法蘭克‧洛伊‧萊特建築之平面與立面碎形維度的關係：比較草原風格、紡織積木與美國風時期

The Relationship between the Fractal Dimension of Plans and Elevations in the Architecture of Frank Lloyd Wright: Comparing the Prairie Style, Textile Block and Usonian Periods

Fractal geometry was first used as a quantifiable method for analyzing the visual complexity of a building in the mid 1990's. Since then the method has been repeated many times - by scholars using both its manual and computational variations - to mathematically analyse architectural elevations. As a result of this practice, a large amount of comparative data describing the visual complexity of the exterior facades of famous buildings has become available. However, very little research has been undertaken into the fractal analysis of architectural plans and even less into the relationship, if any, that exists between visual complexity in plans and elevations. In order to test whether there is any pattern to the relationship between visual complexity in plans and associated elevations, this paper undertakes a comparative fractal analysis of 15 houses by Frank Lloyd Wright. Importantly, these houses are drawn from three distinct stylistic periods in Wright's work. This suggests that, if the relationship between plan and elevation is significant, then clear trends should be discernable for each period. This paper describes the standard method of fractal analysis along with its computational variation that is used to calculate the present results. A description of each of the houses is then provided, followed by the presentation of the fractal dimension results. Finally, the paper analyses these results in detail and provides a conclusion regarding the proposed relationship between the visual complexity of plans and elevations in Wright's domestic architecture. 碎形幾何學最早是在1990年代中葉被用來分析建築之視覺複雜性的一種量化分析法。爾後許多學者即重複使用各種手算及電腦計算的碎形分析法，以數學方式來分析建築的立面。此法廣泛應用於描述知名建築作品立面的視覺複雜性，結果產生大量的相關比較資料。然而，碎形分析應用在建築平面的相關研究極少，更少的是應用在探討平而與立面視覺複雜性的相關性，或這樣的相關性究竟是否存在。本文以碎形分析法比較十五件法蘭克‧洛伊‧萊特設計的獨立住宅作品，測試建築平面與其立面的視覺複雜性之間的相互關係是否有脈絡可循。重要的是，這些獨立住宅來自萊特三個不同風格的時期，意味著倘若建築平面和立宙之間真有顯著的關係，那每一個時期的作品都應體現出明顯不同的趨勢。本文除了介紹標準的碎形分析法，也說明了用來計算取得本研究結果的電腦計算法。文中分別描述每一棟住宅及其碎形維度的分析結果。最後詳細分析本研究結果，結論中嘗試提出萊特的住宅建築平面與立面視覺複雜性之間的關係。