Reconstruction of an Ancient Islamic Fractal Structure - using AutoCAD/Rhino

Exploration of Ancient Fractal Spatial Constructions

Islamic Arches

[Reference: Necipoglu, G. The Topkapi Scroll - Geometry and Ornament in Islamic Architecture, Santa Monica: The Getty Center for Art and

the Humanities, 1995]

The construction of ancient islamic ‘arched-structures’ from simple two dimensional drawings occurred years ago, obviously without any computer technological imput, and thus makes the works of architecture seem even more unbelievable and amazing to the contemporary eye. ‘The black ink out- lines of these pasted drawings, which generally provide the repeat unit of the overall design, were once again generated by various grid systems and often high-lighted with red and other lively colours.’2 The symmetry and repetition effectively aided the design and construction of these architectural elements, whilst representing the divinity of god and nature through the beatuy of unifi ed symmetry.

Fractal Geometry Analysis

Characteristics of Fractal Compositions

[Reference Wolfgang, E. Lorenz. ‘Fractals and Fractal Architecture’. Vienna: University of Technology, 2001]

- Fractals have infinite length, when viewed at a small scale

- They can’t be described by one perameter, like euclidean geometry however in 2D each point of a fractal can be mapped with two co-ordinates (x,y).

- Their composition is defined by a heirachy of geometric size that usually possesses elements all of the same proportion.

- The rate at which the geometry of the elements in the fractal composition decrease/increase in size can be regarded as ‘the rate of infinity’1.

- The ‘self-similarity’ characteristic of fractals enables them to be measured in relation to themselves ( ie. self comparitive analysis.)

(Below: sketches of analysis)

History of Fractals in Architecture

Historically, fractals have been found to be present world-wide, particularly in places such as, Africa, Europe and India. However their uses and origins differ. For example, 'African fractals are more directly informed by nature' and their composition is derived from the social structure of their day-to-day village life and patriarchal values. Where as the Indian architectural use of fractals demonstrates their Hindu belief in the infinite cosmos, which is thought to be composed entirely of fractal elements. On the other hand, the use of fractals in European architecture is greatly varied ranging from the organized hierarchy of St Peter's Dome (plan image above), the complicated fractal ornamentation of

Gothic, Renaissance and Baroque Cathedrals, to the ambiguous scale of K. Malevich's Arkitectonic models (perspective above) and the complex fractal construction of the Eiffel tower(detail below). Reference: http://classes.yale.edu/Fractals/Panorama/Architecture/Arch/Arch.html

use of ULTRAFRACTAL for 3D modelling

This video shows how elaborate fractal geometry can become controlled through the use of computer programs (in this case 'Ultrafractal') that enable a virtual visualization of the architecture.

Use of this software could perhaps allow us to explore and analyse the composition of ancient architectural buildings (that possess elements of fractal geometry) more efficiently.

Fractal Architecture

The last article by Jean-Michel Kantor raised issues of spatial associations, configurations, networking and hidden geometry within architecture. It also questioned the 'liberty of movement' that the design possesses according to its geometries (hidden or evident).

This initiated my interest in the study of geometry in architectural design, particularly fractal geometry. 'A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"^[1] a property called self-similarity.' ( Reference: http://en.wikipedia.org/wiki/Fractal )

Fractal Geometry can be seen in the above image of the facade of Federation Square amongst other contemporary buildings. In my studies I will attempt to further research into the computer process/s by which these geometries are generated, investigating either surface or volumetric architectural compositions.

My interest in topological architecture has taken me to this reading below;

http://www.emis.de/journals/NNJ/Kantor.html

In it Kantor raises several issues regarding; Liberty of movement in architecture in regards to geometry, theories on networking and virtual proprioception.

All which have the potential to be tested using either built architectural forms or techniques that are used for form generation.