Architecture

This paper will present the main principles of Goethe’s Theory of Colours and formulate a theoretical approach for the study of polychromy in digital design pedagogy. In the first part of the paper a survey on colour theory will be presented comparing Goethe and Newton’s works on colour. The concepts of polarity [Polarität] and intensification [Steigerung] will be introduced as the two main principles of Goethe’s dynamic notion of colour. These terms will be used to explain how Goethe considered colours to induce sensual effects on the onlooker. In the second part a digital design studio that focuses on colour will be presented. The pedagogy will show how a dynamic notion of colour could be studied using digital tools. Some of the student works will be presented while addressing how a Goethean notion of sensual colours could be studied as spatial parameters. The goal of the paper is to distill a theoretical approach towards the study of colour in architecture and contemplate on how it could be applied within the digital design curriculum.

Tangle Jungle was an experiment in an alternative method of design and making for the digital age. The aim of the project was to interpret and reenact traditional craftmanship through today's digital tools. For a particular study on the subject, we looked at the theory and works of William Morris. Morris had an exceptional taste for medieval art and produced, among other things, hand-woven carpets that are still studied today. Morris reinvented the art of his time by reviving pre-industrial modes of production and designs. Today, the digital age is experiencing a similar paradigm shift. Digital tools already work, in many instances, as a direct extension of the hands of a new breed of digital artisan makers. It is possible to assess that the digital is getting closer to Morris's notion of craftsmanship. Tangle Jungle became a testing ground for this historical connection, bringing forth the question, can we redefine our own digital craftsmanship as a form of digitally reenacted Gothic revival?

In this paper a theoretical and computational framework for a contemporary study of morphogenesis will be presented using a pulsation model. This study will revisit some of the valuable historical ideas on form developed by Goethe in the late eighteenth century. This investigation will be developed in three main parts. In the first part a brief outline of Goethe’s scientific methodology will be described positioning his achievements against the epistemology of Kant. In the second part Goethe’s main works on morphology will be presented with a focus on his botanical writings. Using a fragment titled "Formative Impulse" some of Goethe’s ideas on polar tendencies and metamorphosis will be used for a computational framework in the final part. By bridging among history, theory and technology the paper aims to present a novel approach to the study of computational form and growth in architecture.

In this paper we present a studio framework that connects Ruskin’s conception of beauty and digital design tools. We define eight different aspects of beauty that are studied via natural and artificial patterns. These studies developed by students are later applied to a site and program in the second half of the studio. Some of the works of the students are presented while narrating the overall pedagogical process. The aim of the paper is to present a unique approach that combines theory on beauty with digital tools in order to re-define design research as an open-ended and dynamic practice.

Recent developments in theory and technology in performance based design show an interest towards generative systems. In this paper a morphogenetic approach will be introduced that looks at Goethean morphology and leaf venation patterns. To instrumentalize this approach an algorithm will be introduced to generate various leaf venation patterns on complex mesh surfaces. As a case study, the paper tests the applicability of such system as performative algorithms for building envelopes. The role of simulation is to generate self-organizing forms and provide a framework for design development. The overall approach is to consider performance as a direct input to guide the computation of form at an early design stage.

This paper will discuss how Shoowa Kuba textiles could be analyzed as an ornament that can be digitally constructed and applied in design. An historical outline of ornament is provided by briefly comparing Classical and Gothic ornaments. This theoretical framework is then compared to the art of Shoowa Kuba focusing on their textile embroideries. Various patterns and techniques will be introduced showing how Kuba people implement rules as well as how they break them. These patterns will be digitally reconstructed to show their applicability to the digital design domain.

The paper introduces a method for structuring and ornamenting double-curved geometry, which is developed through the lens of Walter Crane. Crane's method for pattern making is based on underlying scaffolds and infill patterns for two dimensional surfaces. The presented research uses his method and applies it through digitals means to three dimensional surfaces. The scaffold is used to solve the problem of curvature: it creates flat facets. This approach is tested through a prototypical installation at the Musee d'Jurassien d'Art and d'histoire using aluminium sheet metal and water-jet cutting, but can also be transferred to other architectural applications.

This paper will articulate on how the intrinsic principles of gem making could be applied in architectural form finding. It will speculate that the technical accumulation of expertise and knowledge in this crafty technique could be implemented algorithmically. This robust and efficient process could provide solutions for architectural design problems. It will conclude that faceting, as we can observe it in jewelry making and lamp design, produces facets that are not just reacting to an underlying geometry, but also add expression and articulation to an object.

This paper discusses an approach to adapting trabecular bone structures for the design of complex architectural components exemplified through structural nodes. Based on the paradigm shift in additive fabrication, namely the ability to print structural metals, this paper identifies new methods for architectural and structural design that allow to create porous, intricate architectural components. Those components are designed in analogy to bone structures. The paper presents a metaball-based application, programmed in Processing, which allows creating n-legged nodes using parametric gradient maps. The approach aims at reduction of weight and waste, while exploring the novel aesthetic properties of such bio-constructed networks.

This paper discusses a type of graph called "homeomorphically irreducible tree" (HIT) and its applicability for a formal study of symmetry in building plans. As a theoretical introduction, the mathematical properties of HITs are introduced through different historical building samples all of which display symmetry, proportion and homologous wings in their formal organization. The extracted principles are used to formulate a generative algorithm that reduces graph complexity to simple sequential numeric representation. This method is converted to a "homeomorphic machine" that is explored through generative plans. The aim of the paper is to introduce a new graph-based approach for potential morphological research into architectural symmetry.

This article introduces an algorithm influenced by Goethe’s concept of metamorphosis capable of generating a wide range of parametric leaf forms. Metamorphosis is defined as alternating stages of expansion and contraction that are observable during the development of flowering plants. This principle is extended toward leaf morphology, where two main developmental trajectories are outlined. By formulating simple two-dimensional geometric rules, the author tests the concept of metamorphosis on parametric leaf forms.

This paper will introduce Goethe’s concept of polarity to discuss its
theoretical and computational implications on natural and architectural
morphogenesis (1). Polarity, as a dualist principle, is found in most
of Goethe’s body of works, particularly in his treatise on colour and
botanical writings. This concept is explored from a morphogenetic
perspective to reconsider Goethe’s engagement with natural sciences
during Enlightenment where he transfers his ideas on form and growth
to architecture. In the first part, morphogenesis as a concept for the study
of organic growth is discussed that combines modern research in biology
and architecture. In the second part, Goethean morphology as a unified
science founded on polar principles is presented to discuss a historical
perspective to morphogenesis. Here, Goethe’s concept of metamorphosis is
highlighted as a principle founded on polarity, formulated with alternating
cycles of expansion and contraction. These concepts are explicated using
an algorithmic study of leaf development to discuss its morphogenetic
application to the study of form and growth in natural morphogenesis.
In the last part, Goethe’s morphological views are extended towards
architecture within the framework of organicism where his ideas on
the polarity are directed towards the aesthetic reception and formal
development of the built environment. Comparing the form of two Gothic
cathedrals, Laon and Noyon, the paper will offer a developmental model
based on the concept of metamorphosis as an alternative trajectory for
morphological research in architecture.

The morphogenetic design process of networking patterns produces anisotropic structural systems that can offer generative solutions for custom design applications. As an example of this type of pattern application, the leaf venation algorithm is introduced that can be customized through parametric inputs and density maps. This method is extended onto mesh surfaces incorporating multiple software applications combining aspects of parametric design, optimization and digital fabrication. The dynamic workflow is presented using a case study project titled ''Calyx,'' a public artwork completed using the computational tools developed as part of the research. The networking structural pattern of the sculpture yielded to the development of a geometry optimization process that allowed the digital fabrication of planarized structural members. The technical aspects of the design development and post-rationalization process for the construction of leaf venations patterns are discussed.

This paper introduces a type of graph called 'homeomorphically irreducible tree' (HIT) and explores its analytical and computational aspects in the architecture of radial prison plans. As a theoretical introduction, HITs are first diagrammatically presented using a taxonomy of 20 different radial prisons. Using this analysis, a generative algorithm that transforms plan connectivity to a simple sequential numeric representation is developed. This method is applied as an architectural plan generator that is parametrically explored using graphs as building skeletons with configurable wing typologies. The aim of the paper is to lay the foundation of a new graphbased approach for the morphogenetic study of symmetry in architectural plans.

As a historical and ornamental building element, muqarnas are widely found among the entrances of madrasas, mosques and hans in Anatolian Seljuk Architecture. In Kayseri (Turkey), muqarnas structures are characterized by symmetrical distribution of patterned geometric layers that presents computational rules for the design and construction of these ornamental structures. The presented research focuses on twelve unique muqarnas structures that are analyzed through a computational methodology combining photogrammetry, 3D modeling, symmetry and graph theory. The computational analysis shows that Seljukid muqarnas exhibit patterned branching of the symmetry axis between layers radiating from their geometric center. Using the modeled samples, the paper analyzes inherent symmetry rules and growth patterns while offering a novel way of studying, modeling and categorizing muqarnas.

This article describes a parametric design and fabrication workflow influenced by Frei Otto's form-finding experiments on soap films. The research investigates minimal surface geometry by combining physical and digital experiments in a computational framework. Operating on mesh topology, various parametric design tools and plug-ins in Rhinoceros/Grasshopper are presented to discuss the translation of minimal surfaces to flat strips suitable for planar fabrication using flexible materials. These tools are tested on a case study to show the automated design and manufacture of double-curved surfaces as double-layered strips running in perpendicular directions that can be affixed at point connections for structural stability. The development of the parametric workflow, material constraints, and stripped fabrication of layers are discussed.

Recent developments in archeological research extend diverse technological methods for the geometric deciphering and cultural understanding of various historical building components. One of the emerging methods in this field is the development of generative algorithms to develop computational models for the comparative study of variation among different structures belonging to a common era, style, or region. In this study, we present a novel approach for the computational analysis and parametric modeling of muqarnas found among Anatolian Seljuk architecture in Kayseri and Sivas built in the 13th century. Using four different octagonal muqarnas structures, we outline common generative rules showing recursive stacking of geometric layers, fractal patterns and hierarchical branching of the axis of symmetry. A recursive algorithm is developed that can offer a generative study of muqarnas structures using proportions based on the 'silver ratio.' The development of the algorithm is presented through rules and variations that can offer a novel perspective for the geometric understanding and categorization of muqarnas in the region.