DIMENSIONALITY
Dimensionality is a term used to describe a number of aspects of games: the aspect ratio of a game’s imagery; the simulation of depth in two-dimensional images; the simplicity or complexity of a game’s narrative; and the decision space a player occupies during their play experience. Each of these forms of dimensionality enriches the play experience of games writ large, and video games in particular.
Game Aspect Ratio
Though it may seem like a subtle point, the aspect ratio of a game is a form of dimensionality in video games. Here, dimensionality refers to the aspect ratio of the play space, which is typically expressed as a ratio of width to height: 4:3, 5:4, 3:2, 16:9, etc. The aspect ratios of video games are almost always tied to those of the displays on which they are viewed and, to a lesser degree, their platforms. During the era of cathode-ray-tube-based screens, for example, most video games adhered to the 4:3 ratio of the screens on which games were played (or 3:4, in the case of the many arcade games that turned the screen sideways). As television and monitor screens transitioned to high definition, the typical console and PC video game shifted toward a 16:9 ratio to match the prevailing televisions and monitors.
4:3
Most early video games were designed to fit within the 4:3 aspect ratio, which is often referred to as “square” even though it is technically rectangular. This is because the viewing effect of these screens is perceived as square. Part of what drove development of 4:3 video games earlier in the game industry were graphics computing technologies. Pixel resolutions of early graphics cards were almost all expressed in 4:3 ratios: QVGA (320 × 240), VGA (640 × 480), SVGA (800 × 600), etc.
4:3 video games have a play space that echoes the televised images people were already used to watching, and so provides an image format players were already familiar with. Early arcade games such as PONG (Atari, 1972) used actual televisions as their displays, and golden-era games such as Pac-Man (Namco, 1980) and Asteroids (Atari, 1979) used similar display hardware.
A variation on the 4:3 aspect ratio, wherein the display was turned on its side (resulting in a 3:4 ratio), is found in many arcade games. Space Invaders (Taito, 1978) and Galaga (Midway, 1981) were both 3:4 aspect ratio games that turned the cathode-ray display on its side in order to have a vertically-oriented screen. For both games, the top-to-bottom movement of the aliens was better accommodated by the 3:4 aspect ratio. Mike Tyson’s Punch-Out! (Nintendo, 1984) is an interesting mix of 3:4 and 4:3. The game used two different screens. The primary screen on which the player focused was 3:4, while a secondary 4:3 screen included statistical information on the two boxers’ performance and the time remaining in the round.
16:9
More recently, console and PC games have begun to use the 16:9 aspect ratio of highdefinition television. This wider aspect ratio brought about the need to produce games with higher pixel resolutions. The two most common resolutions in the 16:9 format are 1,280 × 720 and 1,920 × 1,080. The 16:9 ratio is closer to the 2.39:1 and 1.85:1 aspect ratios of film. Games such as Halo 4 (343 Industries, 2012) and Bioshock Infinite (Irrational Games, 2013) are designed with the wider screen format, which better creates a cinematic visual experience.
Alternative Aspect Ratios
Not all games adhere to these standard screen resolutions. For example, early games such as Tennis for Two (William Higginbotham, 1958) and Spacewar! (Steve Russell, Martin Graetz, Dan Edwards, Alan Kotik, Peter Samson et al., 1962) were designed for round screens, giving them an aspect ratio of 1:1. And games such as Passage (Jason Rohrer, 2007) and Gravitation (Jason Rohrer, 2008) both use unexpected aspect ratios: Passage has an aspect ratio of 25:4, while Gravitation has a 1:1 aspect ratio. The majority of games with alternative aspect ratios tend to be designed for PC, Mac, and browser-based play. Windowing a game to sit atop the desktop allows game developers the freedom to make their games whatever aspect ratio suits them, so long as it fits within typical pixel dimensions. Anna Anthropy’s dys4ia (2012), for example, uses a 4:3 aspect ratio even though it is primarily played through a web browser on devices with screens that can accommodate any aspect ratio. The shape of the game was an aesthetic choice made by Anthropy, likely as a reference to early 8-bit games.
Simulation of Depth
The simulation of depth in two-dimensional images is an idea that goes back quite far in the history of visual art. For centuries, West European artists strove to create the illusion of dimensional space; it is out of this desire that linear perspective was developed and codified by the Italian architect Filippo Brunelleschi. For screen-based games, the most noticeable form of dimensionality is that of the simulation of depth, or lack thereof, in the spaces represented on the screen. There are five kinds of simulated depth in games relevant to this essay: two-dimensional; simulated three-dimensional; “2.5-D”; 3-D that uses stereoscopic imaging techniques; and three-dimensional graphics created by twodimensional images (a more complete discussion of the subject is found in Wolf, 2008). Each of these methods not only impacts the appearance of video games, but also the ways players can engage within the play space.
Two-dimensional games are those that represent the game world along the horizontal, or x-axis, and vertical, or y-axis, to simulate a flat world. This approach to video game images has been with us since the beginning. Indeed, Tennis for Two, an early screen-based analog computer game, and Spacewar!, an early digital computer game, both represent a simulated two-dimensional space. On the one hand, Tennis for Two positions an implied camera in front of the play space, creating the appearance of a tennis game seen perpendicular to the net. Spacewar!, on the other hand, is seen from above the play space, looking down at the two spaceships as they move along a single plane in outer space.
Two-dimensionally-represented video game spaces typically position the play action along a single plane. Defender (Williams Electronics, 1980) is a classic example. All enemies, people, and environmental elements are positioned along this plane, creating a clear representation for the player to interpret and act within as their play experience unfolds.
Because all elements in a simulated two-dimensional space are on a single x–y plane, their representations are proportionately sized and positioned within the play space in order for players to perceive all elements as logically organized for their role in the game. In Super Mario Bros. (Nintendo, 1985), the top edge of the ground is used to establish the plane along which all play activity will occur. Blocks, pipes, gumbas, coins, and of course Mario, all to appear to move along the implied plane. Mountains and clouds, however, appear in a scale that makes them clearly part of the background, and not elements of concern for gameplay. To some degree, the illusion of planes moving back in depth is created through a combination of color and line. Background elements tend toward more desaturated colors and have thinner black outlines. These visual strategies, borrowed from early twentieth-century animation techniques used in films such as early Disney animation, allow the background elements to recede and draw less of the player’s attention.
Simulated Three-Dimensional Games
A similar approach is found in games where the illusion of depth is pre-rendered in background (Wolf, 2008). Mario Bros. (Nintendo, 1983) is a useful example; the pipes at the top and bottom of the screen have the appearance of z-axis depth to them, yet they are flat graphics. The illusion of depth is heightened by the seeming emergence of and exit of the enemies from the pipes.
2.5-D Games
Pseudo-three-dimensional games, also called 2.5-D games, create the illusion of threedimensional depth through the use of two-dimensional graphics. Here, there is an implied depth dimension, or the z-axis, that recedes in space in the background. This creates the sense of a deeper play space, and indicates that the play experience will take place on more than a single x–y plane.
In some cases, two-dimensional assets are created that include the illusion of dimensional space, while in others, three-dimensional graphics are used. SimCity 2000 (Maxis, 1994) is a classic example of the former, where two-dimensional assets create the illusion of depth. An isometric view gave players the advantages of a top-down view and a side view, providing a more interesting view of the objects in the space (Wolf, 2008).
The other version of 2.5-D video games occurs when the game world is produced using three-dimensional graphics, but gameplay is confined to a single-plane space as in two-dimensional games. LittleBigPlanet (Media Molecule, 2008) is a perfect example. Though the game world appears to have depth, gameplay is limited to movement first along a single plane, and later along several parallel but distinct planes of activity.
Earlier games such as Alone in the Dark (Infogrames, 1992) used two-dimensional environments on which three-dimensional characters and objects were placed. The three-dimensionally modeled and animated player-character appears to move through a dimensional space, though it is positioned atop a flat background. The player-character appears to move freely (albeit slowly) through the space until s/he encounters an object such as a table or a chest. Upon touching the object, the player-character’s movement stops. This technique produced the illusion of movement through depth.
“3-D” Games
“3-D” games are those that use stereoscopic imaging techniques that take advantage of the way human vision produces a single dimensional image from the discrete images produced by each of our eyes. The classic example of stereoscopic images is the View-Master (Sawyer’s, 1939), which uses two images of the same physical scene shot from two adjacent views that are separately viewed through binocular lenses.
Two early video game uses of stereoscopic imaging are TomyTronic 3D games (Takara Tomy Ltd., 1983) and Nintendo’s Virtual Boy system (Nintendo, 1995). On the one hand, TomyTronic 3D games such as Planet Zeon (Takara Tomy Ltd, 1983) used two LCD panels that showed slightly different angles on an outer space corridor along which rockets traveled to create the sense of real depth when the player looked through the two viewfinders. The Virtual Boy, on the other hand, used LED screens to create a similar effect in games such as Mario’s Tennis (Nintendo, 1995) in which the player sees Mario’s back as he plays a game of tennis.
Three-Dimensional Games
Compared to other types of games, the simulation of depth in three-dimensional games is more complete, tying the illusion of depth together with the simulation of free movement through the simulated space using the mathematical modeling of three-dimensional environments, characters, and objects. Game engines such as Epic’s Unreal Engine or Unity Technologies’ Unity3D allow the creation of two-dimensional game environments that represent space that recedes in space. Instead of limiting player movement to a single plane, or to a series of parallel planes, three-dimensional games allow more open play movement into the depth of the play space. Crash Bandicoot (Naughty Dog, 1996) is an early three-dimensional game that provides this open-ended play experience.
The illusion of depth and openness creates a play expectation of freedom of exploration, so the design of the environment is used to indicate where the player-character can and cannot go. The use of walls, cliffs, and sloping surfaces were developed to provide the visual language of which spaces can and cannot be explored. DOOM (id Software, 1993) uses three-dimensional models to produce a space that appears fully open and explorable. As a result, the only limitations that appear to limit player-character movement are environmental obstacles such as shut doors, ledges that drop into deep holes, and walls. More recent games such as Halo 4 (343 Industries, 2012) and Call of Duty: Black Ops 2 (Tryarch, 2012) create environments that use natural (hills, cliffs, rivers, etc.) and man-made objects to define the play space, creating a field of sorts on which the game takes place. Anything that is not impassable is assumed to be open for player exploration in these games.
Depth of Story World
The depth of a game’s story world is the third kind of dimensionality to consider in video games. Depth as a narrative concept is borrowed from film and literature, where it speaks to the amount of information available about a character or a situation the viewer or reader can use to understand and interpret what is taking place. The story world of a game can be quite simple, providing only the most basic context for the goings-on of the game, or complex and nuanced, including meaningful interactions with the game’s goals, mechanics, and progression.
The depth of a narrative is impacted by the range of information provided. This speaks to the breadth of the narrator in the case of literature, and of the cinematography and directing (and sometimes, the narration) in film. A novel such as To Kill a Mockingbird (Harper Lee, 1962), on the one hand, has limited range, as its story is told from Scout’s point of view, a young girl who does not fully grasp what is happening around her; The Lord of the Rings (J. R. R. Tolkien, 1954–1955), on the other hand, has greater range because of the narrator’s omniscient understanding of the goings-on in the story. The more range a narrative has, the greater the potential for depth.
In the context of video games, range differs from literature, and is closer to film. Games are seen rather than read (with the exception of text-based games, of course), and so the range of information is limited to what we can see, and what we can do. A game such as Asteroids (Atari, 1979) provides the player with the full range of information available given the fixed position of the “camera” on the play space. Yet the depth of information is shallow, as all we ever know about the actors—the player’s ship, the asteroids, and the two flying saucers—is embodied in their appearance and behaviors within the game. There is no additional in-game narrative context or information available to the player beyond what is on the screen during gameplay. This was supplemented by arcade cabinet art, game packaging, manuals, and other materials around, but not in, a game.
Contrasting with this is a survival horror game such as Silent Hill (Konami, 1999). The range of information provided is often narrow, as we only can know what the player-character can see within the expansive game world. Yet the game is much deeper in its development of the player-character, the environment through which the character moves and acts, and the situations the player engages. The use of steep, overhead camera angles combined with tight framing limits the player’s ability to see the environment uses limited range to build suspense. The depth of information comes through the player-character’s voiceover, the objects encountered while navigating the game world, and through the player’s abilities and power as they progress. Silent Hill therefore has a greater degree of narrative dimensionality than Asteroids.
It should be noted that not all games are intended to provide a story experience. Asteroids can be said to have more a theme—a spaceship in an asteroid belt populated by a few alien ships—than a story. Silent Hill, however, is clearly a story-driven play experience.
The last form of dimensionality relating to video games is the decision space of a game. The more complex a game’s mechanics, goals, resources, etc., and the larger the play space within which the game is contained, the more depth there is to the decision space. The decision space of a game can also be called the space of possibility, a term also popularized in Rules of Play: Game Design Fundamentals (Salen and Zimmerman, 2003, pp. 66–67). The basic idea is that a game has a designed space of possible decision points as defined by the overlap of the game’s goals, the mechanics of the game, the rules of the game, the resources available, the play environment, and, should it be a multiplayer game, the other players’ actions. There are a number of factors that influence a player’s understanding of a game’s decision space: perfect and imperfect information, progression and emergence, game goals, game mechanics, and player perceptions of available decisions.
Meaningful play is a concept originating in Salen and Zimmerman’s Rules of Play (2003, pp. 61–67) that elucidates on the quality and quantity of choices a player encounters and makes during gameplay. Qualitatively meaningful choices are those that have a real impact on the player’s experience, including their pursuit of in-game goals. Quantitatively meaningful choices are those that provide the player with multiple options for their decision. On the one hand, chess is a game with both qualitatively and quantitatively meaningful choices. Each movement of a token in a game of chess has lasting ramifications for the player’s likely success or failure in the game, while there are always numerous options during the game up until the last couple of moves in the game. Monopoly (Parker Brothers, 1934), on the other hand, has fewer qualitative and quantitatively meaningful choices as player movement is dictated by the rolling of a die, leaving only the option of buying an available property, or not.
Perfect and Imperfect Information
Perfect and imperfect information are the two kinds of information spaces that games can have. In a perfect information game, all information about the game and its state is made visible to the player. A classic non-digital example is checkers. Everything the player can know about the game is visible on the board, allowing him/her to make decisions with all available information.
Poker is a classic imperfect information system. The initial unknown information comes from the random shuffle of the deck of cards. Which cards will be dealt at any moment is not known. The second cause of imperfect information comes from the cards held by the other players, which the player cannot see. These combine to leave any given player with incomplete information for making their decisions. So a player must weigh the visible information against the unknown information as part of his/her decisions about which cards to play, when and if to bet, when to fold, etc.
Dungeons and Dragons (TSR, 1974) is a different form of imperfect information. Here, information is available through character sheets, through the dungeon master’s storytelling, and through the outcomes derived through the rolling of dice.
In video games, things are more complex, but we still have perfect and imperfect information games. For example, Space Invaders (Taito, 1978) provides the player with all most all pertinent information, but not all. The player does not know when the flying alien will pass across the top of the screen, or when the aliens in the formation will shoot.
In a game such as World of Warcraft II: Tides of Darkness (Blizzard Entertainment, 1996), the maps are known, as are the location of the gold mines. What is not immediately visible, however, is what is found in unexplored terrain, and in unoccupied terrain. Unexplored terrain is displayed as solid black on the player’s inset map. Territory that has been explored but that is not currently in the player’s primary field of vision allows the player to know the terrain as well as the presence of opponent forces. This use of “fog of war” makes World of Warcraft II an imperfect information system for the vast majority of the play experience.
Games of Progression and Games of Emergence
Knowing whether a game is one of progression or emergence also factors into a player’s decision-making. These are concepts introduced by Jesper Juul in Half-Real: Video Games between Real Rules and Fictional Worlds (2005). Games of progression are those that lead the player along a set path as they move through the game. Half-Life 2 (Valve, 2007) is a good example of a game of progression. For all intents and purposes, the player moves along a set path as they advance through the game. Though there is some agency for how players go about achieving smaller goals (such as where to hide when taking fire, how many shots to shoot, or the exact path to walk through a courtyard), the larger goals must be achieved in a particular order. Progression-driven games tend to be story-driven.
Games of emergence are those in which the player moves through the play experience in more open-ended ways. Dishonored (Arkane Studios, 2012) illustrates this type of game very well. Players can move through the decision space in a fairly open-ended way, achieving goals in the way they see fit. More importantly, the player’s actions change the way the game unfolds. Killing more non-player-characters will lead to one type of play experience, while focusing more on stealth tactics in order to progress leads to another.
Games of progression have narrower spaces of possibility due to the constraints placed upon player decision-making by the narrative progression. Games of emergence have broader spaces of possibility because the choices are more open, allowing greater player agency. The greater the space of possibility a game has, the greater dimensionality a game has. Candy Land (Milton Bradley, 1949) can be said to have a shallow decision depth because play is driven by the drawing of color cards from a randomized deck. In contrast, Go has greater depth, as players have greater agency in how they approach each decision in the game.
Affordances
Adding to a player’s understanding of what they can and cannot do inside a game is the concept of affordances. Originally conceptualized by J. J. Gibson in his essay, “The Theory of Affordances” (1977), affordances were popularized by Donald Norman in his book, The Design of Everyday Things (1988). Affordances are qualities of an object or being that suggest its or their use or abilities. So a hammer suggests its use through its appearance. The handle looks like something we would hold, while the metal ends suggest they are good for hitting things, and prying things. Affordances can further be divided into perceptible, hidden, and false categories (Gaver, 1991). A perceptible affordance is one that can be seen. A hidden affordance is one that exists, but is not visible. A false affordance is one that appears present, but is not actually a property of the object.
In video games, the appearance of an object factors into its potential use and value in the game (Pinchbeck, 2007, 2009). In video games, affordances come into play in many ways—can the player go there, pick that up, climb that wall, jump across that span, etc. Half-Life (Valve, 1998) and its crowbar is a classic example of how a video game communicates a choice to a player. Prior to encountering the crowbar, the player sees very little that they might want to pick up. When the crowbar is encountered, it is given a place of prominence to increase the likelihood the player will see it and try to interact with it. Uncharted 2: Among Thieves (Naughty Dog, 2009) provides players with clear information on what can and cannot be climbed. In most cases, climbable surfaces have brightly colored “handles” that player can see, and just importantly, perceive as within reach.
The amount and quality of information available to a player, the organization and scaffolding of the challenges a player encounters, and the player’s perception of what they can and cannot do within a game all work together to define a game’s decision space. The richer and more meaningful the decision space, the deeper a game can be.
Conclusion
These factors all contribute to what a player perceives as their choices when playing a game: what they can see, what they do, and how they make decisions to reach their goals. Dimensionality, in all its forms, is not only a consideration of both the design and development of video games, but also of the qualities and depth of players’ experiences. The aspect ratio of a game dictates the game’s shape and therefore how the game should be composed on the screen. The method for simulating depth in two-dimensional imagery impacts how a player interprets the game space, and establishes how a player will move and act within a game. The simplicity or complexity of a game’s story world impacts the degree to which a player engages narratively with a game. And the depth of a game’s decision space factors into the richness of a player’s experience.
References
Gaver, W. (1991). Technology affordances. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. New York: The Association of Computing Machinery.
Gibson, J. J. (1977). The theory of affordances. In R. Shaw and J. Bransford (Eds.), Perceiving, Acting, and Knowing: Toward an Ecological Psychology (pp. 67–82). Hillsdale, NJ: Lawrence Erlbaum.
Juul, J. (2005). Half-Real: Video Games between Real Rules and Fictional Worlds. Cambridge, MA: The MIT Press.
Norman, D. (1988). The Design of Everyday Things. New York: Basic Books.
Pinchbeck, D. (2007). Counting barrels in Quake 4: affordances and homodiegetic structures in FPS worlds. Situated Play. DiGRA 2007 Conference Proceedings.
Pinchbeck, D. (2009). An affordance based model for gameplay. Breaking new ground: innovation in games, play, practice and theory. DiGRA 2009 Conference Proceedings.
Salen, K. and Zimmerman, E. (2003). Rules of Play: Game Design Fundamentals. Cambridge, MA: The MIT Press.
Wolf, M. J. P. (2008). Z-axis development in the video game. In M. J. P. Wolf and B. Perron (Eds.), The Video Game Theory Reader 2 (pp. 151–168). New York: Routledge.