24th April 2010 (updated 25th April)
The dimensionality of gaming
I recommend two physical dimensions. Very few people have 3-dimensional displays, and one dimension just isn't enough to cut it for most games.
On flash developer websites, there are often people asking how large they should make their games. This is because many games portals have size restrictions so that the game will fit into their layout. The above was my (admittedly facetious) response to someone who accidentally asked a slightly different question. In any case, I think the dimensionality of games are interesting to consider. I discuss here how there are several almost independent concepts of game dimensions.
Some games are described as 'linear' - sometimes, but not always, disparagingly. This tends to mean that the game offers very little in the way of meaningful choice. One starts playing at the beginning, then do exactly what the designer specified, until you complete the game. That's not to say that the player is always heading in the same physical direction - rather that there is no choice about what to do to progress. The extreme opposite is a sandbox style game - a player can do many things which all develop their game in some sense, and there may be a range of satisfactory endings.
The dimensionality of gameplay is almost independent of how the game-world is drawn. Games generally considered 'two-dimensional' and 'three-dimensional' often have a one-dimensional objective. Similarly, many supposedly 3D games actually have movement in a two-dimensional plane, or even restricted to a virtually linear pathway. Interestingly, even very basic use of a horizontal plane (often in first-person perspective) is commonly described as three-dimensional, while games in vertical planes are not promoted in this manner. This mirrors our behaviour in the real world, which we ascribe to be three-dimensional, even though for the most part our movement through it is essentially in two dimensions. A large amount has been written about 2 vs 3D display, I won't consider it any further here.
Large and small-scale dimensions
Games are often divided into a series of levels - and typically, each level must be completed in turn; an apparently very linear experience. Games are commonly largely linear at the global scale because this makes efficient use of hand-crafted assets and level design. An alternative is to use procedurally generated data, enabling an enormous landscape or other branching pathway. However this is often at the cost of a certain degree of 'tightness'. Without very careful algorithm design and planning, the output can quickly feel repetitive and predictable. This makes procedural generation inappropriate for many classes of game. However, over smaller time-scales, almost all games are multi-dimensional.
Imagine a simple platformer where the objective is to reach the end (typically at the extreme right), like a level of the early Mario games. The player character can walk or run left or right, and jump or perhaps climb. The game-world is one screen tall and arbritrarily wide. In a global sense this is essentially one-dimensional, and the side-on view re-inforces this aspect. If there is only a single layer of platform at any particular x-position, then the player is very contrained in where they can be at that stage of the game.
There is of course the flexibility of waiting, moving fast or slow, jumping and/or perhaps falling from an earlier, higher platform, but these are small-scale, progression-based movements rather than decisions which affect the development of the game. One-dimensional games in this sense are not necessarily bad - I am convinced of the fun inherent in skill-based movement, and have a game very near completion which relies on this for its gameplay.
In any case, platform games tend to have a variety of immediate actions affecting motion in at least 2 dimensions, and potentially other state. Thus a game can be locally (gameplay) multi-dimensional while still telling a linear story of some kind. This is similar to some theories of space-time which suggest that there are more than 3 physical dimensions (perhaps 10 or so), but that some of them are restricted to extremely small scale, essentially being rolled up into a hypertube.
Now imagine a similar game but with more platforms at each x-position. The player may have a choice of which platform to walk on at many positions. This constitutes a decision in that the player may walk on one set of platforms or another for at least a certain distance. If the platforms are restricted to a height of one game-screen then routes must merge periodically, so this is still globally linear. Even if the height of the gameworld is increased so there are progressively branching routes, provided the objective remains the same then I would argue that this is in this sense one-dimensional gameplay. Progression is gained by moving right, regardless of the path taken. Taken to its logical extreme, this means that all games with a single goal are in some sense linear. Games with multiple alternative objectives are less linear. Sand-box games where a player chooses their own purpose are non-linear, however, these are often arguably toys rather than games.
Often games have levels which can be played out of order to some extent, or even, with some levels being skipped entirely. This is a subtle sort of non-linearity, but is commonly used to balance the game in some way - for able players to skip ahead to more challenging areas or for struggling players to route around a section they're having difficulty with or similar.
In many games the player's character(s) can be upgraded in a variety of ways. Where upgrade paths are mutually exclusive, this opens up the prospect of multi-dimensional gameplay. Temporary upgrades are equivalent to separating and rejoining routes in an overall linear pathway, while permanent upgrades can open (and close) gameplay possibilities to the player, as pathway branches.
Independent upgrades are an intermediate case. If a single acquisition is equivalent to a pathway branch, further upgrades are a merge as well as a branch, since the same state can be reached by different orders of acquisition. This means that allowing a player to acquire all upgrades is not ideal from the perspective of reducing linearity (although this should not be the only consideration).
Varied upgrades can drastically change a game's flavour, as well as modifying which physical routes are possible or desirable, so there is a synergistic effect on reducing linearity when used along with physical path branches.
Here is a summary in table form
|view||very few||games almost universally 2 or 3D display|
|local - player interaction||non-interactive media||all worthwhile games|
|global - path||appropriate for hand-crafted content||appropriate for procedurally generated content|
|character development||single series improvements||mutually exclusive or independent upgrades|
Non-linearity is often striven for in games, but it's not essential at the large scale. Try to make sure there are options open to the player from moment to moment - ideally there should be several approaches to dealing with a set of hazards, potentially with different risks and payoffs. At intermediate scales you can provide a lot of freedom of movement within individual areas and still have linearity within the game as a whole. This fits within the setting of game levels. If you don't segment your game into levels, you can add breadth along a 'corridor'. However, it's probably better not to fixate on this width; it's fine to narrow down occasionally. I recommend keeping it organic - enlarge occasionally into loose areas, add secret bonuses and so on to keep the player guessing as to the game's limits.
With permanent and granular upgrades in particular, one significant risk is that the player doesn't understand the choice until after they've made it. This is also true of physically branching pathways of course. It's only on the third playthrough (at best) that a player has all the knowledge to make an informed decision. If the game is only going to get played once, the choice is probably irrelevant. Ways of mitigating this need significant attention in the design phase if your game is long and decisions are permanent and significant. You might be able to give the player a taster of each option before they make a commitment, for example.
I would caution against giving players too much freedom - if they can do anything they want, they won't know what to do. If you do provide completely open movement on a landscape, make sure to signpost targets. Long-term goals direct the player to action.