(Originally written by Mike Anderson. Please note that this guide only contains the essential parts about the algorithm, nothing else from his guide)
In this algorithm a "feature" is taken to mean any kind of map component e.g. large room, small room, corridor, circular arena, vault etc.
1. Fill the whole map with solid earth
2. Dig out a single room in the centre of the map
3. Pick a wall of any room
4. Decide upon a new feature to build
5. See if there is room to add the new feature through the chosen wall
6. If yes, continue. If no, go back to step 3
7. Add the feature through the chosen wall
8. Go back to step 3, until the dungeon is complete
9. Add the up and down staircases at random points in map
10. Finally, sprinkle some monsters and items liberally over dungeon
Step 1 and 2 are easy once you've got the map set up. I have found it very useful to write a "fillRect" command that fills a rectangular map area with a specified tile type.
Step 3 is trickier. You can't pick random squares to add new features because the rule is to always add to the existing dungeon. This makes the connections look good, and also guarantees that every square is reachable. The way Tyrant does it is to pick random squares on the map until it finds a wall square adjacent (horizontally or vertically) to a clear square. This is a good method, since it gives you a roughly even chance of picking any particular wall square.
Step 4 isn't too hard - I just use a random switch statement to determine which of a range of features to build. You can change the whole look of the map by weighting the probabilities of different features. Well-ordered dungeons will have lots of regular rooms and long straight corridors. Cave complexes will tend to have jagged caverns, twisting passages etc.
Step 5 is more tricky, and the key to the whole algorithm. For each feature, you need to know the area of the map that it will occupy. Then you need to scan outwards from the chosen wall to see if this area intersects any features that are already there. Tyrant does this in a fairly simplistic way - it just works out the rectangular space that the new feature will occupy plus a square on each side for walls, then checks to see if the entire rectangle is currently filled with solid earth.
Step 6 decides whether or not to add the feature. If the area under consideration contains anything other than solid earth already, then the routine loops back to step 3. Note that *most* new features will be rejected in this way. This isn't a problem, as the processing time is negligible. Tyrant tries to add 300 or so features to each dungeon, but usually only 40 or so make it past this stage.
Step 7 draws the new feature once you've decided the area is OK. In this stage, you can also add any interesting room features, such as inhabitants, traps, secret doors and treasure.
Step 8 just loops back to build more rooms. The exact number of times that you want to do this will depend on map size and various other factors.
Step 9 is pretty self-explanatory. Easiest way to do it is to write a routine that picks random squares until it finds an empty one where the staircases can be added.
Step 10 just creates a host of extra random monsters in random locations to add some spice. Tyrant creates about most of the monsters at this point of the map generation, although it does add a few special creatures when individual rooms are generated.