Athanassios Economou

• Ph.D. Architecture
• Professor at Georgia Institute of Technology

A workshop in formal composition using machine-based specifications of parametric shape rules is presented. The workshop is structured along two different trajectories: one starting from existing grammars and one starting from scratch, and both in a rising complexity in the specification of the rules and the ways they affect design. Rules, producti...

A brief survey of the expressive power of Shape Machine, a new shape grammar interpreter, is presented. The work is presented in two parts: A brief presentation of a series of shape computations that have been routinely used as benchmarks for the design tasks a shape grammar interpreter should be able to accomplish; and a brief exploration of desig...

Shape grammar interpreters have been studied for more than forty years addressing several areas of design research including architectural, engineering, and product design. At the core of all these implementations, the operationof embedding – the ability of a shape grammar interpreter to search for subshapes in a geometry model even if they are not...

As a ubiquitous paper folding art, origami has promising applications in science and engineering. Many software and parameterized methods have been proposed to draw, analyze and design origami patterns. Here we focus on the shape grammar formalism and the Shape Machine, a shape grammar interpreter that has managed to automate the seamless shape cal...

Shape queries based on shape embedding under a given Euclidean, affine, or linear transformation are absent from current CAD systems. The only systems that have attempted to implement shape embedding are the shape grammar interpreters albeit with promising but inconclusive results. The work here identifies all possible 14 cases of shape embedding w...

The recent success of a class of mechanical applications of shape rules in CAD shape grammar interpreters has produced a renewed interest in the design and support of shape embedding and shape rewrite technologies. Despite this, some fundamental constructions in rule-based modeling, namely, any of Euclid's straightedge and compass constructions, ap...

The process of shape embedding, that is, the inquiry whether for two shapes u and w there is a transformation f that embeds the shape f(u) in w is the most critical – and elusive – process for all shape grammar interpreters implemented within CAD systems. This paper identifies three major challenges underlying the implementation of shape embedding...

Generative design is emerging as an important approach for design exploration and design analysis in architectural practice. At the interior design scale although many approaches exist, they do not meet many requirements for implementing generative design in practice. These requirements include the need for end-user accessible tools and skills, rap...

Three computer implementations of one of the earliest and most iconic shape grammars are given to showcase different ways to use shape rules in Shape Machine. These three modes of working with shape rules-manual, automatic and conditional-are used interchangeably to produce three skeuomorphic variations of the original checkerboard lattice grammar...

Shape grammar interpreters have been studied for more than forty years addressing several areas of design research including architectural, engineering, and product design. At the core of all these implementations, the operation of embedding—the ability of a shape grammar interpreter to search for subshapes in a geometry model even if they are not...

This special issue of AIEDAM aims to present cutting edge, state-of-the-art research in design computing and cognition from DCC'20, the Ninth International Conference on Design Computing & Cognition (http://dccconferences.org/dcc20/). Design is a fundamentally important topic in disciplines ranging from the more commonly associated fields of engin...

Some of the data in the main article text are not consistent with the data in Tables 2–4 in the article and they have been corrected as follows.

This paper aims to better understand how building density and shape jointly influence building energy performance in downtown urban environments. Three research questions are addressed: (1) How does the building density influence energy performance? (2) Given the same density, how do different building cover ratios create different impacts on energ...

Current planning and design decision support systems show limitations in the integration of design, science, and computation. Planning support systems with manual design and post-design evaluations impose major challenges in exploring huge design spaces. Generative design systems largely neglect the wicked nature of design problems and lack appropr...

A generative description of Mies van der Rohe’s courthouse design language is presented in the form of a three-dimensional parametric shape grammar and its significance in the discourse of courthouse building type is discussed.

The shape grammar formalism has offered a visual, rule-based framework for interpreting architectural languages for over forty years. However, the ability to implement grammars within a technology that allows for direct engagement with shape rules and productions so that they can be dynamically simulated, shared, understood, modified, and brought i...

Two formal exercises in hotel composition are presented. In both, the hospitality work of the architect John Portman is the focus. His language of hollow forms is addressed following his unique claim on the organizing principles found in his 1964 house, Entelechy I. The first exercise outlines a generative specification for his atrium hotel languag...

The asymptotic relation between the three Vitruvian prerequisites of design (firmness, utility, and delight) and the six principles of design (order, arrangement, eurythmy, symmetry, propriety and economy) has been one of the most striking and unresolved characteristics of the foundations of architectural theory from Vitruvius’ text onwards. The co...

This paper introduces the special issue “Advances in Implemented Shape Grammars: Solutions and Applications” and frames the topic of computer implementations of shape grammars, both with a theoretical and an applied focus. This special issue focuses on the current state of the art regarding computer implementations of shape grammars and brings a di...

The shape grammar formalism has been discussed theoretically extensively. Recently there has been increased activity in implementing shape grammar interpreters, yet there is a lack of implementations that support parametric rules and emergence. Here the structure of a general parametric shape grammar interpreter is discussed in detail. The interpre...

A workshop in formal composition using machine-based specifications of parametric shape rules is presented. The workshop is structured along two different trajectories: one starting from existing grammars and one starting from scratch, and both in a rising complexity in the specification of the rules and the ways they affect design. Rules, producti...

Despite his controversial political background, the leading architect of the Italian Rationalist Movement, Giuseppe Terragni, has attracted the attention of a large group of architectural scholars. He has often been acknowledged as an enigmatic architect whose work oscillated between classicism and modernism. This work takes on two of the most embl...

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 th...

AI EDAM Special Issue, November 2017, Vol. 31, No. 4 - Volume 30 Issue 4 - Sara Eloy, Pieter Pauwels, Athanassios Economou

AI EDAM Special Issue, November 2017, Vol. 31, No. 4 - Volume 30 Issue 3 - Sara Eloy, Pieter Pauwels, Athanassios Economou

John Portman's work attracts much interest, although little scholarship exists that directly engages his contribution in formal composition. Most of the discussion of Portman's architecture tends to focus on his commercial work and hotels, although a key to understanding his work is found in his personal domestic projects where he has had the freed...

A generative description of Mies van der Rohe's courthouse language is presented in the form of a shape grammar. The grounding of the work is based on a set of 135 sketches produced by the office of Mies during the design process of the Everett McKinley Dirksen United States Courthouse in Chicago, and documented in the Mies van der Rohe Archive at...

This paper aims to better understand the impact of urban context on building energy consumption. The factors of external shading, shapes generated from zoning ordinances, and local climate are examined concerning three main questions: (1) how density influences building energy consumption generally, (2) how a given density generates alternative bui...

An approach to automating the rule selection process of shape grammars is introduced. A shape grammar interpreter is extended by a computational framework to allow the rule selection to be executed by agents. Hereby each agent is based on a different paradigm taken from the field of artificial intelligence. The results are compared.

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 postulat...

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

The rule editor of a parametric shape grammar interpreter is presented. The problems that arise are discussed along with their solutions.

The notion of a generative description of architectural typology is discussed. Two different approaches are identified and contrasted in terms of their expressive power in design. The building type of the courthouse is selected to showcase and test the approach. Two case studies are briefly presented to pictorially illustrate the findings.

The sieve is a powerful formal tool developed by Xenakis to create integer-sequence generators that can be used for the generation of various numerical patterns to represent pitch scales, rhythm sequences, as well as patterns of loudness, density, timber and so forth. Sieves produce a series of patterns that rise from the simplest ones possible to...

A graph grammar for the generation of topologies for the U.S. federal courthouse typology is introduced. Possible configurations are enumerated and a nomenclature is proposed.

An implementation of a shape grammar interpreter is described. The underlying graph-theoretic framework is briefly discussed to show how alternative representations from graph theory including graphs, overcomplete graphs and hyperedge graphs can support some of the intuitions handled in shape grammars by direct visual computations with shapes. The...

The design machine, an algorithmic structure for design (Stiny and March, 1981) is considered within current trajectories of architecture discourse to suggest a generous cast of contemporary architectural design strategies and to produce eight systematic studies in formal composition in architectural design.

Presented on February 24, 2011 from 11:00 am to 12:00 noon in the Georgia Tech Architecture Library. Runtime: 61:29 minutes Dr. Athanassios Economou is Associate Professor in the College of Architecture at the Georgia Institute of Technology. Dr. Economou's teaching and research are in the areas of shape grammars, parametric design, computer aided...

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,...

An implementation of the Palladian grammar using a graph grammar and a graph to shape mapping is presented. The application is embedded in a parametric CAD environment and allows the exploration of Palladian villas by hand or by using a random generator.

A computational approach for the automated graph representation and diagrammatic notation of all underlying symmetry structures of three-dimensional shapes with a center of symmetry is briefly presented and some applications with shape grammars to illustrate these ideas are discussed in the end.

A graph grammar for the generation of topologies for the U.S. federal courthouse typology is introduced. Possible configurations are enumerated and a nomenclature is proposed.

The notion of congruence in formal composition is briefly examined and it contextualized within current architecture discourse. A computational tool is presented in the end to illustrate alternative usages of congruence in analysis and synthesis in spatial design.

This work proposes the use of partial order lattices along with represent-ational 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...

A computational approach for the generation of all underlying structures of three-dimensional shapes with an n-fold symmetry axis is briefly discussed and an automated environment for the complete generation of all partial lattices of three-dimensional shapes with an n-fold symmetry axis is presented in the end.

The design machine, an algorithmic structure for design, is considered within current trajectories of architecture discourse to suggest a reinterpretation of the Vitruvian discourse and to produce eight systematic studies in formal composition in architectural design.

A computational approach for the generation of all underlying structures of three-dimensional shapes with an n-fold symmetry axis is briefly discussed and an automated environment for the complete generation of all partial lattices of three-dimensional shapes with an n-fold symmetry axis is presented in the end.

A computational approach for the generation of all partial lattices of two-dimensional shapes with an n-fold symmetry axis is presented and an application in formal analysis in architectural design is presented in the end.

A group theoretical decomposition of one of the major canons of architectural production in the twentieth century, the Smith House by Richard Meier. This paper briefly traces the history and logic of the abstracted formal vocabulary of the early white Meier houses and focuses on the Smith House as the generator of the language. The formal theory fo...

A computational approach for the generation of all partial lattices of two-dimensional shapes with an n-fold symmetry axis is presented and an application in formal analysis in architectural design is presented in the end.

Comparing space allocation programs computationally is a resource intensive task. This paper introduces a method which reduces the complexity of floor plan graphs to facilitate the problem. In a first step the nodes are labeled according to a laid out classification scheme. This in its own right reduces the complexity of the comparison by introduci...

The relevance of music theory as an interpretive framework for the understanding of Palladio’s work has been one of the most debated subjects in the realm of architectural theory and criticism. Typically the debate is quite abstract and it focuses on possible mappings between the ratios found in Palladio’s plans and corresponding ratios used in con...

A model of correlation of arithmetical ratios in models of space, models of sound and models of light is presented. A computational environment is designed to allow an interactive movement of a virtual agent within the rooms of a given arrangement of spaces using either the body movement or the eye movement of the agent as the basic trigger of soun...

Hermann Weyl, one of the greatest mathematicians of the 20th century, in his famous lectures on symmetry in 1951, attempted to set up a formal framework for a theory of space pursued earlier by Leibniz, Newton and Helmholtz. The key idea in his method of describing the structure of space is the notion of congruence as a specific mapping that does no...

A computational tool for proportional analysis and synthesis in architectural composition is presented. The various components of the software are briefly explained and two case studies, one in analysis and one in synthesis of form are presented. Both studies presented here are drawn from Palladio’s second book of architecture

Shape grammars applications have been developed with great success in various fields including architectural design, landscape architecture, engineering design, painting, furniture design, ornamental design, and others. Despite the remarkable success of these applications in so many different and diverse fields, shape grammars haven’t yet manage to...

The structure of the direct product group C2C2C2 is examined in detail. The foundations of the group structure in Pythagorean arithmetic are briefly presented, the realization of the group in three-dimensional space is discussed and illustrated, and some notes are suggested for its implication in music notation. A special emphasis is given in four...

A constructive program for the generation of three-dimensional languages of designs based on nested group structures is outlined.

The foundations of a contrapuntal composition with shapes are considered. Rules in counterpoint in music composition are briefly presented and correlated with rules in formal composition with shapes in architectural design. In this context, spatial canons and fugues are defined as specific spatial studies generated by spatial relations and shape ru...

A systematic inquiry into some of the geometric possibilities inherent in Frederick Froebel's kindergarten method. A series of studies pertaining to counting, coloring and computing issues is proposed. The Froebel building gifts are used as samples for this approach. The symmetry groups and subgroups of these building blocks are identified and thei...

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

The structure of the dodecagon is postulated as a model for the structure and the symmetry properties of the equal temperament scale. The cycle index of the permutation group of the vertices of the dodecagon is used in Polya's theory of counting configurations non-equivalent with respect to a given permutation group; the numbers of structurally dif...

The relevance of music theory as an interpretive framework for the understanding of Palladio's work has been one of the most debated subjects in the realm of architectural theory and criticism. Typically the debate is quite abstract and it focuses on possible mappings between the ratios found in Palladio's plans and corresponding ratios used in con...