JARDJournal of Architectural Research and Development2208-35292208-3537Bio-Byword Scientific Publishing Pty. Ltd.10.26689/jard.v9i4.11532ArticleResearch on Dimension Analysis of Spectative Buildings Based on Fractal Theoryhttps://artdesignp.com/journal/JARD/9/4/10.26689/jard.v9i4.11532ZhengYunyang,ZhuJiayao,GuoJingjing,HuHao2025942025-08-07Based on the fractal theory, this paper takes the form of performing architecture as the research object, and systematically discusses the application value of fractal dimension in architectural design. By expounding the self-affine, self-similarity, and iterative generation characteristics of fractal geometry, the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane, facade, and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre. The research shows that the geometric complexity of Wuzhen Grand Theater in the “fifth façade” and multi-faceted façade is significantly higher than that of Harbin Grand Theater, and its morphological design is more inclined to echo the texture of the surrounding water towns. The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines. The research proves that fractal dimension can effectively quantify the complexity of architectural form, provide a scientific basis for the form design, environmental integration, and form interpretation of performance architecture, and expand the mathematical analysis dimension of architectural form design.

Mao Z, Mao Y, He J, 2016, Research and Prospect of Fractal Architecture Abroad. Architect, 2016(4): 13–20.

Huang L, 2020, Research on the Application of Fractal Geometry Theory in Architectural Disciplines in China. Scenic Spots, 2020(7): 0326–0327.

Pu X, Zhang Y, 2019, Application of Fractal Theory in Morphological Analysis of Architecture from the Perspective of Complex Phenomena. New Architecture, 2019(5): 86–91.

Wang J, Men Z, Dong D, 2024, Construction and Thinking on the Externalization Design of Performing Building Space. Zhonghua Architecture, 42(08): 78–82.

Malan, Zhang H, Guo Z, 2019, The Visual Complexity of Architectural Geometry Is Measured by Fractal Dimension. Journal of Computer Aided Design and Graphics, 31(10): 1809–1816.

Lin X, Wu Y, 2004, Fractal Aesthetics – A New Aesthetics Beyond Traditional Formal Beauty. New Architecture, 2004(3): 70–71.

Mong Y, 2017, Research on Architectural Design Based on Fractal Theory. China Construction Industry Press, China.

Liu X, 2023, Study on the Spatial Morphological Characteristics of Traditional Villages in Mianyang City Based on Fractal Theory, thesis, Southwest University of Science and Technology.

Li Y, 2020, Research on the Fractal Dimension Algorithm and Its Evolution of Historical Buildings. Shanxi Architecture, 46(03): 36–38.

Zhang H, Zhang K, Guo X, 2024, Research on the Protection and Renewal of Military Fortress Villages in Yuxian County, Zhangjiakou City – Taking Baihoupu Village as an Example. Urban Architecture, 21(05): 120–123.