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:

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

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

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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.

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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.

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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.