Math Objects an Origin of Architecture

Math Objects An Origin of Architecture

Daniel Baerlecken 1, Olaf Kobiella 2 1 Georgia Tech, College of Architecture, 2 TU Braunschweig, IGE 1 http://www.coa.gatech.edu, 2 http://www.ige.tu-bs.de/e 1 [email protected], 2 [email protected]

Abstract. The paper discusses mathematical form generation as an academic 1 methodologyMath Objects to develop new approaches to architectural design. The academic designAn Origin studio of Architecture‘Math objects’ investigates the relationship between complex

3d-surfaces Danieland mathematicsBaerlecken 1, Olaf Kobiella in order 2 to expand the formal repertoire of architecture.1 GeorgiaIt claims Tech, thatCollege the of Architecture, process 2of TU form Braunschweig, generation IGE can be seen as an 1 2 autonomous entity,http://www.coa.gatech.edu, which is independent http://www.ige.tu-bs.de/e from an overall strategy or any a 1 [email protected], 2 [email protected] priori meaning. Architecture has always originated from a concept, eventually progressing Abstract.towards The a paper certain discusses form. mathematical This formmethodology generation as an has academic been reversed. The methodology to develop new approaches to architectural design. The academic paper discussesdesign twostudio studios “Math objects” undertaken investigates the in relationship the last between year, complex led by 3d- Daniel Baerlecken surfaces and mathematics in order to expand the formal repertoire of and Olaf Kobiellaarchitecture. at It the claims TU that Braunschweig, the process of form generation Germany. can be seen as an autonomous entity, which is independent from an overall strategy or any a priori meaning. Architecture has always originated from a concept, eventually Keywords: progressingGenerative towards design a certain; form.design This methodologymethodology: has been reversed.architectural The design paper discusses two studios undertaken in the last year, led by Daniel Baerlecken teaching; parametricand Olaf Kobiella form at the generation; TU Braunschweig, NURBS-modelling Germany. . Keywords: Generative design; design methodology: architectural design teaching; parametric form generation; NURBS-modelling. Research Setup: Research Setup:

Inputs

Digital Techniques Subject and Educational Proceedings Architectural and Digital Theory

Design Studio

Manuals & Evaluations MA Students Architectural Projects Writings

Outputs

Math objects is generated out of a digital research framework as shown above. It ‘Math objects’ is generatedintegrates researchout of awork digital into theresearch students educationfeedback: curriculum Theoretical on the base and of atechnical digital results (part of design studio. This process can be seen as a program loop, with a continuous framework as shownfeedback: above. Theoretical It integrates and technical research results (partoutput) of output) of each of each iteration iteration directly inform the input work into the studentsinform education the input ofcurriculum the next de signon thestudio. Theof thedesign next studio design Math objects studio. has The been design studio ‘Math executed by two iterations of research and design work as presented below. base of a digital design studio. This process can be objects’ has been executed by two iterations of re- seen as a program loop, with a continuous search and design work as presented below.

Section 17: Shape Studies - eCAADe 26 677 Mathematical Form: mathematical prototype by its deviates 3. Transference of the models and principles to the There has always been a deep connection be- context of a given project scenario (program and tween geometrical, mathematical principles and site). architecture – from the great pyramid of Giza, over 4. Exploration of interior spaces (massing) and sys- Brunelleschi, Palladio, to Le Corbusier up to today’s tems (structure and texture) in the scenario of architecture. Often these abstract and invisible, a model (ranging from large scale CNC-milled numeric machines have served as an architectural models over Z-CORP models to analogue mod- fountain of youth. ”Moreover, the perfection of math- els). ematical form is such (as Colin Maclaurin learned of This sequence of design techniques and com- the bee), that whatsoever is most beautiful and regu- puting skills fosters the student’s ability to question, lar is also found to be the most useful and excellent “. shape and interrogate space: The studio interrogates (On Growth and Form, D’Arcy Wentworth Thompson, the computer as an advanced design tool of form P.1097) generation and experimentation. The continuous Mathematical principles can inform architecture integration of analogue and digital modelling tech- in three different scales: massing, structure and tex- niques gives a substantial feedback to this design ture. This relationship has been explored in a series approach. of academic design studios and professional work In the following paragraphs the design works of the using a specific methodology, which is not just re- studio are presented, discussed and evaluated from search and also not just design, but both. The stu- four different perspectives: dios always focus on one or more of the three scales 1. Variables, formulas and geometries: An analysis (massing, structure or texture), although they are in- of specific mathematics and its ability to control terdependent and inform themselves vertically. The and shape complex form (Moebius-, Henneberg-, specific research ranges from mathematical form Klein-surfaces, etc.) structure and texture) to tessellation like Penrose Til- 2. Subjective choice and individual manipulation: ing, Danzer, Kite etc. (texture). an introduction and analysis of the rules, by

Figure 1 form catalogue and form studies,Frauke Busdieker und Alke Malzahn

In order to guide the students through the experi- which the mathematical shapes can be trans- mental design process, a gradual work flow has been formed to fit an architectural scenario (contex- developed. The elaboration of the mathematical tual alteration of variables, object scaling and model proceeds in four phases: morphing, non-parametric and manual inter- 1. Research on complex, mathematical forms. ventions (dirty-ism), integration of architectural 2. Creation of a form catalogue that explores the detail)

678 eCAADe 26 - Section 17: Shape Studies 3. Rapid prototyping and physical models: an anal- situations: grove, beach and sea. ysis and critique of the cross-media work flow, The design methodology aims at formal innova- with a focus on its ability to evaluate space and tion. This formal research is based on the assumption to inform the design process. that formally enriched architecture also has a higher 4. Design pedagogic: an evaluation of the Math- degree of functional complexity. In that sense formal objects studio as an approach to academic research is directly linked to programmatic research. teaching of architectural design. This aspect focuses on the transformative role of such digi- Project 01 - Julian Hartwig and Andre tal techniques for architecture - versus digital Stossun: techniques/ practices with a purely auxiliary approach. Variables, formulas and geometries: Math Objects 01 - waterscape: The project from Julian Hartwig and Andre Stossun is based on the exploration of sine and cosine waves The design studio math objects 01 is based on mod- as deformative tools on a structural level. elling with Rhinoceros and the usage of the Math Starting with a stacked system of planar planes plug-in developed by Jess Maertterer which allows each plane deforms into a three-dimensional surface for the creation of complex geometry without time- creating grotto-like spaces with pockets of intersect- consuming rhino scripting. ing geometry. From this mathematical approach a Starting point of the process is an initial phase system of open and closed spatial configurations of abstract form generation using the Math plug-in emerges which has inherent structural properties.

Figure 2 form catalogue, Julian Hartwig and Andre Stossun

to create a catalogue of form variation. As a second Subjective choice and individual manipula- step the students are confronted with a building site tion: and a program and the resulting transformation of The transformation of the mathematical model fol- the prototype, which then has to be further devel- lows a multi-performative approach. By precise oped in the third phase by investigating the internal manipulation of the surface – using transitions with properties of the building and finalized in the last curvature continuity and clear defined moments of phase by creating a large-scale model. curvature discontinuity - the surfaces allow to be On a programmatic level the studio is deal- used as spatial division, as structure, as circulation, ing with the typology of a wellness spa – located as furniture, as technical equipment etc. in Heiligendamm, Germany in a decisive natural The mathematical model also informs the pro- environment. The side is marked by three different grammatic organisation of the building: By following

Section 17: Shape Studies - eCAADe 26 679 the logic of a stacked and then deformed system between the different functional areas of the build- the building becomes vertically organized and ing. Other peaks provide structural support for the aims for a new type of a vertical spa in contrast to building. the traditionally dominating, horizontally organised typology. Rapid prototyping and physical models: Figure 3 design development, Julian Hartwig and Andre Stossun

By re-inventing the ground surface as a new to- The selection of CNC technology is actually di- pography and by manipulating that surface in such rectly resulting from the sine and cosine function a way that it forms pertruding outward peaks the which creates geometry without undercuts. building connects itself with the terrain in a highly articulated manner and creates a smooth transition Design pedagogic: between the surrounding terrain and the new artifi- The project demonstrates how a methodological cial landscape. computational approach can develop into architec- The main peak of this ground surface serves ture almost on its own - just using a systemacy that as fast access whereas a system of a slow diagonal, informs every phase of the design process. almost topographical circulation is employed in

Figure 4 model fotos, Julian Hartwig and Andre Stossun

680 eCAADe 26 - Section 17: Shape Studies Math Objects 2- Skin-deep: Based on studies of different weaving techniques Ju- lian Busch creates an ubi-directional prototype that “Textile techniques become computing techniques, merges those studies by changing its informative surface becomes structure, and structure becomes system: weaving is used to inform micro-deforma- geometry. It goes beyond the pure transformation tions on the surface level, slim mid-scale filament- of textile techniques into design techniques: it is… like transitions and buckling pockets on a massing a completely textile way of thinking.” level. The central idea is what Lars Spuybroek calls the Subjective choice and individual “Semperian Reversal”: manipulation: “I call it a reversal, but it is a reversal of the order of the four elements, where the tectonic proceeds the Rapid prototyping and physical models: textile. I want the textile to become the tectonic The final model is produced by mixing digital and itself. In that case the soft elements become rigid analogue techniques: Z-Corp model parts are com- through collaboration, by teaming up…”( Lars Spuy- bined with cast resin parts. broek: 2006, Textile Tectonics). The studio follows this approach and researches Design pedagogic: textile techniques in different scales. Julian Busch’s project is highly artistic, but still based The design method is not based on a specific on the initial diagramming process, even though tool like the math plug-in of the first studio, but on it is hidden and almost unrecognisable because of diagramming of textile techniques that then inform its artistic nature. The design is marked by a certain architecture. The textile is regarded as closely related amount of ‘dirty-ism’, which is resulting from the to rule based processes of mathematics. combination of digital and analogue techniques, Also - in contrast to the first studio - the second from research and artistic thinking, from systemacy studio is dealing with an urban terrain, with the East and intuition. Harbour in Berlin which is about to developed into a centre of Berlin’s young fashion and design industry.

Project 02 – Julian Busch

Variables, formulas and geometries:

Figure 5 form studies, Julian Busch

Section 17: Shape Studies - eCAADe 26 681 Figure 6 design development, Julian Busch

Project 03 - Juliane Demel: Figure 7 model, Julian Busch Variables, formulas and geometries: Juliane Demel focuses in her initial studies on weaving techniques on a structural and textural level. By creating a catalogue of varying weaving techniques the studies develop different spatial systems linked to the applied technique. The catalogue explores rigid, tight conditions and loosened conditions. Es- sentially structure and texture generate massing by loosening and tightening of strands.

682 eCAADe 26 - Section 17: Shape Studies Figure 8 model, Juliane Demmel

Subjective choice and individual manipula- Rapid prototyping and physical models: tion: Z-Corp technology is used to produce the model. A In phase 2 the project addresses and invents multi- sectional technique has been used to join the parts linear urban conditions: the transformation of the together. prototype succeeds by incorporating multiple linear trajectories of the urban fabric. To some extend Design pedagogic: the transformation of the prototype is generated From a pedagogic point of view the project dem- by using the weaving technique on a massing level onstrates how applying a diagramming technique (weaving of pedestrian paths and its resulting nega- to two different reference systems can transform a tive volume) instead of the former component level project without re-designing. (structure and texture). On a programmatic level the crossbred of inter- Conclusion nal design parameters and external constraints create a series of multifunctional, fluid spatial arrange- Comparing the two studios it becomes evident that ments that can be re-configured temporally. the research of the first studio is more focussed on a mathematical aspect, which is automatically Figure 9 Design development, Juliane Demmel

Section 17: Shape Studies - eCAADe 26 683 Figure 10 Design development, Juliane Demmel

implanted by the use of the Math plug-in. The sec- References: ond studio is more open, because the starting point is a diagramming technique, which allows for greater Thompson, D`A. W.: 1942, On Growth and Form, Dover variety of individual approaches. Publications, INC., New York, pp. 1097 In general the combination of research and artis- Spuybroek, L.: 2006, Textile Tectonics, interviewed by tic work and also the experimentation with a given Ludovica Tramontin, in M. Gracia (ed.), Architectural project scenario has proven to be highly productive, Design Architextiles, Wiley-Academy. because research and design can interact during different design stages. Also it links the research closer to the profession by making the output assessable. The production of models and imagery becomes in that sense essential. Both studios clearly reject the sole use of rational arguments. Instead, they define an experimental area of architecture between pure rational processes and highly intuitive decisions. In future studio the research will be deepened by extending the first phase in a more instructive way. This allows both: more research on techniques and more integration of time-consuming techniques such as scripting. Also other programs such as Math- ematica and Generative Components are going to support a deeper understanding of the underlying mathematical operations. But still the context of project scenario and the production of models and imagery will be essential to evaluate the results in an architectural context.

684 eCAADe 26 - Section 17: Shape Studies