Environmental Parametrics 2 10.0 Environmental Parametrics 2 | Kim + Lee

ENVIRONMENTAL PARAMETRICS 2 10.0 ENVIRONMENTAL PARAMETRICS 2 | KIM + LEE

A SYSTEMIZED AGGREGATION WITH GENERATIVE GROWTH MECHANISM IN SOLAR ENVIRONMENT

Dongil Kim ABSTRACT KL’IP; University of California, Berkeley The paper demonstrates a work-in-progress research on an agent-based aggregation Seojoo Lee model for architectural applications with a system of assembly based on environmental KL’IP; University of California, Berkeley data acting as a driver for a growth mechanism. Even though the generative design and algorithms have been widely employed in the field of art and architecture, such applications tend to stay in morphological explorations. This paper examines an aggregation model based on the Diffusion Limited Aggregation system incorporating solar environment analysis for global perspective of aggregation, the geometry research for lattice systems, and morphological principles of unit module at local scale. The later part of this research paper demonstrates the potential of a design process through the “Constructed Cloud” case study, including site-specific applications and the implementation of the systemized rule set (Figure 1).

Figure 1 Fully aggregated model in response to solar vector.

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1 INTRODUCTION 1.1 GENERATIVE DESIGN Generative design is a design methodology in which the output is generated by a set of rules or algorithms, normally implemented on the computer. In the early 1970s, Prof. Ralph L. Knowles at the University of Southern California implemented an external fac- Figure 2 tor, a solar vector data, as the main principle for the design rule set in The Solar Envelope Tetrahedron liner aggregation study 01. project where all adjacent neighbors are capable of solar access. While the early project was operated manually, generative design process using a computational method has been triggered to mediate a rule set between humans and the environment factors in this fast changing and unpredictable contemporary period.

1.2 GENERATIVE DESIGN IN COMPUTATIONAL ECOLOGIES Parametric design and generative algorithms have been investigated in architecture as a way to integrate environmental factors into the design process. Morphosis Architects integrates technologies into high-performance skin systems that minimize solar heat gain while maximizing glare-free daylight by using parametric design technique in the

Phare Tower project. Also, the Concept_Face_C project (Banke 2013) demonstrates a Figure 3 form generation toolset that use the analysis and simulation of daylight conditions and TetraGO unit geometry & aggregation study 02, plan view during assembly. indoor comfort to drive the form in early design phases. However, such recent applications of parametric design with environmental data still tend to stay on envelope design or frozen morphological moment even though generative algorithms are more suitable for responsive and adaptable real-time outcomes. Therefore, this research investigates a reciprocal design process by a generative algorithm that involves a decision making process, enabling positive impacts on both human and the environment.

1.3. SYSTEM MAKING AND GEOMETRY A system design is a set of interacting or interdependent components forming an integrated whole (Bohnacker 2012). The concept of systematic architecture has been widely used on structural concepts, module systems, and space organization. In 1950s, in Philadelphia, Louis Khan and Anne Tyng proposed City Tower, a synthesized space system that uses tetrahedron structure modules as a basic rule set for the floor slabs and three-dimensional space at multiple scales for the entire building (Figure 5). This is a seminal example of earlier systematic architecture with a rule set.

Our system design also offers the possibility of diverse morphological transformations by connecting and modifying the geometry of the components in different ways. Early studies show diverse transformations and assembly possibilities using identical geometric components during the aggregation. For example, a tetrahedron aggregation study shows the assembly mechanism in a linear growth model (Figure 6) and the Tetra- GO project demonstrates the multi-directional growth and divergence mechanism in the module system of the elongated octahedron during the aggregation (Figures 7, 8). The former study worked with a single path growth based on a generative algorithm known as L-System. The latter project applied asymmetrical modules which result in Figure 4 TetraGO unit geometry & aggregation study 02, tracking assembly sequence and logic. 10.0 ENVIRONMENTAL PARAMETRICS 2 | KIM + LEE

more diverse possibilities of assembly by using the Diffusion Limited Aggregation algorithm. Both studies represent the synergy between component systems and generative algorithms as an integrated rule set.

1.4 MINIMAL SURFACE AGGREGATION The idea of minimal surface aggregation is an advanced system design that produces continuous surface via duplicating, reversing and rotating the modulated minimal surface. Toyo Ito’s Taichung Opera House demonstrates an application of minimal surface aggregation system in large scale architecture. The independent aggregation modules not only become a unified component, but also demonstrate the whole system of building. As a result the assembly logic can be applied to the component system design to Figure 5 DLA simulation in solar vector environment. control both individual and collective logic of morphology simultaneously.

2 METHODOLOGY 2.1 DATA RESPONSIVE DIFFUSION LIMITED AGGREGATION SYSTEM Data responsive generative design is initiated by a generative algorithm, Diffusion Lim- ited Aggregation (DLA)—an algorithmic model of fractal growth that produces dendritic forms that was introduced in 1981 by Witten and Sander. In the DLA model, a sphere surrounds an attraction point at the center, a growth starts from the sphere surface, and Figure 6 then a seed from the surface wanders around randomly until it is attached to a branch Five Platonic solids are the tetrahedron, icosahedron, dodecahedron, octahedron, and cube. The 13 Archimedean of the existing cluster. Finally that seed becomes a new agent to attract the following solids are the truncated tetrahedron, truncated icosahedron, seed. This process repeats creating a divergent aggregation. Because the DLA system snub cube, snub dodecahedron, rhombicosidodecahedron, truncated icosidodecahedron, truncated cuboctahedron, can be grown toward enacted directionality and parameters, it offers a possibility for the icosidodecahedron, rhombicuboctahedron, truncated user to set a rule and operate it systematically. In this project, the DLA system is driven dodecahedron, cuboctahedron, truncated cube, and truncated octahedron. The cube and truncated octahedron by environmental data, especially solar factors, and the sunlight direction toward an are the only Platonic and Archimedean solids, respectively, attraction point which circumscribes the possible growth surface of seed on a sphere. that tile space. As the agent can only grow within a certain volume determined by sun analysis, the framework of the cluster will be developed toward specific direction (Figure 5). As a result, the environmental-data-driven DLA system provides an aggregation system that is adaptable to the solar conditions.

2.2 LATTICE SYSTEM FROM TRUNCATED OCTAHEDRON The DLA model constructed using solar data is developed by exploring geometry studies in Platonic solids and Archimedean solids. Among the eighteen solids (Figure 6), the geometry of truncated octahedron offers a high degree of density because the distance from a center point of one truncated octahedron cell to another is relatively shorter than other solids (Figure 7, Figure 8). Furthermore, truncated octahedron each of which consists of six squares and eight regular hexagons can assemble into zero gap tessella- tion and the lattice system that is generated by connecting the centers of the truncated octahedron becomes the fundamental lattice system of the DLA model. Therefore, the Figure 7 DLA system with a lattice system of truncated octahedron results in a stable growth Tetra octahedron density study to evaluate the total number structure with high density. of center point of 3m radius geometry in 15 X 15m cube.

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2.3 MORPHOLOGY The form of the truncated octahedrons is optimized via a process of evolvement and degeneration in order to improve its function and the connection between neighbors in DLA lattice structure. In detail, one truncated octahedron unit is surrounded by fourteen neighbors by touching six square faces and eight hexagonal faces, and the six square faces are positioned farther from the center of the truncated octahedron so that during transformation they are fixed to maintain the maximum volume, but the hexagonal faces become alienated from their neighbor (Figure 9). With regard to six possible outlets out of fourteen faces, two squares among six are degenerated to secure sufficient passages for sunlight between the DLA structure layers, eventually four squares are selected as outlets to connect to neighbors (Figure 10). The geometry results in four outlets and six surfaces by merging vertices of a unit. Then the four outlets become an inner space, a circulation or termination of the unit depends on the surrounding condition, resulting Figure 8 in an asymmetrical form that diversifies possibilities of assembly in aggregation. As the Tetra octahedron lattice as the connection between the new form is optimized into minimum number of faces, six faces, each surface is capable center of units. of exposing to maximum amount of sunlight, moreover the alienated faces offer cavity space between units, which allows sunlight to passing through multiple layers in the lattice system (Figure 11). Due to these transformations, the truncated octahedrons have been converted into different geometric forms, resulting in maximum surface area expo- sure for the ultimate amount of sunlight within the multiple layers of the DLA structure (Figure 12). Thus, the aggregation system has achieved varying morphology at global scale, and still remains as a unified form underlined by the lattice system.

3 APPLICATION Figure 9 3.1 BACKGROUND Possible connectivity research of geometry within 4 outlets. The project “Constructed Cloud” showcases a specific application of the methodology in the previous session. The growth mechanism is driven by a parameter defined by the Geographic Information System (GIS). Specifically, the potential sites are office buildings in New York City that are under fifteen-story heights with leftover air right in restriction of reconstruction. An area of seed growth within a sphere of the DLA system is circumscribed by the range of the sun vector, whose direction is perpendicular to the designated volume and the area that is capable of daylight inflows for at least three hours per day. Then the data-responsive aggregation system is operated according to the specific environmental conditions.

3.2 LOCALIZED CLUSTER SYSTEM After the DLA model along the lattice structure of the truncated octahedron is con- Figure 10 The degradation of outlet to secure sunlight access. structed, it is grouped into several looping clusters in order to achieve structural and functional qualities on large scale from the independent integrated systems in unit scale. Each cluster can function as one or any combination of circulation, ventilation, occupi- able space, utility, vegetation, space separation, or visual connection. As a result, one cluster distributes the functions of among its units (Figure 13). 10.0 ENVIRONMENTAL PARAMETRICS 2 | KIM + LEE

3.3 MULTI-DIRECTIONAL ORIENTATION One unit is shaped into an asymmetric form after transformation, consequently, the clusters within the DLA model are capable of creating different configurations depending on circumstance by rotating, mirroring, or duplicating units as a rule of minimal surface aggregation. Therefore, the various configurations enable the unit within each cluster to a range of different directions (Figure 14).

Figure 11 The cavity of aggregation in truncated octahedron lattice. 3.4 SPACE ORGANIZATION The aggregated model is placed on the lattice system of the truncated octahedron, so the unit spaces of each cluster are accessible from the same floor level and circulation stairs. These spaces contain a skip floor type office (4 modules), a trail type office (6 modules), a lattice type office (6 modules), a ring type office (8 modules) and a switch- back type office (6 modules)(Figure 15, 16).

3.5 PARAMETERIZE THE RULE SET This rule set operates from the site selection process, generative algorithm to systematic design, and we have shown that the rule set can be parameterized into the selected volumetric spaces and adapted to different physical urban context and environmental Figure 12 conditions (Figure 17). Example of fully aggregated inner and outer simulation model. This work-in-progress research project aims to explore an environmental-factor-driven generative design process that highlights the reciprocal relationship between architecture and environment. Also, in response to the Anthropocene, the employment of systematic design in generative algorithm enables adaptable and responsive parameters in diverse environmental criterion. In this paper, the Diffusion Limited Aggrega- tion (DLA) system as a generative algorithmic language serves as a self-sun-oriented aggregation model within limited volumetric parameters with a global perspective. The geometry of the truncated octahedron was used as a unit of the lattice system in the DLA aggregation. The relationship between the truncated octahedron units bring about a transformation of geometry that results in 4 outlets and 6 surfaces by the process of evolvement and degeneration. The generated form is shaped as a collection of multi- oriented units that can adapt to diverse directionalities of evolvement. Also, the cavity space in the aggregation allows solar access for all units. The outcome of the aggregation represents not only the continuity of surface on aesthetic level, but also the connectivity of volumetric spaces on spatial level (Figure 18, 19). Figure 13 Multidirectional system diagram.

5 FUTURE WORKS The project focused on the daylighting directionality as an actuator of Diffusion Limited Aggregation. Future researches can include different environmental actuators such as thermal or acoustic data, additionally other generative algorithms including L-system, Cellular Automata, Flocking or Evolution can serve as a basic aggregation rule set as well. Furthermore, it is interesting to explore geometry different from truncated octahedron

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as a basic unit for the lattice structure and also the possibility of combining two or more geometric types.

Lastly, this project tried to aggregating basic geometric elements into complex forms. The reversed process, in which complex structure in Physics and Biology is broken down to simple elements, can also be potential area to research.

AKNOWLEDGEMENTS The research was developed as part of the Master of Architecture Program at University of California, Berkeley. The large portions of research were conducted as part of digital design seminar and design studio under supervision of Assistant Professor Kyle Steinfeld at University of California, Berkeley. The project was awarded Sandy Hirshen Prize in 2014. All figures copyright of the authors and KL’IP.

Figure 14 System module skeleton model.

Figure 15 Cluster models with outer surface system.

Figure 16 Cluster models with inner lattice system. 10.0 ENVIRONMENTAL PARAMETRICS 2 | KIM + LEE

Figure 17 Renderings of the applications on sites.

Figure 19 1:30 scale physical model.

Figure 18 Applications of aggregation in different parameters.

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REFERENCES Banke, T. (2013). Parametric Practice (Parametri i Praksis, generativ performance i arkitektur). Ph.D. Thesis. Center for Information Technology and Architecture at The Royal Danish Academy of Fine Arts, School of Architecture, Design and Conservation. Accessed July 21, 2015. http://cita.karch.dk/Menu/PhD+Projects/ Tore+Banke+%28completed%2c+2013%29. Bohnacker, H. (2012). Generative Design: Visualize, Program and Create with Processing. New York, Princeton Architectural Press. Burry, M. and J. Burry. (2010). The New Mathematics of Architecture. London: Thames & Hudson. Davids, D. (2015). How Big Data is Transforming Architecture. Architect Magazine Online, April 23, 2015. Accessed August 1, 2015. http://www.architectmagazine.com/technology/ how-big-data-is-transforming-architecture_o. Glaeser, L. (1972). The Work of Frei Otto. New York: The Museum of Modern Art. Killian, A. (2006). Design Innovation through Constraint Modeling. International Journal of Architectural Computing 1(4): 87-105. Knowles, R. L. (1999). The Solar Envelope. Los Angeles: University of Southern California. Menges, A. and S. Ahlquist. (2011). Computational Design Thinking: Computation Design Thinking. Chichester, UK: John Wiley & Sons. Otto, F. and B. Rasch. (1995). Finding Form, Towards an Architecture of the Minimal: The Werkbund shows Frei Otto, Frei Otto shows Bodo Rasch: Exhibition in the Villa Stuck, Munich, on the occasion of the award of the 1992 Deutscher Werkbund Bayern Prize to Frei Otto and Bodo Rasch. Stuttgart: Axel Menges. Pottmann, H., A. Asperl, M. Hofer and A. Kilian. (2007). Architectural Geometry. Exton, PA: Bentley Institute Press. Roland, C. (1970). Frei Otto: Tension Structure. New York: Praeger Publishers. Stravic, M. and M. Ognen. (2010). Application of Generative Algorithms in Architectural Design. In Advances in Mathematical and Computational Methods, 12th WSEAS International Conference on Mathematical and Computational Methods in Science and Engineering, ed. L. Rogozea. University of Algarve, Faro, Portugal, November 3-5, pp. 175-180. Sugihara, S. (2014). IGEO: Algorithm Development Environment for Computational design coders with integration of Nurbs Geometry Modeling and Agent-Based Modeling. In ACADIA 14: Design Agency, Proceedings of the 34th Annual Conference of the Association for Computer Aided Design in Architecture, Los Angeles, October 23-25, pp. 23-32. Tibbits, S. (2011). A Model for Intelligence of Large-scale Self-Assembly. In ACADIA 11, Integration through Computation, Proceedings of the 31st Annual Conference of the Association for Computer Aided Design in Architecture, Banff (Alberta), October 13-16, pp. 342-349. Torquato, S. and Y. Jiao, (2009). Dense Packings of the Platonic and Archimedean Solids. Nature 460: 876- 879. DOI:10.1038/nature08239. Weiss, S. J. (2011) The Life Geometric. Domus 947. Accessed July 21, 2015. http://www.domusweb.it/en/interviews/2011/05/18/the-life-geometric.html. Witten, T. A. and L. M. Sander. (1983). Diffusion-Limited Aggregation. Physical Review B 27: 5686. 10.0 ENVIRONMENTAL PARAMETRICS 2 | KIM + LEE

DONGIL KIM SEOJOO LEE

Dongil Kim is a Director of KL’IP architecture and research office. Seojoo Lee is a Founding Director at San Francisco based He is the recipient of the Jhon. K Branner Fellowship 2015 which architecture and research office KL’IP. Previously, her allows him to develop his design theory “self-formation” through professional works include practicing at Pritzker architecture year-long research and travel funded by University of California, prize winning offices such as Richard Meier in New York and Berkeley. Dongil has won many international architecture Morphosis Architects in Los Angeles. Seojoo won several and urban design competitions and his projects have been international design competitions and her award winning design introduced in many publications. He is currently a graduate projects were published and exhibited in many cities. Seojoo student in Master of Architecture at University of California, is currently pursuing a Master of Architecture at University of Berkeley where he received T.Y Lin Prize and Sandy Hirshen California, Berkeley where she is a recipient of a Merit-Based Prize. He has practiced at many international firms including Full-Tuition Scholarship and a Design Workshop Prize in Practical Morphosis Architects in Los Angeles and REX Architecture P.C Construction in 2014. She was invited to join at the Institute of in New York. Prior to his professional experience and studies in Computational Design at the University of Stuttgart as a visiting the US, he received undergraduate degree in architecture with scholar. She graduated with a Bachelor degree in Architecture distinction and first thesis prize from the Kyung Hee University from Kyung Hee University in 2008. in Korea.

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