Explanation of Fractal Geometry Laws in the Structural Form of Architecture; Presentation of a Form-Based Architecture Model

Document Type : Research Article


1 Ph.D. Student, Department of Architecture, UAE Branch, Islamic Azad University, Dubai, United Arab Emirates.

2 Professor, Department of Architecture, Science and Research Branch, Islamic Azad University, Tehran, Iran.

3 Assistant Professor, Department of Architecture, Central Branch, Islamic Azad University, Tehran, Iran.


Problem statement: From the perspective of modern sciences, fractal knowledge is a study of self-similar and self-organized structures that are the conceptual core of understanding nature’s geometry. From a mathematical viewpoint, nature follows fractal rules to create different forms. In this rationale, a direct interaction between architecture and fractals can be proposed.
Research objective: This research, by posing questions about how fractal geometry is applied, explains the geometric laws of nature in the process of self-organizing in form-based architecture.
Research method: This applied research employs the method of correlation in applying geometries according to fractal properties conducting a qualitative, phenomenological view. In this study, seven stages are explained in fractal geometry as a form-based structure. These stages in form-finding, the hierarchy of connections, and geometric progressions provide a credible process in the application of fractal geometry to architecture. In addition, an architecture inspired by principles of nature’s geometry is based on three laws and functions in structure as described by the research: the law of self-similarity, the law of self-organization, and the law of unity. To validate these laws, three buildings are selected from the Gothic, Art Nouveau, and traditional Persian architecture periods, according to fractal properties. Fractal rules are analyzed in the evaluation of these structures using a comparative-descriptive model.
Conclusion: Based on the results, it can be concluded that fractal geometry has been incorporated into the structure, elements composition, and aesthetic concepts of ornamentation in the architecture of these edifices. Inspired by nature’s geometry, laws of proportions, rhythm, and self-similar forms, these architectural structures have created a wide range of fractal patterns, generating internal connections and external unification among the structural elements and architectural forms.


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