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This research aims to explore the scope of applying the concept of fractal geometry in the field of architecture and construction. There are mainly two different types of fractals – self-similar fractal and random fractal. In this research, both types of fractals are used to design a nature-inspired architectural structure with the strategy of exploring the potency of fractal geometry as a geometric framework that can offer new structural forms. Based on themathematical formulations of self-similar fractal shape and randomfractal shape, tree-inspired branching supports and natural terrain inspired unsmooth crinkled roof are modeled using the algorithms of Iterated Function System and Midpoint Displacement (Diamond Square Algorithm) method respectively. Fractal dimensions are calculated to assess the visual complexity of the roof surface and branching supports. Finite element analysis is performed to assess the structural strength of the model with respect to changing of fractal dimensions.

This research shows how the concept of fractal geometry can be applied in the design of architectural structures. The iterative generation of geometry and the influence that self-similarity can have on the structural behavior are explored starting from the discussion of some relevant aspects of fractal geometry. The transition from regular and derivable surfaces to fractal surfaces is studied through the computational construction and the analysis of the Takagi-Landsberg surface. A parametric model of the Takagi-Landsberg’s fractal surface has been generated for designing a grid-shell structure as a benchmark. The relative size value, a factor of fractal dimension, plays a key role in changing the fractal dimension of the parametric model, thus changing the resulting texture of the surface. Grid-shells are shape-sensitive structures and any geometric changes can impact on their structural behavior. This research shows a particular interest to see the changing of structural behavior of a grid-shell when its smooth paraboloid shape is transformed into an unsmooth fractal shape, and to verify the structural viability of the fractal-based grid-shell structure using the finite element analysis method. After the results that confirm the structural feasibility of such a fractal-based structure, a physical prototype has been constructed in a design workshop which ensures its practical constructability.

The purpose of this study is to apply the notion of fractal geometry in designing structural roof trusses. Fractal geometry, commonly characterized by the features of recursive self-similarity, is considered as a rule-based geometric system that can be generated by using the process of the Iterated Function System (IFS). Lattice configurations of conventional trusses generally show some extend of ‘self-similarity’ features that loosely and sometimes closely resemble with the properties of fractal shapes. The typical configurations of these regular trusses are strategically designed to provide adequate strength and stability to the structures for carrying enough vertical and wind loads. This paper, using the Iterated Function System based on Barnsely's contraction mapping as a generative design method, proposes a new family of truss designs that follow the concept of fractal geometry. The Hausdorff dimensions and the Box Counting dimensions are evaluated to measure the fractality and detailness of the lattices of proposed fractal-based trusses. It also briefly investigates their mechanical properties for analyzing their practical feasibility in construction.

#### FracTree: Fractal Based Branching Canopy

Tree, nature's one of the common examples of self-similar fractals, has been used in designing branching supports even before the development of the concept of fractal geometry. Gaudi was one of those forefront architects who understood the mechanical advantage of self-similar branching forms of trees as a structural support to carry a wide canopy, thus providing a large free space underside. Later, in the mid 20th century, Frei Otto, used the same principle but by sophisticating the form of tree-structure experimenting with some hanging models. In the late 20th century, a list of branching structures were designed by intentional application of fractal geometry idea, such as in the Stuttgart Airport Terminal in Stuttgart. Intentional application of fractal geometry allows architects to computationally design a parametric model of branching structure whose shape can be changeable by controlling the design variables, such as branching angles, branching numbers and scaling factors. This computational model of fractal-based tree is helpful for the shape optimization process too. In this digitally experimental research, a branching structure has been designed to support a wide-span roof so that we can obtain a large-span indoor space. In this experiment, the structural efficiency of such structures will be analyzed, and then a computational search will be performed to find an optimal form of the structure.

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A poplar plywood company financed WoodLab for designing a pavilion to exhibit and promote their architectural, sculptural and furniture products. It was a heavy creative exercise to come up with a unique but sensible design idea. Finally, an interesting design concept came to mind and took shape as ‘why don’t an architectural piece can be a manifestation of a story of poplar tree itself’? Poplar grows from its seed, and then gradually it becomes young plant and finally turns into a perennial woody tree. Poplar trees altogether live in a family making a forest, and finally they are used for making plywood needed for building construction, furniture, and so on. This whole story had to be turned into a shape, a design, a pavilion.

The feature of self-similar repetition is not a new concept even in the field of construction. In the language of civil engineering, this type of configuration is called as hierarchical configuration, and the structures having this configuration are called hierarchical structures. Many of the lattice structures, such as trusses, are the examples of hierarchical structures. The fundamental reason for adopting hierarchical arrangement of members and their sub-members in a structure is to achieve high strength but light weight. In this context, with reference to the design of the Eiffel tower, Benoit Mandelbrot claimed in his book The Fractal Geometry of Nature,

"My claim is that (well before Koch, Peano, and Sierpinski), the tower that Gustave Eiffel built in Paris deliberately incorporates the idea of a fractal curve full of branch points. . . . However, the A's and the tower are not made up of solid beams, but of colossal trusses. A truss is a rigid assemblage of interconnected submembers, which one cannot deform without deforming at least one submember. Trusses can be made enormously lighter than cylindrical beams of identical strength. And Eiel knew that trusses whose 'members' are themselves subtrusses are even lighter."