Design by: ahylo with danielle willems
Year: 2009
Combinatorics is a system of evolutionary growth that assumes a multitude of viable formations. Combinatorics works within the specified language of its locality to build intelligence yielding a variety of outcomes. The methodology behind Combinatorics utilizes local information to propagate volumetric tiles. This genetic information is built into the code to fit specified design constraints. The result then manifests varied differences, which become neatly packed clusters of formal programmatic organizations. There are two dominant systems that represent scale shifts in the project, dealing with both the overall organization of space and intricate design incrustations.
Combinatorics draws upon the non-deterministic nature of the generative forces behind the process of urban sprawl. Through a series of feedback mechanisms it investigates the emergence of the intricate environments found in Mediterranean cities. The success and failures become part of the code in the form of statistical data driving the form to oscillate on the site. This allows for the system to evaluate which elements become incongruent and therefore deletes growth in order to reform the next topographical solution. The algorithm accomplishes this through enumerative combinatorics which sets the criteria that each module must undergo a rigorous analysis before it can reach a stable state. Discrete optimization runs natural connections through numerous probabilities to formulate the complexities of material formations.
The location of this project defines strict design parameters or information input. This code quickly aggregates the precise allowable square footage for each dwelling unit and builds in appropriate adjacency. It then retains that organizational information and distributes it throughout the sites buildable area. Substitution, orientation and distribution then become an elegant orchestration which is intrinsic to the logic of the algorithm. Locality and its constraints become an integral part of the design methodology.
“What is the most economical way to create a plane wave in an amplitude – time space (atmospheric pressure-time), encompassing all possible forms from a square wave to white noise? The foundation of their nature and therefore of their human intelligibility is temporal periodicity and the symmetry of the curves.”
Iannis Xenakis
Combinatorics is based on the A3 Ammann tiling. The A3 consists of 3 aperiodic prototiles i.e., prototiles with matching rules forcing nonperiodic tilings. Translational symmetry is not present in this system rather it is constructed through regional tiling or finite local packing. These three planar tiles are arranged in the Cartesian space to formulate a series of volumetric modules whose aim is to depart from the linear logic of space filling process. In fact the project glorifies the architectural expression of the nuances produced by exploring all the possible combinations of these volumetric manifestations. In doing so Combinatorics inhabits the edge of a contradiction: while using a rigorous and concrete geometrical process, the potential for the emergence of an architectural proposition is found in the radical subversion of its nature.
The texture of Combinatorics embodies the intricate differences between each aggregation. These incrustations of the surface, not unlike the friction ridges on fingertips, are generated from the analysis of momentary vector fields. Each module in the aggregation functions as a stem of forces whose interaction in space is indexed through a series of projective transformations: a sequence of trajectories is drawn from one stem to the next; these trajectories create oscillating waves which get captured from the ground; the ground reflects that signal back on to the modules in the form of inflected straight extrusions. The generative process of texturing Combinatorics emphasizes the collective character of the aggregation. It signifies each module with discrete properties because of its placement in a larger organism.