This research focuses on proposing a foundational list for designing metal pergola structures by applying the concept of generative design. This approach is based on the principle of repetition with fractal geometry, employing a recursive function system to create metal pergola structures. This research avoids the use of Euclidean geometric shapes—squares, triangles, circles, etc.—which have resulted in flat, inconsistent works. Instead, the use of fractal geometry is considered closer to the process of shape and transformation in nature. The concept and method of designing with fractal ideas is a design process implemented through experimental thinking, producing quality works. This new method is designed to address these limitations by providing improved control over the properties of fractals, including symmetry, scaling, and self-similarity. These are based on new concepts of self-similarity and infinite complexity, which are capable of understanding nature and its infinite scales. Unlike standard methods, it incorporates adaptive iteration and symmetry-preserving transformations, enabling the creation of complex patterns with consistent structural properties. This allows for the strategic design of typical configurations of these regular structures to provide sufficient strength and stability for the structures to withstand vertical, horizontal, and wind loads, resulting in lighter structures. This method also improves computational efficiency by reducing duplicate calculations and achieving faster convergence with fewer iterations. The research adopts a theoretical approach, delving into the fundamental theories related to fractal geometry, and uses an Iterated Function System (IFS) based on the concept of fractal geometry. To demonstrate the intersection of mathematics and design in both modern and traditional design process practices, the details of the design unit networks in the context of applying the concept of fractal geometry in the field of construction aim to activate a geometric system in design that is typically characterized by recursive self-similarity properties. A rule-based geometric system can be constructed using the recursive function system process, and based on fractal construction methods and algorithms for their visualization and practical applications, they achieve a high degree of visual and geometric balance, which makes them appropriate for high-precision applications. The design elements are formatted to obtain the best solution to the fundamental concepts of design problems.
Fractal Geometry, Repetition, Steel Pergola Structures, Iterative Function Systems (IFS)
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