Hermes: Computing with the Eleven Proportionalities in Design

Sectional parametric variations of the Villa Economou based on the 11 proportional means

The architecture of the Hermes app--a The structure of the analysis module b The structure of the synthesis module

The thirtytwo parametric design components encoded in Palladios Rotunda

Proportional variations of Palladios Villa Rotunda in section and side elevation--a Villa Rotunda b Villa Papalambros c Villa Kim

Hyoung-June Park, Panos Papalambros and Athanassios Economou
2005

Keywords: Proportion; Eleven means; Design automation; Palladio; Villa Rotunda

The absence of computational tools for the application of proportional theory in analysis and synthesis in design has been a persistent problem in the field of formal composition in architectural design. A computational tool, code-named here Hermes, is introduced as a tool for proportional studies based on the theory of the eleven proportional means. The analysis component of the application evaluates existing designs and provides statistical measures about the proportional structure of the design. The synthesis component of the application generates new designs from known ones with additional prescribed proportional properties. The analysis component is written in Autolisp and runs within AutoCAD. The synthesis component is written using the Genetic Algorithm Toolbox of Matlab and an AutoLisp application within AutoCAD. Both cases are built using extensively design optimization methodologies. The corpus of the designs for both analysis and synthesis has been selected from Palladio’s buildings to link this project to the long list of research projects that have tackled proportion using Palladio’s work as an exemplary body of work.

White Geometries

Levels of representation of the Smith House Bottom--Architectonic level 1--2--3 floor Middle--Spatial 1--2--3 floor Upper--Diagrammatic 1--2--3 floor

The complete set of all the combinations of the symmetry parts of the house D--Dihedral V--Vertical H--Horizontal S--Rotational C--Identity

Partial order lattice of the diagrammatic model of the first floor of the Smith House

Partial order lattice of the architectonic model of the first floor of the Smith House

Group theoretic ternary models of the Smith house--a DVS b DVH

Group theoretic ternary models of the Smith house--c DVC d DSH

Group theoretic ternary models of the Smith house--e DSC f DHC

Group theoretic ternary models of the Smith house--g VSH h VSC

Group theoretic ternary models of the Smith house--i VHC k SHC

Edouard Din and Athanassios Economou
2006

Keywords: Smith House; Symmetry; Group Theory; Diagrams; Partial order

The 1967 Exhibition New York Five (NY5) on the work of five New York City architects, namely Peter Eisenman, Michael Graves, Charles Gwathmey, John Hejduk and Richard Meier, and the subsequent book Five Architects published in 1972, have indelibly stamped the course of the history of modern architecture of the late twentieth and early twenty-first century. Among this early work of NY5 the Meier’s buildings were closer from all on the modernist aesthetic of the Corbusian form and in fact even the later buildings that Meier produced since then have all remained truest to this aesthetic. This work traces the history and logic of the evolution of Meier’s early language and its direct relationships to spatial and formal investigations of early-twentieth-century modernism as well as its direct reciprocal relationships with the rest of the NY5 languages. The departure for this inquiry of such centrifugal relationships between representation and formal analysis for the purposes of this work is Richard Meier’s Smith House, an early pivotal work, an acknowledged forerunner and embodiment of the full repertory of Meier formal strategies and language.