Topological space through surfaces, minimal surfaces-space enfolded in a Cartesian space

Minimal surface displaced, informing Cartesian space

   ARC 482 MASTER M.ARCH. II Post-Graduate Program, The Cooper Union, Professor Pablo Lorenzo-Eiroa

Structure and Instability: Simulation Laboratory

Professor Pablo Lorenzo-Eiroa 

As a laboratory, we experimented with a vectorial nine square grid structure and dealt with surface as a “ground” through analog and digital computer assisted architectural constructions and transformations. This content-oriented workshop’s intention is meant to critically construct an architecture autonomy within the virtual informational space of the computer, through specific software strategies. Alternative processes of instability, that brought about contemporary architecture canons and resulted in an expansion of the discipline, were studied to inform space by affecting the structure of this organization by enfolding these canons back as a contraction. Surface writing and parametric design as algorithms relied both on analog and digital strategies between sketches and multiple software interfaces. The exercise was presented with an animated digital simulation that reworked time-based sequential diagrams that indexed and edited its constitutional process. Students were tutored using a comprehensive +400 pages manual developed by the professor.

Two aspects of the contemporary displacement of the tectonics of the surface were part of the initial assumption in relation to the current expansion of the discipline. First, the dissembling of the object towards the expanded field condition was resolved in the thickening of the ground as an inhabitable surface. The surface became the interface by which architecture shifted the tectonics of the wall surface to the horizontal-topological, as topo-logos or the specific logic of the place. Second, as part of this process of expansion of the discipline, the surface and its digital displacement induced by the computer, and in opposition previous tectonics, is an external model that was incorporated to architecture referencing spatial warping and continuity. This model transformed the architecture envelope and its interior-exterior relationship as well as the substitution of Cartesian space for a mathematical topologically-based space, a space of bi-continuous deformation. These post-structuralist tendencies opposed typological displacements as absolute forces with topological displacements as relative forces, propelling non conceptual differentiation.

The use of the vectorial surface is understood as analogous to both of these tectonics. In order to enfold these canonical processes and confront them with more stable historical structures, the mathematical writing of this surface is understood as a strategy to inform topological displacement to Cartesian space. As originally external to the field, the mathematical parameterization of geometry of computer space, parametric surfaces, minimal surfaces were developed and reformulated inducing structural displacement and then spatial warping. Informational binary numeric control parameterization of mathematically striated computer language and, as a consequence its visual translation as an image of perspectival space, is confronted through parametric design that forces the formal disjunction between information and its visual translation but that recognizes the design product as autonomous an independent to that previous informational moment. The interface surface-matrix works as an analog program in which transformations are accumulated in a layered process distinguishing degree change from conceptual difference. This conforms a visually driven analogically produced architecture based algorithm which informs space indirectly and that resists the automatic array of non-critical solutions of the binary tree-like organizational structures of algorithms or the computer logos.


ARC482 B, The School of Architecture of The Cooper Union, Master Program (M.Arch. II)