Examining the mathematical basis for human similarity assessments of architecture: an analysis comparing survey data and fractal dimensions

The capacity to differentiate basic levels of aesthetic similarity is a foundational premise in architectural psychology. To assess the ability of mathematical measures to explain human perceptions of building similarity, this research analyses the results of a comparative study that correlates human data (n = 147 participants) with visual complexity data for buildings (n = 204 facades). The human data is derived from a survey, and the mathematical data comprises fractal dimension (D) measurements of three variations of each facade (n = 612 D results) – the overall massing (‘silhouette’), the distribution of detail (‘primary forms’), and a simple three-dimensional representation (‘shadowed forms’). Three hypotheses are framed around these theorized relationships for testing using statistical analysis (correlation analysis, linear regression) of survey and measured data. The results indicate that mathematical measures of formal complexity developed using fractal dimensions are not a significant factor in perceptions of visual similarity.