Phi Divisions of the Square: a Categorization of Composition Strategies

James Mai
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 241–248 Regular Papers


Artists and architects from ancient times up to the modern period have employed proportions based on Phi, also known as the Golden Ratio, as a system of measures for compositions. While Phi-based compositions typically are employed within an overall Golden Rectangle format, Phi divisions of the square format are far less common, despite the rich compositional possibilities. This paper examines Phi divisions of the square format and a method for deriving a Phi-division pattern for compositional purposes. The author identifies first-order and second-order characteristics of the Phi-division pattern, and how those give rise to four distinct compositional strategies in his square-format painting and digital prints.