The Ren Peoples Building: a matter of patterns

It is hard to write on a building which is not yet built. I decided to write on the Ren Peoples Building for I am very fascinated on the skin, particularly these circle packing and stacking used as patterns. This post does not deal, directly, with the Ren Peoples Building. It focuses on patterns. I will open this post with a rapid presentation of this building which is scheduled for completion for the 2010 Shanghai Expo. I, then, will examine how BIG uses pattern to shape the building. The Ren Peoples Building consists of a hotel, conference centre, water culture center and meeting facilities, designed by one of the most talented firms of architecture of his generation BIG. 
This signature architectural statement is composed of two types: the tower and the bridge merged into one. The most significant particularities of this building are the sensitivity to process, form, pattern considerations.
The shape
Firstly, the shape of this building can, topologically, be described as a 3D Ren pictogram character. This form is amazing but poses important issues in terms of technique, and design. As we will see further, the shape is based on a system of stacking and packing of different sizes of circles. BIG’s interest for form-finding is particularly salient here. The shape is the same of that of a project the firm previously failed in Sweden. 
The ren character is one of the simple pictogram character in Chinese and Japanese languages. You need to start with the first stroke then the second one to form this character to write the pictogram character ren in Chinese as well as in Japanese, as shown in the illustration below. While ren pictogram character is basic, it, however, plays an important role in Asian countries as it represents the human being, people. 

The evolution of softwares and technologies makes easier the conception of complex forms like the Ren Peoples Building. One needs to scale 3 times in order to get the Chinese proportion. There is a constant, in the projects of BIG and many architects of this generation to recycle failed projects or elements like the «staircase» and the «mountain».
The architecture firm used the Feng Shui five elements, that is, water (shui 水), metal (jin 金), earth (tu 土), wood (mu 木), fire (huo 火). The shape of the building itself functions as body (shenti 身体) and mind (tounao 头脑), hence its reference to human (ren 人). For Chinese, this 250,000 square meter project «bridges the gap between traditional China and progressive China.»
Architecture, BIM and scripts
The building as I mentioned above has a complex form. Since 1990s, there is an increasing interest for scripted design methodologies, in particular, genetic algorithms based on a biological model (Morphogenesis), mathematics and geometric computing, and advanced parametric modeling tools like Rhino script, Gehry Technologies Digital Project, Bentley Software, or Maya/Mel Script. As former Head of Research and Innovation at OMA Cynthia Ottchen notes, «the profession’s further development of specialist software for structural and environmental analyses and simulations, and building information modeling (BIM) parametisation of material properties as well as fabricated and assembly constraints, has elevated practical, technological data to a newly privileged status.» It is now easier to design complex forms. A large number of research labs such as Material Ecology (Neri Oxman), Ocean North (Michael Hensel and Defne Sunguroglu), Evolutionary Strategies (Achim Menges), Zaha Hadid Architects, and Biothing (Alisa Andrasek) illustrate this recent trend for complex form-finding, using scripts and algorithms in architecture. Cynthia Ottchen calls this new trend the «Petabyte Age». BIG belongs to this Petabyte Age even though its architectural projects are less to do with morphogenetic forms in comparison with Architecture Firms like SHoP and Asymptote. 
What these architects appreciate with this new tool BIM, is that it «opens up a new optimistic world of design possibilities.» BIM offers more options and more types of information for architecture.
To a certain extent, it seems not surprising that architects integrate complex softwares from the onset of the design process to the production phase. It rather seems be a need. As professor Klaus Bollingerm, Professor Manfred Grohmann and Oliver Tessmann argue, «Architectural design needs to incorporate complex organisational and functional requirements, and therefore constitutes a recurrent negotiation of analysing existing and requisite conditions as well as generating and evaluating possible responses.» And, as I pointed out above, the use of these softwares makes easier the design of complex shapes.
Another aspect of this building is the envelope. Ren Peoples Building’s skin is made of different size of circles.
Patterns: Circle-packing structure and the role of discrete mathematics
The use of circles as «tools» for the design the Ren Peoples Building is particularly interesting. Circles serve as «an opportunity for an exercise in ‘packing and stacking’ different sizes of circles». Now that architects have the right tools at their disposal to realize complex structure, it is easier to automate and optimize the circles through gathering and scaling in response to stresses. The use of algorithms and script is particularly notable: the building is embedded into a sequence of circles of different diameters — from small to large — that lie at various distance in response to stresses as just mentioned. The following section will explain the fascinating process of circle packing and stacking.
This analysis is, for the most part, based on research on Apollinian networks undertaken by José S. Andrade Jr, Hans J. Herrmann, Roberto F. S. Andrade and luciano R. da Silva, among others.
This arrangement of circles on surfaces is derived to ‘Circle-packing’ meshes. As Helmut Pottmann mentioned, «CP meshes enjoy a high aesthetical value and lead to various remarkable surface patterns as well as to a number of unsolved mathematical problems.» to pack circle, adds Pottmann, neighbouring in-circles of CP meshes must be tangent to each other in order to form a arrangement of circles. In mathematics, such arrangement form is called «packing». This arrangement of circles as windows arbitrates the building’s internal and external environment and participate to the definition of the shape of the building.
The basic formula of circle packing can be written as follows: r(i)+r(j) ≤ Sqrt[x[i]-x[i]]^2 +[y[i]-y[i]^2 for i, j =1, …, k & i < j. The result is the series of pictures below:

a square packing and a hexagonal packing. 
This series of pictures shows a very basic arrangement of circles that has been made with  a software of mathematics (*). The original code was made for a unit circle. The aim of these pictures is to give a simple example of circle packing in a unit rectangle. Looking at the distribution of circles of the Ren Peoples Building envelope, one notices that this topology looks like the Apollonian networks. There is a large number of research on circle packing, among others José S. Andrade Jr, Hans J. Herrmann, Roberto F. S. Andrade and luciano R. da Silva who have written a very interesting essay on Apollonian networks. They explain that this topology is a class of networks «that can be either deterministic or random; [They] are scale-free, display small world effect, can be embedded in an Euclidean lattices, and show space-filling as well as matching graph properties.» Apollonian networks are from the ancient Greek mathematician Apollonius of Perga. I take this illustration that can be found in Andrade Jr, Herrmann, Andrade and da Silva’s paper «Apollonian networks» into example.


This illustration shows how to pack circles using algorithm*. Three circles touch each other and the hole between them is filled by the circle that touches all three. This connection forms again three but much smaller holes. These smaller holes are one more time filled each in the same way as shown in the below illustration. 

Classical Appollonian packing
© "Apollonian networks", José Andrade Jr et al., June 2004

Looking attentively at Ren Peoples Building, one will note the connection of these circles made according to Apollonian networks system. As these researchers assert, the circle size distribution is «a power-law» with exponent. 
Conclusion (for now): collaboration with engineers
The design and fabrication of this geometrically complex structure depends on intense collaboration between architects, engineers and mathematicians. BIG collaborates with AKT for Adams Kara and Taylor, one of the world’s most sought-after engineers. This agency regularly collaborates with innovative architecture firms such as Zaha Hadid, FOA, Foster + Partners, to quote but a few. As Hanif Kara, one of the three thinkers/engineers of AKT argues, patterns now can be central in the form-finding. Patterns must be understood as tool «not only to affect the conceptualisation of form, but also in the use of nature of materials of the micro/macroscale». To a certain extent, the recent technological advancements enable the construction of complex building. «Straightforward correlation between patterns and any engineering can be a very reductive path, but for structural engineers the triumph of recent technologies is proving to be the simple, most powerful force in shaping new understandings and control of patterns.» Architects and engineers use various tools from CAD to mathematics and geometric computing. Now complex diagrams such as Lindenmeyer System (L-System), Voronoi, Sierpinski cubes, force fields, attractors, Apollonian networks, Fibonacci series, protein folds, or els blobs and virus and micro-organisms are now new challenge for architects.
Looking at the various illustration — sketches, plans, drawing, etc. — I am convinced that the Ren Peoples Building envelope and shape give the building its particularity and its elegance.

To be continued…

Code name: Ren Peoples Building
Architect: BIG
Client : -
Size : 250.000 m2
Location: Shanghai
Status: ongoing (2010)

(*) Various mathematics softwares such as Mathlab, Mathematica, Processing are used to create complex structures. 
(*) It took me more than three months to come with a basic apollonian network, as I'm not a mathematics-friend. Unfortunately, first the apollonian network example that I used for my code was based on a circle unit. I could modify it for a rectangle unit but the code now contains errors.
Form-finding : Form-finding is a design method that uses the ability of materials to self-organize in relation to extrinsic influences.
CP meshes: A circle packing is a non-overlapping arrangement of circle inside a given boundary.
FEM : Finite Element Modeling
Ingels Bjarke, Yes is More: An Archicomic on Architectural Evolution, Evergreen, 2009, 400 pages.

Architectural Design
Bollinger Klausm Grohmann, Tessmann Oliver, «Form, Force, Performance, Multi-Parametric Structural Design», in Architectural Design, vol. 78, no 2, March/April 2008, pp.20-25.
Ottchen Cynthia, «The future of information modelling and the end of theory. Less is limited, more is different», in Architectural Design, Vol. 79, No 2, March/April 2009, pp. 22-27.
Garcia Mark, «Reductive engineering patterns. An interview with Hanif Kara», in Architectural Design, Vol. 79, No 6, November/December 2009, pp. 66-73;
Zaera Polo Alejandro, «Patterns, Fabrics, Prototypes, Tessellations», in Architectural Design, Vol. 79, No 6, November/December 2009, pp. 18-27.
Colletti Marjan, Jencks Charles, Moussavi Farshid, «The return of ornaments», in Icon, December 2009, pp. 67-71;
Wiles William, «Bjarke Ingels. The young architect making global success look easy», in Icon, Issue 79, January 2010, pp. 38-44;
Volume Magazine
Inaba Jeffrey, Ingels Bjarke, «Bjarke Ingels. Yes Men», in Volume Magazine, Vol. 13, December 2007, pp. 48-51.
Pdf papers:
Andrade Jose S. Jr, Herrmann Hans J., Andrade Roberte F., S., Silva (da) Luciano R., «Apollonian networks», June 2004, Pdf;
Baram Mahmoodi Reza., Herrmann Hans J., «Random bearings and their stability», August, 2005, pdf;
Baram Mahmoodi Reza., Herrmann Hans J., Wackenhut, M., «Searching for the perfect packing», in ICA-1, 2003, pdf;
Baram Mahmoodi Reza., and Herrmann Hans J., «Space-filling bearings in htree dimensions», in Physical review Letters, vol. 92, no4, 2004, pdf;
Baram Mahmoodi Reza, Herrmann Hans J., «Self-similar space-filling packings dimensions», December 2003, pdf;
Aström J.A., Herrmann H.J., Timonen J., «Granular packings and fault zones», in Physical Review Leters, vol. 84, no 4, January 2000 pdf;
Roux Stéphane, Hansen Alex, Herrmann Hans J., Vilotte Jean-Pierre, «A model for gouge deformation: implications for remanent magnetization», in Geophysical Research Letters, col. 20, no 14, July, 1993, pp. 1499-1502, pdf;
Herrmann Hans J., «Space-Filling Bearings», pdf;
Herrmann H. J., Mantica G., Bessis D., «Space-filling bearings», in Physical Review Letters, vol. 65, no 26, December 1990, pdf;
Herrmann Hans, Gallas Jason A. C., Lind Pedro G., «Coherence in scale-free networks of chaotic maps», in Physical Review, E70, 1, 2004, pdf.


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