Posts tagged ‘Nature’

March 17, 2013

Fractal Forest (‘Monalisa’) Pavilion: MadeExpo2012, Milan

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Last year in 2012, it was an amazing experience on working in a workshop conducted by ‘Wood Lab’ of ‘Politecnico di Torino’.  A poplar plywood company financed WoodLab for designing a pavilion to exhibit and promote their architectural, sculptural and furniture products. It was a heavy creative exercise to come up with a unique but sensible design idea. Finally, an interesting design concept came to mind and took shape as ‘why don’t an architectural piece can be a manifestation of a story of poplar tree itself’? Poplar grows from its seed, and then gradually it becomes young plant and finally turns into a perennial woody tree.  Poplar trees altogether live in a family making a forest, and finally they are used for making plywood needed for building construction, furniture, and so on. This whole story had to be turned into a shape, a design, a pavilion.

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The challenge of composing this story was done by using two different mathematical design vocabularies –  ‘Algorithms’ and ‘Fractals’. Algorithms helped us to represent the ‘growth’, whereas  fractals helped us to represent the ‘nature’, the forest by tree branches.

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The representation of seed was a small ply panel. Then the panel started growing by increasing its size, then it was budding with two new small branches, it kept on growing and then started taking shape of a tree with the increasing of more branches. Functionally, the seeds were designed for sitting benches, whereas the networks of branches provide the feeling of shelter under the shadow in a poplar forest. Poplar fruited us with furniture and it was represented by benches.  Curvilinear shapes on plan represented the sense of nature.

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To realize the concept into design form, we used computational and parametric techniques in computer by using ‘rhinoceros’ with the help of ‘grasshopper’ and ‘python’. In ‘python’ we scripted the shape of trees with growing branches. Then ‘grasshopper’ was used for making algorithmic benches and arrangement of trees.

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However, after the exhausting creative and designing phases, the next main challenge was how to construct the pavilion by showing the versatility of poplar ply. For this, a structural analysis program ANSYS was used for assessing its stress and bending strength behaviors.

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We started making small scale model to show the freeform character of poplar ply. We made the model in FabLab by using CNC cutter. After that, we made a real scale prototype of one tree module to test its bending strength including other structural potency.

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In October 2012, finally the pavilion was installed in prestigious international ‘MadeExpo’ Exhibition in Milan, Italy. An awesome outcome was ready, and our hardworking were ended by attracting and fascinating a large crowd of visitors !!

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March 15, 2013

Fractal Architecture and Nature’s Geometry

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Fractal geometry, a branch of mathematics developed in 1970s [Mandelbrot 1975, 1984, Edgar 1993] studies abstract configurations characterised by self-similarity patterns and recursive growth [Mandelbrot 1984]. Fractal objects show the properties of being exactly or nearly the same at every progressive scale. From the mathematical point of view, fractal objects are sets that have fractional dimension, so that they are intermediate objects between one and two dimensional shapes (as lines and surfaces) or two and three dimensional forms (as surfaces and solids) [Batty 1985, Falconer 2003]. Recently, thanks to the development of advanced computers, the domain of fractal geometry applications has covered a wide set of scientific discipline, ranging from mathematics [Berkowitz 1998], natural sciences [Vicsek et.al. 1994, Sornette 2004], pure and applied sciences [Peitgen 2004], biology and medicine [Losa & Nonnenmacher 2005], to engineering [Dekking, et. al. 1999, Leung 2004, 2011] and architecture[Bovill 1996, Ostwald 2001]. Fractal geometry is specifically used as theoretical as well as technical tools for the analysis, interpretation and description of complex, natural and human phenomena, where continuous or Euclidean geometry are failed to describe.

Architecture is closely associated with geometry, and that is the reason this new concept of fractal geometry can be used for the advancement of architectural and urban designs. In a very wide range of phenomena, the geometry of nature displays fractal-like properties [Mandelbrot 1975, 1984]. Any form, shape and pattern of a natural object are its phenomenological outcomes [Bertol 2011] and therefore, it is believed that there is a strong correlation between biological forms and mechanical phenomena [Thompson 1917, Turing 1954, Durgun 2007]. Accordingly, fractal geometry of nature possibly has a connection with nature’s structural and mechanical behavior. But, there is a recent debate about the fractal geometry and its definition to explain the form and pattern of nature. Adrian Bejan critically argues in his much acclaimed ‘constructal law’ that it is the ‘laws of thermodynamics’ which decides the geometry and form of the natural objects [Bejan 1994], and there is no logical connection between nature’s forms and fractal geometry [Bejan 2000].

For many centuries, a variety of nature’s forms, which in many cases present fractal geometry in their structural appearance, such as trees, cells, crystals etc., have been creatively used by architects and engineers in projects like shells, light-weight structures, arcs, tents and bridges (e.g. Stuttgart Airport, Stuttgart; Galleria & Heritage Square, Toronto; Heart Tent, Riyadh) [Blanco 2001, Otto 1995, Portoghesi 2000]. In the past, several technical ways were exercised to connect fractal concepts with architecture by the method based on physical modelling process. But, nowadays, a procedural generative approach based on a composition of mathematical functions can be practiced by using the advantages of contemporary computer technology for connecting the fractal concept with architecture (e.g., Federation Square, Storey Hall in Melbourne; etc.) [Huylebrouck & Hammer 2006].

The main intention of my research is to increase the knowledge and understanding of nature’s fractal phenomena and forms, and try to apply the results for a better comprehension of human and social behaviour and to the architectural design. Biomimetics is the study of the structure and function of biological systems as models for the design and engineering of materials and machines. Therefore, the area of my research is oriented towards ‘Biomimetic Architecture’ but by means of computational and algorithmic techniques, used as advanced tools for the study, analysis and forms generation.

References:

ENGINEERING:

BARNSLEY M. F. (1988), “Fractals Everywhere”, Academic Press, Inc.

BATTY M. (1985). “Fractals – Geometry between Dimensions”. New Scientist (Holborn Publishing Group) 105 (1450): 31.

BEJAN, A. (1997) “Advanced Engineering Thermodynamics”. (2nd ed.). New York: Wiley.

BEJAN, A. (2000), “Shape and Structure from Engineering to Nature”, Cambridge University Press.

BERKOWITZ J. (1998), “Fractal Cosmos: The Art of Mathematical Design”, Amber Lotus.

DEKKING M., et. al. eds. (1999), “Fractals: Theory and Applications in Engineering”, Springer.

DURGUN M.E. (2007), “Geometric Generalization of the Structure of Nature: A theory of everything and a mathematical formulation of a philosophy”,http://www.unitytheory.info/ggsn.pdf.

EDGAR G. A., ed. (1993), “Classics on Fractals”, Addison-Wesley.

FALCONER K. (2003), “Fractal Geometry, Mathematical Foundations and Applications”, 2nd ed. Wiley, London.

LEUNG A Y T, , WUB G R, ZHONG W F. (2004), “Exterior Problems of Acoustics by Fractal Finite Element Mesh”, Journal of Sound and Vibration, Volume 272, p 125–135.

LEUNG A Y T. (2011), “Fractal Finite Element Method for Thermal Stress Intensity Factor Calculation”, ICF11 Proceeding.

LOSA, G. A.; NONNENMACHER, T. F., eds. (2005). “Fractals in Biology and Medicine”. Springer.

MANDELBROT B. (1982), “The Fractal Geometry of Nature”, San Francisco: W.H., Freeman.

PEITGEN H, JÜRGENS H, SAUPE D. (2004), “Chaos and Fractals: New Frontiers of Science “ 2nd ed. Springer.

SORNETTE (2004). “Critical Phenomena in Natural Sciences: Chaos, Fractals, Self-Organization, and Disorder: Concepts and Tools”. Springer. pp. 128–140.

THOMPSON, D W. (1992), “On Growth and Form”, Dover reprint of 1942 2nd ed. (1st ed., 1917)

TURING, A. M. (1954). “The Chemical Basis of Morphogenesis”. Philosophical Transactions of the Royal Society of London 237 (641): 37–72

VICSEK T, SHLESINGER M, MATSUSHITA M. (1994), “Fractals in Natural Sciences”, World Scientific Publishing Co Pte Ltd

VON B. P. (2009), “A Geometric Comparison of Branching Structures in Tension and Compression versus Minimal Paths”, University of Michigan, Ann Arbor, MI, USA.

VYZANTIADOUA M.A., AVDELASA A.V., ZAFIROPOULOSB S. (2007), “The Application of Fractal Geometry to the Design of Grid or Reticulated Shell Structures’, Computer-Aided Design, Volume 39, p 51–59.

ARCHITECTURE:

BEN-HAMOUCHE M. (2011), “Fractal Geometry in Muslim Cities, Succession Law Shaped Morphology”, Nexus Network Journal, Volume 13, No 1.

BERTOL D. (2011), “Form, Geometry, Structure – From Nature to Design”, Bentley Institute Press.

BOVILL C. (2000), “Fractal Geometry as Design Aid”, Journal for Geometry and Graphics, Volume 4 No. 1, p 71-78.

BOVILL C. (1996), “Fractal Geometry in Architecture & Design”, Birkhäuser, Boston.

HUYLEBROUCK D, HAMMER J. (2006), “From Fractal Geometry to Fractured Architecture: The Federation Square of Melbourne”, The Mathematical Intelligencer – Volume 28, No. 4, p 44-48.

JOYE Y. (2011), “A Review of the Presence and Use of Fractal Geometry in Architectural Design”, Planning and Design, Volume 38, No. 5, 2011, p 814-828.

JI Z., ZIYU L., XIAOZHOU L. (2011), “Remote-Sensing Expert Classification of Land Use/Land Cover Types Using Fractal Dimensions Over A Subtropical Hilly Region in China”, Fractals, Volume 19, No. 4 p 407–421.

LORDICK D. (2009), “Architectural Fractals”, Rutgers University, New Jersey.

LORENZ W E. (2004), “Fractal Geometry As An Approach To Quality In Architecture”, 1st International Conference on Fractal Founder 21st Century Architecture and Environmental Designations f.

OSTWALD M. J. (2001), “Fractal Architecture”: Late Twentieth Century Connections Between Architecture and Fractal Geometry”, Nexus Network Journal – Volume 3, No. 1. p 73.

PADRÓN V., SALINGAROS N. A. (2000), “Ecology and the Fractal Mind in the New Architecture: a Conversation”, RUDI — Resource for Urban Design Information.

PORTOGHESI P. (2000), “Nature and Architecture”. London: Thames & Hudson.

SALINGAROS N. A. (1999), “Architecture, Pattern and Mathematics”, Nexus Network Journal, Vol. 1, p 75-85.

SALINGAROS N. A. (1998), “A Scientific Basis for Creating Architectural Forms”, Journal of Architectural and Planning Research, Volume15, p 283-293.

VAUGHAN J., OSTWALD M. J. (2012), “Using Fractal Analysis to Compare the Characteristic Complexity of Nature and Architecture: Re-Examining the Evidence”, Architectural Science Review, Volume 53, No 3.