Tessellation in Architecture

The seminar will seek to produce a graphic manual for the use of tessellation in architecture. We will examine architectural projects, with the aim to identify how tessellation has produced consistency across multiple and differentiated functional elements of a building. The seminar will aim to distinguish the uses of tessellation versus modulated geometries, and will therefore examine an extended list of projects involving both systems. Particular focus will be placed upon the use of geometric and repetitive forms in Islamic architecture and the use of allometric systems of ordering part to whole in Gothic architecture. The history of constructing part-to-whole relationships can be framed in two opposing directions: universal systems that tried to construct an abstract or ideal order to regulate the entirety of built form or modular systems that established rules for the flexible proliferation or combination of basic units. Universal systems of part-to-whole include the use of geometric systems of proportion in Western classical architecture, the use of perspective in the Renaissance, and the use of regulating and ordering systems connected to modes of production in Modernism. Modular systems of relating part-to-whole include Islamic architecture\'s use of geometrical and repetitive forms, Dutch Structuralist attempts to aggregate standard functional \”units\”, and Robert Le Ricolais and Louis Kahn\'s investigations of integrated three-dimensional modular organizations.Neither the universal, nor the modular part-to-whole systems are able to exploit diversity as a contemporary architectural material as they are systems that repeat entities through an internal process, detached from the specific domains within which they would operate. In order to exploit differentiation as an architectural material, we need to look for systems of correspondence between parts and wholes that allow different entities to emerge in contact with specific domains. This capability to proliferate forms that vary according to their circumstances of use is best represented historically by Gothic architecture, based on an abstract protogeometry that, when applied to varying plan organizations, acquired specific form in each case while maintaining a consistent topological relationship between part and whole. Tessellation in architecture is an example of a part-to-whole system that can become locally specific. Tessellation is a geometric system that is able to create specific organizations/patterns through repetition of a simple set of parts against a boundary (whole). Early attempts at tessellation in Islamic architecture were periodic, based on the filling of space with regular polygons. Such attempts can now evolve into a-periodic and non-recursive part-to-whole relationships, which are still based on simple and limited parts and can vary according to domains. As such tessellation is an ideal tool for producing species, as opposed to types, that can not vary across time and space. This possibility in tessellation – to organize flexible, complex part-to-whole relationships that can become domain-specific, as well as rationalized into regular geometric panels – is precisely what makes tessellation an effective tool today, as it produces systems of relationships that are at once tied to the cultural as well as the technical domain. Tessellations can be categorized in terms of their behavior or in terms of their method of application. Whereas applications tend to fall into two basic categories of two-dimensional applications, or three-dimensional application, behaviors of different tessellation systems are more varied and include repetition or periodicity, axiality, regularity, symmetry, connectivity, self-similarity, or multi-scalarity. A taxonomy of different tessellations and their behaviors (related to part-to-whole) can allow us to select tessellations specific to the needs of archi