way out.
I wrote this, not as a game, per se, but as a way to experiment with AI. I created what I thought was a pretty clever Darwinian engine for the monster, who always started out dumb as dirt, bumping into walls. Eventually, it collected enough sense to "see" the walls and go in the direction of an opening. It had no recollection of revisiting, though, so it was always pure luck when it got out. :)
My prototyping program generates grid-based boards, which can contain several layers, such as images, text, fill colors and fill patterns. It can generated different cell sizes and can draw circles or boxes with or without connectors and with or without gaps. Cells can be turned off, creating many different effects, such as a maze :)
If you check out Haulin' Assets, my August GDS entry, you'll see a board that I created and then fleshed out in Photoshop.
(The skeleton is the track, the flesh is the stylized graphics. Sometimes it's easier to import graphics into Photoshop so that you have more control than you do with the prototyping tool.)
I'm going to upload it to my website either today or tomorrow.
Cheers,
Mitch
In the light of the math of it all, while math may not be necessary in game design or art or music. Mathematics are vary beautiful. It is the launguage to describe reality and life, not the creator of it, the language. In a great musical composition, we hear math in our ears and it creates order and harmony in our brain. In great art we see it without being aware of it. Same in games, subonsciously the math sings in beautiful mechanics.