How Far Can Symmetry Create Coherence in Architecture? A Quantitative Analysis of the Impact of Sub-symmetries on Coherence in Architectural Façade
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Abstract
Despite recognizing coherence as a primary goal in architectural design, and the increasing acknowledgment that overall symmetry is not always the optimal solution for achieving it, the role of sub-symmetries and how they contribute to overall coherence remains underexplored, particularly from a quantitative and analytical perspective. Our research posits that the sub-symmetries across multi-levels of change in scale is related to coherence. Accordingly, we aim to quantitatively investigate the relationship between the number and distribution of sub-symmetries across the multi-scaling ratio (r) in architectural façades and the concept of coherence (C), considering the latter as an objective dependent, and measurable property. The study is based on the hypothesis that the distribution of sub-symmetries across different scales is not random, but rather follows a specific mathematical structure that can be measured and directly linked to the overall coherence of the façade. To achieve this, a quantitative methodology was applied to analyze several samples of architectural façades including calculating the total cumulative number of sub-symmetries in relevance to the scaling ratio. At first, the relationship between the scaling ratio and the number of cumulative sub-symmetries was examined. Then, the relationship between the total number of sub-symmetries and the level of coherence was measured using the proposed coherence index (CI). The results revealed a clear inverse relationship between the scaling ratio and the cumulative number of sub-symmetries, where the number increases as the scale decreases. More importantly, the study demonstrated a strong and direct relationship between the total number of sub-symmetries and the level of architectural coherence, suggesting that increasing the density of sub-symmetries significantly enhances coherence. The research concludes that architectural coherence is not merely an abstract concept, but a measurable property that depends heavily on the density and organization of sub-symmetries. These findings provide a quantitative basis to understand how precise structural organization, through sub-symmetries, contributes to achieving higher levels of coherence in architectural design and suggests the potential for developing analytical and design tools to enhance this property.
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