The application of self-similarity in architectural design

Under the influence of complex theory, fractal, as a nonlinear geometry, reveals the appearance and operation law of the real world, and has the ability to accurately quantify the complexity of the system, and has been widely used in many disciplines in recent years. Especially in the field of architecture, which is closely related to geometry, fractal geometry, as a guiding form and rule system, can greatly expand the scope of architectural design and related theoretical research. Starting with self-similarity, the most essential morphological feature of fractal, through deconstruction and analysis of classical fractal geometric patterns, the three elements of fractal geometry are extracted, which are “initial graphics, generation logic and iteration times”, and applied to the generation and analysis strategies of architectural skin, space and structure. The research conclusion shows that self-similarity can be used as a generation method in the design of architectural skin, space and structure, with the advantages of simple and fast generation process and rich and diverse generation results. This construction method can break through the limitations of direct imitation of fractal patterns in previous architectural design, and enrich design diagrams from the perspective of generation strategy. It is found that the morphological mechanism, algorithmic logic, and fractal dimension in fractal geometry theory can have guiding significance for architectural design form, design thinking and design quantification. But fractal is also a science with mathematical rigor, and the combination with architectural design needs to be refined and optimized to a certain extent, to better expand the feasibility of its application in architecture.