Figure 1: Batwing tile formation. Complied by author. Figure 2. Batwing. Complied by author.
T
riply Periodic Minimal Surfaces, often referred to as minimal surfaces, are three-dimensional modular forms that derive from complex mathematical equations. Just as the circle and its area derive from a specific equation; minimal surfaces also derive from studies of more complex equations. The importance of minimal surfaces lies in their natural qualities to obtain the maximum amount of space through the most minimal amount of surface area. One of the simplest ways to approach the formation of minimal surfaces is to think about the natural formation of soap films. For instance, if we were to “dip a metal wire-closed curve into a soap solution, when we pull out, a soap film forms. A nature solves a mathematical question of finding a surface of the least surface area for a given boundary. Among all possible surfaces soap films find one with the least amount of surface area”(Kostic, D., Stankovic, M., Radivojevic, G., Velimirovic, L, 2008, p. 89). Of course, there is a strong mathematical background behind the natural behavior of soap films that relates to surface formation of minimal surfaces. The pragmatic mathematics behind minimal surface formation establishes the credibility for mathematicians and engineers to practice their real-life applications. Thus, “minimal surfaces are extremely stable as physical objects, and this can be an advantage in many kinds of structures. From architects point of view, computerized illustrations of some minimal surfaces are intrigued by the possibility of adapting them to structures, both interior and exterior” (Kostic, D., Stankovic, M., Radivojevic, G., Velimirovic, L, 2008, p. 90). There are many minimal surface forms ranging from different “families” and types. The particular focus of this exploration will be solely examining, mathematician Alan Schoen’s, “Batwing minimal surface” as a prime example. One of the natural wonders of these forms is that they begin in the form of standardized tiles. As shown in Figure 1, the fundamental Batwing unit can be derived by a set of simple geometrical pragmatic steps. These steps include the simple creation of cones and planes from lines and parameters within the cube. The manipulations of such tiles also lead to
38 | Urban action 2012