Palladio Computatus

Possible Palladian plans based on the 210 3x5cell configurations 1-35

Possible Palladian plans based on the 210 3x5cell configurations 36-70

Possible Palladian plans based on the 210 3x5cell configurations 71-105

Possible Palladian plans based on the 210 3x5cell configurations 106-140

Possible Palladian plans based on the 210 3x5cell configurations 141-175

Possible Palladian plans based on the 210 3x5cell configurations 176-210

Athanassios Economou and Thomas Grasl
2018

Keywords: Palladio; Shape grammars; Grammar Interpreter; Formal languages

The subject matter of the study is the Palladian language and especially the language of the Palladian villas as it has proposed by Stiny and Mitchell (1978a) and automated by Grasl and Economou (2014). The goal of the study is to show how a complex design language (sets of designs) can be captured and constructed in a shape grammar interpreter. The output of the computation here is the automated pictorial enumeration of a number of Palladian villas encoded in the Grape software. All designs are based on the complete catalogue of the Palladian partis on the 5 x 3 cell-size by Stiny and Mitchell. Clearly for any parti there are several proportional schemes that can apply to it and for any of these proportional schemes there are several architectural designs that can be generated with respect to specific architectural elements used in the production, namely, porticoes, loggias, wall inflections, colonnades and so forth. Out of all these possible designs, only one is chosen here to instantiate each underlying parti.

Portm-ino Automated

Automated plans of m x n Portmino series From left to right--2 x 2 2 x 3 and 2 x 4 configurations 02

Automated plans of the m x n Portmino series--From left to right--2 x 2 2 x 3 and 2 x 4 configurations

Automated plans of the m x n Portmino series--From left to right--3 x 2 3 x 3 and 3 x 4 configurations

Automated plans of the m x n Portmino series--From left to right--4 x 2 4 x 3 and 4 x 4 configurations

Automated plans of the m x n Portmino series--From left to right--2 x 5 2 x 6 configurations

Automated plans of the m x n Portmino series--From left to right--3 x 5 3 x 6 configurations

Automated plans of the m x n Portmino series--From left to right--4 x 5 4 x 6 configurations

Heather Ligler and Athanassios Economou

2018

Keywords: John Portman; Design automation; Shape grammar interpreter; Shape machine

The shape grammar formalism provides a robust framework to try ideas in analysis and synthesis in design. Still what might work in paper does not necessarily work in a shape grammar interpreter. if a computation fails, it is clear who is to blame? Did the user of the grammar follow rightly all the rules when she attempted to make a production of her own? Did she erase the labels properly? Did she apply the rules in all possible parts before she would move one to the next stage? If a mistake happens, is it in the designer’s side? Is it in the publisher’s side? Is it on the reader’s side? And so on. A most satisfying effort, and a great lesson to learn for everyone involved, but error prone too.

This work here takes on a given paper grammar that formalizes basic compositional moves in Portman’s practice and puts them in action within the shape machine, the shape grammar interpreter currently developed in SCL. Interestingly, the expressiveness of the new medium not only checks and spellchecks the thesis as its was expressed in the original paper but it transforms it too. A visual catalogue of several possible designs is mechanically produced in the shape machine software to test the expressiveness of the grammar for a variety of n x m cell configurations. The term “Portmino villas” is assigned to the series to refer to Portman’s inverse of Corbusier’s villa Domino.

The Atrium Hotel Grammar

From diagrams to atria hotels--a circular hotel a triangular hotel a pentagonal hotel a hexagonal hotel

The plans of the 1967 Hyatt Regency in Atlanta--GA--USA--from bottom to top--the lobby level LLr a typical guestroom level LG and the roof level LR

Shape rules 01-05 for Stage 1--Framework

Derivation of the framework for a square atrium hotel

Shape rules 06-11 for Stage 2--Configuration

Derivation of the configuration for a square atrium hotel

Derivation of the style for a square atrium hotel

Five dihedral configurations Five cyclic configurations Five initial shapes for atrium hotels

A sketch for the derivation of the typical guestroom level for five initial shapes in the atrium hotel language Part I

A sketch for the derivation of the typical guestroom level for five initial shapes in the atrium hotel language Part II

Heather Ligler and Athanassios Economou
2018

Keywords: John Portman; Formal specification of architectural style; Shape grammars

John Portman’s atria are among his most celebrated and contested forms, captivating the popular imagination while also setting the tone for principles of architectural hospitality imitated worldwide. Still, both Portman’s contributions and subsequent replication inspired by his work remains difficult to assess, with no coherent theory to differentiate the subtlety and value of the originals, or even to distinguish between a copy and the real thing.

This project opens up the subject by addressing the hospitality corpus from its introduction in the emblematic and speculative 1967 Hyatt Regency in Atlanta, Georgia, Portman’s first atrium hotel. The commercial language of hollow forms initiated in the hotels is considered here as a unique iteration of the organizing principles Portman claims can be found in his 1964 personal domestic work, Entelechy I. This productive myth is one that can be engaged today in a vital way to research and remix Portman’s architectural language by looking and looking again at Entelechy I to constructively experiment with its resourcefulness as an innovation engine. This starting point is intriguing to map Portman’s claims, but more importantly to engage his work in another way and likewise inform additional applications. In all, the study here focuses on the atrium hotel language and its implicit relation to the house to begin structuring this effort. The outcomes include: a) a formal analysis of the atrium hotel; b) a parametric shape grammar for the atrium hotel; and c) a transformation grammar that explores the logic of atrium hotel composition in a variety of contexts, here simulated by a series of varied initial shapes.

The Dirksen Variations

Formal analysis of a typical courtroom plate of the Dirksen Courthouse--a Polygon representation b Dual graph representation and c Ad quadratum diagram

The set of 36 twodimensional diagrammatic representations of the postulated Miesian courtroom plate design variations from the Mies van der Rohe Archive at the Museum of Modern Art--New York 1-16

Rule 16 of the Dirksen grammar presented in four types of representation--a a sketch of the threedimensional parametric shape rule in axonometric projection b a graph representation of the sketch c a script encoding the graph representation and d a twodimensional representation of the rule

Stage 2 of the Dirksen grammar--Courtrooms Rules 7-14

Stage 3 of the Dirksen grammar--Scaffold Rules 21-28

Stage 6 of the Dirksen grammar--Section Rules 71-77

A sample derivation of a Miesian courthouse design from the software implementation of the Dirksen grammar in GRAPE--the final design of Dirksen Courthouse

Six sectional models of Miesian courthouse designs all satisfying the requirement of having 24 courtrooms and the appropriate volume of public--office and support spaces--a the final design of Dirksen courthouse b the design variation 4-09 in the corpus c the design variation 1-05 in the corpus d a hypothetical design with two courtrooms per courtroom plate e a hypothetical design with three courtrooms per courtroom plate and f a hypothetical design with four courtrooms per courtroom plate

James Park and Athanassios Economou

2018

Keywords: Mies van der Rohe, Courthouse design, Generative description, Shape grammar, Ring schema

The ring typology provides the most essential morphological characteristic of all contemporary courthouses in the United States (US) and abroad. From its genesis at Waterhouse’s revolutionary rethinking of the courthouse building type in the nineteenth century in the United Kingdom to its formal consolidation in Mies Van der Rohe’s pristine Everett McKinley Dirksen United States Courthouse (Dirksen Courthouse) in the early 1960s in the US, the ring has emerged as the most significant morphological element that organizes the functions and defines the form of the building type. The work presented here takes on the architectonic arrangement of the ring especially as it was deployed generatively over several iterations in the office of Mies producing a seemingly inexhaustible variations of courtroom plate. A generative description of Mies’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.

Mughal Gardens Redreamed

A catalogue of six parametric Mughal gardens in the original grammar

Flow charts of a border formation function b subdivision function border formation function

A catalogue of three parametric Mughal gardens in the original grammar Second row--Different motifs for water reservoirs

Different motifs for canal ends 1-3 Different nesting of initial rules 4-6

Nirvik Saha, Dennis Shelden and Athanassios Economou
2017

Keywords: Mughal garden; Shape grammars; Grammar Interpreter; Formal languages

The original Mughal garden grammar (Stiny and Mitchell, 1978) still remains one of the most enduring examples of the visual precision and generative power of shape grammars and since then it has been routinely referenced as an exemplary work in the shape grammar discourse and its applications in landscape design. The original Mughal garden grammar ended up with the image of an elder Shan Jahan, builder of the Taj Mahal, deposed and imprisoned in the Red Fort at Agra by his son Aurangzib, looking out from his pavilion in the fort, and dreaming of the char-baghs that might have been. The conviction of the authors was clearly that the grammar specified in their work enabled such dreams of char-baghs to be dreamed again by all the readers who were presented with the rules of the grammar; A poetic excursion indeed but enabling too because there is no better way to dream figuratively or literally but to play constructively with things and ideas of all sorts. This work picks up exactly where the original grammar ended and provides a computational application to implement and enable the play with the rules spelled out in the original shape grammar and the trial of possibilities that cannot be seen unless they are worked out – including the ones that are already dreamt and built by their original authors as well as others, potentially new, allowed within the rules of the game. The implementation of the rules does not follow one-to-one the rules as explicitly discussed in the grammar but instead it consolidates them in a parametric schema that consists of variables and combinations of sets of variables and is instantiated when values are assigned to these variables. This bundling of the rules in a parametric modeler is attempted here to take advantage of existing computational packages in Rhino /Python and shift the interest this in the automated production of designs and their possible extensions in other domains.

Terragni’s Riddle

Plans--sections and elevations of the two Terragni projects a The Mambretti Tomb b The Danteum

Composite axonometrics a The Mambretti Tomb b The Danteum

Underlying geometric relations a Golden rectangle b The Mambretti Tomb c The Danteum

Shape rules for the parti schemas of two grammars a The Mambretti Tomb b The Danteum

Automated generation of the ground plan of the Mambretti Tomb

Automated generation of the ground plan of the Danteum

Automated composition a Variations on the Mambretti Tomb b Variations on the Danteum

Hayri Dortdivanlioglu and Athanassios Economou
2018

Keywords: Shape grammars; Generative design; Architectural language; Type and style; Italian rationalism

In 1991, the Yale exhibition ‘Giuseppe Terragni: Two Projects’, coupled two unbuilt projects by Terragni, the lesser known Mambretti Tomb and the well-known Danteum in the same architectural setting to foreground the architect’s formal language and reﬂect upon his possible motives and intentions. The two projects shared many commonalities: they were both unbuilt; they were both designed during the later mature career of the architect; they were both amply documented and developed allowing for an in-depth analysis; they both foregrounded a commemorative and symbolically laden program; and signiﬁcantly, as the curators of the exhibition wrote, both exempliﬁed “a personally imposed agenda which informs, indeed drives, these works”.

This work here takes on the same two unbuilt projects by Terragni to reﬂect upon the exhibition, test its outcome and claims, offer alternative methods to foreground the principles and the logic upon which such claims can be made, and ultimately suggest a new interpretation of the work. More precisely, the work here provides a formal speciﬁcation of the Mambretti Tomb and the Danteum in the form of two parametric shape grammars that can be used to reconstruct them. Contrary to the formal analysis of the exhibition that concentrates on the relation between form and symbolism using underlying schemata of speciﬁc proportional shapes and spatial relations, this work deﬁnes speciﬁc visual rules for each project that when taken together foreground explicit similarities and differences between the two projects and suggest logical inferences and constructions between both. More broadly, this work aims at uncovering systematic deep structures behind both projects in order to gain a better insight in the ways formal vocabularies and spatial relations within Terragni’s work express the architect’s constructive deployment and transformation of compositional principles of neoclassicism and modernism.

Entelechy I

Entelechy--Transverse and longitudinal sections

Lattice of possible and built configurations of the eightpanel exploded column

Underlying grid and isovist diagrams for both floor plates of the house

The Entelechy shape grammar--Style rules 25-32 40-47

A production in the Entelechy shape grammar Part 13

A production in the Entelechy shape grammar Part 23

A production in the Entelechy shape grammar Part 33

Formal variations of the Entelechy grammar--S--M--L and XL

Heather Ligler and Athanassios Economou
2016

Keywords: John Portman; Formal specification of architectural style; Shape grammars; Isovists

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 this aspect of his contribution is in his widely recognized and published commercial portfolio, yet throughout his life he maintained that his design principles are to be found in his personal domestic projects. More precisely, he describes his 1964 residence Entelechy I as a crucial project for the ongoing definition of his work, claiming that “It was in my house that I first began to experiment with the concepts that I had identified as constant elements in the way that people related to their environment. Perhaps I am the only one who can see it, but much of my later work is implicit in that house. It contains the basis for my architectural philosophy: organizing principles that work for a room or a restaurant, a building or a group of buildings “ [Portman and Barnett, 1976].

This notion of the house as generator is the subject of this research, which aims to unpack the house as a productive construct that can shed new light on Portman’s architectural language, its instances, and influences. This project looks closely at the house to provide: a formal analysis of the house outlining its key features and relations and a parametric shape grammar that generates the original design as well as a series of variations.

Ice-ray Tilings

Rules and designs in a checkerboard grid

Production of the symmetry structure of the 18th c window design at Chengtu--Szechwan

Designs in the language The original design of 18th c window design at Chengtu--Szechwan is at the first row from left 1-9

Athanassios Economou and Kurt Hong
2018

Keywords: Shape machine; Shape grammars; Visual programming; Algorithmic composition; Ice-rays

In 1949 Daniel Dye published his book A Grammar of Chinese lattice showcasing an influential catalogue of Chinese ornamental and grilled window designs ranging from the 10th c. to the 19th c. Some of the designs published in the book were reworked by George Stiny during the ’70s in his paper Ice-ray: A note on the generation of Chinese lattice designs, to showcase his new theoretical method to approach design in terms of visual rules that apply recursively to generate designs.

This work takes on Stiny’s grammar of an 18th c window design at Chengtu, Szechwan, one of the two rule-based compositional methods outlined in the paper, and puts it into practice as an introductory exercise in the shape grammar class at Georgia Tech. The grammar was implemented individually by each student using the shape machine, the shape grammar interpreter of SCL in Rhino, and transformed appropriately as needed. The deliverables of the study are a series of new designs implementing different motifs and compositional ideas to transform the rule 6 of the original grammar. Significantly, all different motifs tried by the students were drawn directly within the modeling environment of Rhino showcasing a truly visual programming environment for spatial design.

Acknowledgments: We want to thank Nunggu Ahn, Zeinab Babalou, TJ Bogan, Yousef Bousehri, Warren Campbell, Vincent Chang, Alexander Clegg, Fatima Javeed, Zachary Lancaster, Andressa Martinez, Amelia Mclean, Eri Natsumi, Victoria Olaogun and Yuqin Zhong for their enthusiasm and hard work during the project.