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Fractal Based Grid Shell 

This research applies the notion of fractal geometry and fractal dimension as a venture for designing an irregular form of a grid-shell. The main intention of this research is to exploit the geometric dimensionality of a smooth shape, here a paraboloid shape, and change its geometric dimension from its integer value to a non-integer value using the Midpoint Displacement Method (MDM), and accordingly, transform its smooth surface to an unsmooth surface that is known as Takagi-Landsberg’s fractal surface. A parametric model of the Takagi-Landsberg’s fractal surface has been computationally generated using a mathematical fucntion and Iterated Function System (IFS) for designing the grid-shell structure. A textural factor which is known as the ''relative size value'' (w) of the Midpoint Displacement Method plays the key role in changing the geometric dimension, more specificaly, the fractal dimension of the model, thus changing the final outcome of the surface. A finite element analysis has been performed to verify the structural viability and capacity of this fractal-based grid-shell structure. It also analyzes the changing structural behavior of the grid-shell structure with the changing of relative size value (w), or subsequently, the changing of the fractal dimension. A physical prototype has been constructed in a design workshop ensuring its practical constructability and strength.

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Based on this geometric venture of exploiting a regular geometric shape into a fractal shape, we intended to apply this shape morphology for structural form design as a gridshell structure, and see how it mechanically reacts and changes structural behavior with the changing of ‘w’ value.

However, after finite element analyses process, as a structural feasibility check, we had decided to make its real scale physical prototype by taking ‘w’ value as 0.5. ‘FracShell’ was a design team which devoted their times to fabricate the structure by facing some critical challenges. However, in the end, we were able to complete the job, and see the physical realization of a mathematical entity as an innovative structural form in architecture.

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