Athanassios Economou

From topologies to shapes: parametric shape grammars implemented by graphs

A method for implementing parametric shape grammars is presented. Subgraph detection is used to find subshapes. Parametric shapes are described by restricting topologies.

The symmetry lessons from Froebel building gifts

The symmetry properties of the Froebel building gifts are discussed in detail. A special emphasis is given to the cycle indices of their permutation groups. They are used in the enumeration of n ≤ 3 colour assignments on the faces of the building blocks.

Entelechy revisited: On the generative specification of John Portman’s architectural language

John Portman’s work attracts significant commentary, although the focus is typically on the commercial and social aspects of his work as opposed to the actual designs and their related architectural implications. The obvious place to start unpacking his contribution is in his widely recognized and published commercial portfolio, yet he maintains that his design principles are found in his personal domestic work. Here, his 1964 residence Entelechy I is analyzed to inform the development of a parametric shape grammar that generates the original design as well as a series of variations. The goal of this research is to engage Portman’s architectural philosophy and constructively assess his claims of its implicit relationship to his work to date. Key rules suggesting his principles and anticipating his ongoing architectural contribution are outlined. The structure provided by shape computation, involving both shape rules and rule schemas, is positioned as the theoretical basis for an ongoing study of transformations within Portman’s language.

From Shape Rules to Rule Schemata and Back

Shape rules and rule schemata are compared in terms of their expressive and productive features in design inquiry. Two kinds of formal processes are discussed to facilitate the comparison. The first proceeds from shape rule instances and infers rule schemata that the shape rules can be defined in. The second proceeds from rule schemata and postulates shape rule instances that can be defined within the schemata. These two parallel processes mirror our intuition in design: the conceptual need to frame explicit actions within general frameworks of principles, and the productive need to supply general principles with an explicit system of actions.

Surface Symmetries: The Smith House Revisited

This work proposes the use of partial order lattices along with representational schemes to account for patterns of ambiguity and emergence in the description of designs. The complexity of such designs is viewed as an aggregation of spatial layers that can all be decomposed by the subgroup relations of the symmetry of the configuration. At the end, this methodology points to a combinatorial approach that generates visual prototypes for future use in design synthesis. Here, Meiers work is just a case study that validates the group theoretical approach.