An interpretation of "2D" and "3D" games

Super Smash Bros is and always has been a 2D game.

Have I lost you yet? How about this:

Tekken is a 1D game.

Let's go to math class here, probably around the Algebra and Geometry level. What sort of coordinate system do you need to display a two-variable equation, or just shape that is 2D? You need a two-coordinate plane, of course: the X coordinate and the Y coordinate, your standard Cartesian grid. Left-right and up-down, or west-east and north-south if you prefer. If you plot a point into an X-Y system, it can move in those two directions: up-down and left-right. This is what, for instance, Super Mario Bros 1 had. Mario could run to the right, or to the negative-right; and he could jump up, and he could fall negative-up. That's a 2D game, because there are two dimensions of action.

We live in a 3D world, right? Walk outside with me. Houses to the left, right, front, and behind. Sky or tree branches above and presumably copious amounts of coal, iron, and diamonds underground. But is this world really 3D? Can you, as a point-in-space the shape of a person, go directly into the sky? Can you simply drop underground? Not without tools and vehicles, no, meaning the world is just as flat (not in that way) for a human who doesn't have a jetpack or rappelling gear as Mario's world was before the N64. Mario can't walk toward the TV screen or into the background just as much as we can't just float up or descend through the topsoil. The only difference is where Mario's two dimensions are left-right and up-down, ours are more like forward-backward and left-right. Even if you climb the stairs to a new level of a building, is that really any different from walking through a doorway? It's truly no different from in a top-down Zelda game taking the stairs into a new 2D room. The place you're in and your interactions in it are still flat, you can move to the front wall and the back wall, and the left wall and the right wall. Not any closer to the ceiling or floor. You have only two dimensions, and this new floor may as well be to the horizontal side of the previous room with weird doors between them.

This is a different world for birds and squirrels and fish and squids, because they're all playing a different game than us. Birds do have a useful vertical dimension, because they can fly. Squirrels can climb up and down trees as easily as they run north-south and west-east, and fish and squids might not even care where the floor or ceiling of the ocean is, because they do have all those dimensions: Left-right, forward-backward, ascend-descend. A 3D world, with three directions of travels, three useful coordinates to their position..

So let's go back to Super Smash Bros here. In those games, everyone is 3D. They can spin around in a circle so you can see the bottoms of their shoes and their armpits and stuff using the "camera angle", they stand on floors and stages that have length, width, and height; three spatial dimensions. I'm not arguing that, but their mobility is strictly 2D. Just like Mario of the 1980s, they can only move left-right and up-down, two dimensions. The picture is 3D, but the accessible actionable world is 2D. It could be turned into a visually flat game like Super Mario Bros and literally nothing about the gameplay would change. You could play it on a sheet of grid-paper, because the third visible dimension does nothing.

That other thing I said, about Tekken (and Mortal Kombat, and most traditional arcade-style fighting games) being 1D? You could argue that it's 3D. You could. After all, the view of the stage can rotate with dodges, and you can jump and crouch, all that 3D-like stuff. But how much mobility in that world do you really have? You can move left and right. That's one dimension. The rotating of your position in the arena may as well be replaced with a message of "you can be hit out of the arena by an opponent at this time" and nothing would functionally change. For crouching and jumping, those could be replaced by a feature of being immune to attacks of certain high or low elevation strike and a shifting of your moveset. Kind of like how Super Smash bros could be played on a 2D grid, you could play Tekken on a number line. Your one coordinate (your one dimension) either adding or subtracting as you move right or left with the caveat of a status effect "crouched" or "jumped" replacing what would be the second interactive dimension entirely.

This is all just an idea that's been bouncing in my head sometimes over the past. I welcome criticism, counter-arguments, or anything. I mostly wanted to get this idea onto paper to free up some RAM in my brain, and maybe give you something to think about if you wanted it.

I guess we could also go into time dimensions with retrying after failure or loading old saves, and hypothesize about a 0 spatial dimensional game... but I feel like I've bored you criminally already.

 

@BZRich64 I'm going to have to argue against 2.5D, or at least naming it that way. Now, I've never played DKCR specifically, but are you talking about, for instance, item barrels or activation levers that are off the "track" of the primary 2D plane? Like floating a few inches, feet, or hypothetically even miles away?

I'm going to just proceed as if that is the case, or rather change to talking about something similar in ordinary Kirby games, since I'm more familiar there (but feel free to link me to screenshots or video if I'm misunderstanding your example). We can talk about doors, for instance, being in the background. Kirby can walk right past them, and it's implied that they're usually a few Kirbys away in the distance. So logically, Kirby has to walk a few steps away from the TV screen's front to enter them, but in practice it makes no difference. Kirby can still just walk right and negative-right, jump up and fall negative-up. Through the door isn't really negative-front, it's something else in the 2D plane that can be activated.

If interaction with background and foreground objects count as an additional half dimension, then how about (in top 5 platformers ever in my book) Super Mario Bros 3? Level 1-1 (and maybe a few others), you're able to crouch on a particular platform and sort of fall behind a lot of set pieces. Behind bushes and blocks, Mario's sprite is halfway or entirely covered by those obstacles, and even behind enemies, untouchable by them. He interacts with the solid ground and nothing else in the ordinary 2D plane, but that sounds like a stretch to call it 3D or even 2.5D.

And probably related to DKCR, I wonder if it's like Kirby 64 Crystal Shards in one particular way? It's a side-scroller in a 3D world, it looks a lot like Super Smash Bros if you're unfamiliar - but wait, there's more! The track that you walk is not a straight line, it curves and bends etc. One early stage the track will lead you on a path along the front of a castle, then take a gentle 90 degree turn into the castle. Inside that building, you'll follow a spiral path gradually ascending a turret tower, and you can see upcoming enemies on the opposite side of the spiral (kind of like the penultimate boss fight in Milky Way Wishes for the SNES). It has a better claim to 3D than Smash does, tbh. But even though the path curves and bends and sometimes even overlaps itself... it's still on a track, and there's still only two dimensions of coordinate change: up and down, and left (along the path) and right (along the path). Several bosses have their stages set as a circular path with the boss in the middle, so visually the boss is to kirby's right or left off the path, but the attacks sent at you from that middle may as well be non-hitbox hints that turn into hitbox attacks when they reach your circular track. But throughout all of this, Kirby is bound to a left and right mobility, and objects in the "background" may as well be sprites in 2D that have no hitbox until they appear to move forward. That extra dimension exists in visual only.

Yet another thing, I would suggest that 3D rendering of graphics doesn't matter at all. A 3D game made with entirely 2D graphics? How about Castle Crashers? It's mostly 2D, in that the stages are 100 side-to-side long and 5 meters foreground-to-background, but you can move freely to the left and right, you can go toward and away from the game's screen to fully dodge obstacles, and you can jump several times your height and stay airborne for several tactical seconds at a time. Three dimensions of full mobility and interaction, just bounded in a long rectangle instead of a squarish world/level.

Detaching from that and circling back to the original examples, I said what I (firmly) think of as 1D and 2D fighting games, but never mentioned a 3D fighter. I can think of one, which really brings the example together: Final Fantasy Dissidia (not including Opera Omnia). If anyone doesn't feel like looking up a gameplay video, it's a lot like Kingdom Hearts. Fully open arena world, you can run forward and backwards and left and right and you can jump high and levitate as you like (to a high ceiling). You can move in fully any direction and attacks can come from fully any direction. So compare the directions you need to worry about your opponents attacking you from in those games: In Tekken your opponent can attack (pretty much) only from the right or left, the directions on a number line. In Smash your opponent can attack from left, right, above, or below; the directions on a Cartesian X-Y grid. In Dissidia you can be attacked from left, right, above, below, behind, in front; all the directions in a 3D volume space. That mobility, those dimensions of interaction are what I think should be used to label how many D a game has.