Research on Dimension Analysis of Spectative Buildings Based on Fractal Theory

Based 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.