From fractal geometry to architecture: Designing a grid-shell-like structure using the Takagi–Landsberg surface

Abstract

This paper has applied the concept of fractal geometry in designing a grid-shell-like complex spatial structure. The property of the fractal dimension which characterizes the level of roughness of a shape has been particularly explored in this study for designing a complex-shaped spatial structure by taking a paraboloid as a basic shape of reference. A factor of fractal dimension which is known as the relative size value (w) plays the key role in changing the surface texture in accordance with the changing of fractal dimension. In this paper, the relative size value (w) has been specifically applied to study the texture-based shape morphogenesis of a paraboloid by using the reference of the Takagi–Landsberg’s fractal surface. This research is curious to see how this surface morphogenesis impacts on the structural behavior and unveils an opportunity to develop a new kind of form. For this purpose, we have computationally generated a parametric model of a grid-shell-like structure by making a paraboloid as a basic geometric framework and by adding an extra supporting frame in order to avoid any structural failure during the surface morphogenesis of the outer profile. A structural comparison has been done in between the grid-shell-like structure having the paraboloid-based smooth outer profile and the structure having a fractal-based unsmooth outer profile. A real-scale physical prototype of a fractal-based grid-shell-like structure has been constructed to see its architectural appearance, real-world structural behavior, practical applicability and constructability.