Jacob’s Matrix by by Jeff Lait
“The Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. That is, the Jacobian of a function describes the orientation of a tangent plane to the function at a given point.” [1]
Hmm. Ah. Uh… Yeah. Okay I get that, maybe only because I have a bachelors degree in mathematics. But I still don’t get why rotating the dungeon might be to my advantage. But that’s alright because if you don’t try to figure out how the the developer was working graduate level math into his dungeon generation and just make sure the rooms you’re running towards go around the color wheel in the right way this is a rather enjoyable little game.
Jacob’s Matrix establishes pretty early on that it’s not like other roguelikes. There are control keys for rotation as well as setting portals, all very promising. Then as you start to go around the levels you notice that the level seems to be changing right under your feet. You’ll go around a loop and when you get to the other side the room is different than the map that you see on screen. Disorienting at first, and while it may be powered by an astonishing mathematical feat, I wrapped by head around it pretty quickly by thinking that I must have walked up a slope and that I’m above or below where I was before. The thing to do is pay attention to the colors of the walls, as they’re the biggest clue of which room you’re in and if you’re traveling in the right direction.
The way this uneven geometry is accomplished, it’s made clear, is by applying some high level mathematics to dungeon generation which also allows for the portals. However when playing it’s best just to ignore the developer’s claims at higher mathematics. This to me is a double edged sword. It’s like scarfing down Thanksgiving dinner without so much as a nod to the people who’d been up since 7 in the morning getting it ready. It’s ungrateful, but in this case it’s the only way to enjoy it.
The reason, I think, that the non-linear geometry of the game is better when ignored is that Jeff put it in a gameplay mode that is fairly linear. You have to make it from one place to another timed by the game’s soundtrack. If you don’t make it before the song ends you lose. There aren’t many dead ends or reasons to backtrack. There are a few loops complicated by the fact that the orientation of the room might have changed since you’d been it last, but if you’re only paying attention to the colors you usually won’t notice that. Consequently exploration and marveling at the mathematical feat that you are playing takes a back seat to speeding through the game and the portals and level rotation become supercilious. I appreciate what Jeff has done, I just wish he had chosen gameplay that encouraged more back and forth exploration. Even the monsters or items you run into in the way don’t give you much incentive to let them get in your way as you don’t get to keep weapons you’ve gained from one level to the next, as far as I could tell. The game should hve included finding keys, opening doors, throwing switches that open gates in far off places, anything more than just “find the yellow room.”
There are a number of messages in the game. Each level you’re greeted with a different message, tho to call them unique would be an overstatement as they all basically say “You’re in blue, find yellow.” There’s also messages when you beat a level, tho again they all basically say the same thing. There’s unique descriptions for each creature and yourself, and those are worth it.
In summary, it’s a game worth playing once and pontificating about later. I would love an explanation of the level generation from Jeff included in the game so that I could truely be impressed by what he’d accomplished here, and I’d like to see a game that employed this techinque and encouraged exploration, as well as a reason to use the portals.
RSS Comments.
March 22nd, 2009 - 6:39 am
The Jacobian is actually really helpful once you work out what it means, and it’s pretty much necessary on the later levels where the colours barely differ between neighbouring rooms.
March 22nd, 2009 - 8:07 am
I guess it was in an earlier draft that got edited down, but I had recommended that you spell out what the Jacobin means in the documentation. I know you want to keep something for the player to find out for themselves, a little riddle of sorts, but do you actually think that most people will? I’d say it’s probably better to reveal it in some way. Maybe mark is spoilers, but do something so that those who don’t have advanced mathematics degrees can be on the same footing.
I haven’t figured it out yet, but I haven’t played it long enough to, I think. Maybe it I played it a lot more.