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A fractal hexagon dome. central section
Source publication
Authors described a fractal lattice dome generated by seven contraction mapings in 3D space onto an original one. This paper reveals mathematical condition that the seven small domes as subsets generated by contraction mapping never overlap to keep one to one function (Barnsley, M. F [1]). The useful formula to calculate Hausdorff dimension is also...
Citations
... Recently, some structures based on the form or phenomena in nature have been proposed (Rian and Sassone [1], Kishimoto and Natori [2]). For example, the authors have shown a fractal arch using the process of growth of tree that has self-similarity (MAE and ASAYAMA [3], [4]). And they have shown the mechanical properties of the arch against for the wind pressure distribution through the wind tunnel experiments (MAE, ASAYAMA and KAWAI [5]). ...
Structures and geometry are closely associated; forms and forces are correlated in structures. With the advancement of geometric systems throughout the centuries, structures got new shapes, thus pushing the boundaries of architectural designs. Geometric advancement also contributed to making structures more efficient than before. Fractal geometry is one of the latest geometric systems systematically studied in the 1970s that opened a new avenue for systematically designing lightweight and sustainable structures. The self-similar repetition quality of fractal geometry is a source of making visually complex and structurally effective shapes. This paper has overviewed and summarized the structural potentials of fractal geometry and its applications in structural forms design in some existing structures and recent research works. It also provides insight into the constructional challenges of fractal-shaped complex structures and finds solutions through the recent development of automation in construction, such as digital fabrications and automated assemblies. Finally, in conclusion, the future prospect of fractal’s potential contribution to efficient structural designs has been further briefed.
