Game Design Snacks Wikia
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Since ancient times, people and institutions have studied and utilized the Golden Ratio in their work. Either consciously or subconsciously, the usage and recurrence of the mathematical constant 1.618 and the proportion of thirds in nature, architecture, and biology is significant. We can find use of Golden ratio in game designs as well.

This ratio creates an interesting asymmetrical balance, and is often used as a compositional device. In this guise, the Golden Ratio can be extensively seen in game interface design, camera positioning, and environment layout. This is used to create good aesthetics and design of games. Being a social creature, we are used to existence of golden ratio around us. Games use this to create realism and also provide a familiar way for the gamers to interact with. Consider a building, the height and width of building is maintained in golden ratio to provide player a similar view as he would find in real life.

Examples:

Gears of War 2

Gears of War 2 is a 2008 military science fiction third-person shooter video game developed by Epic Games and published by Microsoft Game Studios for the Xbox 360. it was observed in this game that the camera position is maintained in such a way as it forms golden ratio for its height with viewport. Also many of the building in the game followed golden ratio.

Gears goldenratio

guided by the Golden Ratio, the player's eye and Marcus' path are channeled between the two buildings, with the main action area staying in the bottom third of the screen.

( source : GAMASUTRA, An Artist's Eye: Applying Art Techniques to Game Design)

Example 2:

The other game in which we see the golden ratio camera positioning is "Splinter cell". Splinter cell is a series of games the first game is released in 2002 and developed by Ubisoft. The gameplay of this game is to hide out and chose the routes.

Splintercell ratio
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