Fractal complexity in visual nature: Perceptual preferences of leaf silhouettes and implications for biophilic design

Biophilic design posits that incorporating natural materials and patterns can improve feelings of restoration and well-being in built environments. Nature includes many patterns, such as fractals, which are highly prevalent and characterized by self-similar components that repeat across varying scales. Including fractals in human-made environments might influence perceptual experiences. Nature’s fractals typically vary in complexity (measured using fractal dimension, D) from 1.1 to 1.9. Previous studies have shown consistent preferences for these patterns, as well as differences in how their complexity is perceived.

Our study tested human perception of fractal patterns, focusing on leaf silhouette fractals with d-values ranging from 1.1 to 1.5. We surveyed 235 participants using 60 forced-choice tasks, comparing 12 distinct leaf silhouettes across six judgment types: complexity, natural, excitement, interest, appeal, and relaxation. Leaf shapes were selected to represent varying levels of fractal complexity, categorized into low (1.1), moderately-low (1.2–1.3), and moderate (1.4–1.5) d-values. Our results demonstrated that preferences differed by judgment type: moderate d-value leaves were preferred for excitement, interest, natural, and appeal, while leaves with moderately-low d-values (especially around 1.3) were favored for relaxation. More complex leaves (higher d-values) were perceived as stimulating, whereas simpler leaves (lower d-values) were found to be more relaxing. Additionally, species-specific trends emerged, with leaves from the Platanus orientalis and Aesculus hippocastanum species ranking highly for excitement and interest, while Gingko biloba leaves were highly favored for relaxation.

This study represents the first fractal-based investigation into human preferences for recognizable natural shapes, specifically leaf silhouettes, and supports the preference of perceived moderate complexity within the Fractal Fluency Model. These findings suggest that fractal complexity plays a role in how humans perceive and engage with leaf shapes. This research has potential applications in biophilic design and urban planning, particularly in enhancing human-environment interactions in urban landscapes. Additional research into specific judgment types and the role of branching and tree structures could further optimize biophilic design strategies to foster well-being in natural and urban spaces.