Chen-Gackstatter is a class of complete orientable minimal surfaces of R3 derived from Enneper's minimal surface. They are named for the mathematicians who found the first two examples in 1982. Chen-Gackstatter mesh is as well the first exercise of 2013 Parametric Architecture course, conducted by CODA members, Ramon Sastre, Enrique Soriano and Pep Tornabell. This exercise was intended to be collective, curiosity-driven, introductory but non-surprisingly, it was the last in the course to be concluded. The goal of the first introductory exercise, is to understand how physical behaviour can be interpreted, modelled, and parametrized. The routine is then to collectively produce back a physical object from a digital speculation.
During the first sessions, groups of students receiving large amount of tie-wraps and elastic rubber bands, were exploring patterns of tension aggregation. The laminar models were chosen among the chaotic cellular lattices, by their potential application as understandable minimal surfaces. Revisiting some spider laminar networks, we were triggered to explore a topologically interesting minimal surface introducing in the course, mesh complexity.
Amid minimal surfaces we looked for non zero topological genus, meaning they they had handles or “holes”, since it was searched a definable networked laminar continuity. It was decided to use a genus-two surface of Chen-Gackstatter and the generalization M1,3. This surface is an edge-less enneper-like surface, that could be stopped to a defined continuous curve boundary, and with symmetric three-fold shape with 2 handles, that satisfied arguably the needs. The continuous curved boundary was especially interesting since it was an opportunity to analyze the stiffening effect of elastic boundary in membranes, which in part is an implementation of actively-bent systems.
The surface topology was approximated by the mesh subdivision of a rotated and symmetric three-fold basic repeatable minimum mesh module. This abstract mesh, was then relaxed by dynamic relaxation method in order to approximate a physically built model. The continuous boundary had bending stiffness, whereas the inner membrane was modelled simply as a tension membrane. The coupling effect of both systems where self-stiffening and reaching an equilibrium state from which manufacturing measures were taken. By means of feasibility, the triangular mesh, of average valence 6, was used to create a less complex dual mesh, of valence 3, which could be built with metallic triangles. The mesh was patched back to the minimum assembly modules, and distributed in groups.
We knew it was ambitious and far beyond the safe margins of feasibility, but we are glad to announce that Chen-Gackstatter minimal surface is built and completed. And it has only been possible because of the absolute endeaveour of all of the students and because of a rare collective mix of wonder and trust in geometry.