For a Proportion Principle-based Gameplay Design

Key insights

7 takeaways

01
The paper proposes using the Golden Mean (Phi) as a structural design principle for videogame gameplay, an area it describes as largely unexplored, and positions it alongside established frameworks such as the MDA model, Fullerton's Playcentric Approach, and Björk and Holopainen's design patterns.
02
The central contribution is a method for structuring game elements through proportion so that levels and challenges grow in a controlled way, producing dynamic adaptation with potential relevance to procedural content generation and adaptive play.
03
It specifically proposes Dynamic Symmetry and the Whirling Spiral from Hambidge's work to govern how levels and challenges scale, targeting mission- or stage-based platformers and casual games, drawing on Dormans' Mission/Space model and Smith and colleagues' rhythm-based and 2D platformer models.
04
Two variants are outlined: an adaptive model in which level geography and challenge scale with player performance, and a predefined model in which the game space expands proportionally across stages.
05
The author argues that games' properties (emergence, progression, procedurality, challenge, and engagement) make them suitable for proportional principles, and that measurable or quantifiable components are the main candidates for proportional structuring.
06
The argument rests on observations of Phi in natural structures (DNA models, crystals, planetary arrangements) and in classical art and architecture (the Parthenon, Da Vinci, Raphael), and cites researchers claiming efficient energy distribution in plants, though the paper acknowledges many philosophical accounts of Phi are speculative.
07
The work is conceptual rather than empirical, offering no playtesting data or implementation results, and it explicitly invites further research on how proportional structures affect players.

Summary

This paper argues that the Golden Mean, the mathematical proportion associated with the number Phi, can serve as a structural design principle for videogame gameplay, an area it describes as largely unexplored. It positions this proposal alongside established game design frameworks such as the MDA model, Fullerton's Playcentric Approach, and Björk and Holopainen's design patterns, suggesting that the Golden Ratio offers a distinct, long-established perspective from which to build game systems. The author grounds the idea in the observation that Phi appears across natural structures, from DNA models and crystal formations to planetary arrangements, and in classical art and architecture, including the Parthenon and works by Da Vinci and Raphael.

The paper draws on the work of researchers who attribute practical functions to this proportion, such as efficient energy distribution in plants, while acknowledging that many philosophical accounts of Phi are speculative. The author contends that the properties of games, including emergence, progression, procedurality, challenge, and engagement, make them a suitable domain for applying proportional principles. Videogame components that can be measured or quantified are identified as candidates for proportional structuring, with a specific proposal to use Dynamic Symmetry and the Whirling Spiral from Hambidge's work to govern how levels and challenges grow.

The proposed application is aimed primarily at mission- or stage-based platformers and casual games, drawing on level analysis frameworks such as Dormans' Mission/Space model and the rhythm-based and 2D platformer models of Smith and colleagues. Two variants are outlined: an adaptive model in which level geography and challenge scale with player performance, and a predefined model in which the game space expands proportionally across stages. The paper's central contribution is a method for structuring game elements through proportion to produce dynamic adaptation, with potential relevance to procedural content generation and adaptive play. The work is conceptual rather than empirical, offering no playtesting data or implementation results, and it invites further research on the effects of such proportional structures on players.