Wieringa Surface: The Implementation of Aperiodicity into Architectural Acoustics
Published in Springer Nature - Communications in Computer and Information Science, 2022
Description:
At the intersection of order and disorder exists a balance that is referred to as aperiodicity. This mathematical concept is exemplified by the famous Penrose tiling methods, which display local five-fold symmetries that quickly dissipate globally. Architectural designers have previously exploited this property through floors tiling’s, sculptures, and building facades. However, like mathematicians in the latter half of the 20th century such as Nicolaas Govert de Bruijn and R.M.A. Wieringa, designers in the early 21st century are now looking to the third dimension. In acoustics, surfaces with complex sectional profiles have been demonstrated to have scattering properties where the relationship between depth and width of undulations relate to the amount and frequency of the sound scattered. Mathematical sequences have been demonstrated to have optimal sound scattering properties, however, these mathematical sequences are periodic, and can therefore create unwanted acoustic effects. This research proposes combining the concept of aperiodicity with the predictability of a mathematical formula and defined through a parametric model, where the acoustic performance of these aperiodic surfaces will be analyzed through simulations. The contributions of this research are two-fold: first, we have developed a novel approach to creating a 3D object using parametric modeling to generate a Wieringa Surface, which when orthographically projected to 2D creates a Penrose Tiling; and second, we have carried out preliminary simulations that suggests there is a potential for this complex mathematical surface to exhibit sound scattering properties without periodic effects. This paper documents the parametrization of a specific case of the “Cut and Project Method”, a mathematical method by which a slice of a multi-dimensional periodic space is selected through a cutting window and then projected to a lower dimension to produce aperiodic forms.
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Funding: National Science and Engineering Research Council (NSERC)
Collaborators: Ross Cocks, Brady peters
Recommended citation: R. Cocks, J. Nguyen, and B. Peters, “Wieringa Surface: The Implementation of Aperiodicity into Architectural Acoustics,” in Computer-Aided Architectural Design. INTERCONNECTIONS: Co-computing Beyond Boundaries, Cham: Springer Nature Switzerland, pp. 190–203. doi: 10.1007/978-3-031-37189-9_13.