SPACE IS AN ENVELOPE
MSC. (Computing
and design) Post-Graduate student
School of
Architecture and Visual Art
University of East
London, UK
Osama_architect@msn.com
Hypothesis
“Fractal Geometry in Architecture/Urban
Design implies the presence of a dimension, which exists between line and area”
This
paper will attempt to pose four interrelated questions and their possible
answers and the first one will be:
1) What is the importance of Conceptual design for the architect?
A
study definition of Conceptual Design.
Conceptual Design is the part of
form-making in which designers formulate the initial parameters for an
artefact. At this stage, design ideas are set but not finalized. It can be
argued that conceptual design representations should facilitate multiple
interpretations of design elements, while at the same time, and allow these
elements to be modified in a variety of ways.
(ONTOLOGY
FOR CONCEPTUAL DESIGN IN ARCHITECTURE
SAMIR S. EMDANAT AND EMMANUEL –G. VAKALO )
(http://caadria98.env.eng.osaka-u.ac.jp/pdf/425Emdanat.pdf)
Conceptual Design in architecture/urban design is the earliest
stage where the Architect/Urban Designer finds shapes and gives birth to the
initial physical manifestation of any forms, and therefore attempts to satisfy
the occupational conflicts that result from Human Needs and the Built Environment;
essentially this method is the result of
a mathematical and geometric language (my study definition).
At
the beginning of any project an architect / urban designer normally establishes
the parameters generated by specific physical context. This is then fused with
a more generic abstract idea of the building required. An example of this is a
parking garage on a city site. This procedure can be held to be normal practise
in architectural design and is self evidentially of fundamental importance in realising
an architectural project.
In
early stages of design, especially of Conceptual Design (CD), the designer has
to make many important decisions which seek to balance the aesthetics of design
with engineering precision, but the underlying reason for this is that form
itself is really governed by geometry. Another fundamental question is how many
reiterations in this process are required for a Conceptual Design to achieve
practical fruition.
Until the advent of Modernism in architectural design the use of
geometry was universal in virtually all traditional architecture especially
in conceptual stages. Generally speaking architects thought out the major
spaces, structure and elements of their proposed physical
manifestation via geometry such as example shown which diagrams with the
potential are for generating Islamic Domes ( Figure 1 )
Figure 1
Perhaps
the dismissal of classical geometry from Conceptual
Design has been a case of the Modernist architect arbitrarily rejecting
the lessons of history. However with the discovery of
NEW MATHS in the early 1970’s or greater potential was unlocked for the
architect.
2) How does conceptual design move from two to three dimensions?
To derive area
activity from linear activity we go through what I have termed Intellectual
Compositional Architecture Activity (ICAA). There are several factors which
affect the ICAA, the first factor being the line’s direction and the second is
its proportion, the third, and most important, is human occupation or human
intellectual activity. This has the potential to take fractal geometry into
three dimensions and that particular formulation of the area could generate
fractals in architecture, building or urban design. A good example of these is
shown by Geoffrey Broadbent in his book DESIGN IN ARCHITECTURE, the
illustration shows Euler’s method of analysing the systematic usage of the
seven bridges in Konigsberg
(Figure 2, A view of
showing the seven bridges over the River Pregel)
However when we are in the process of ICAA, we
could also be focussed and autonomous
in our mathematical deliberations and thus directly generate fractals in
architecture or we could be naive, unintentional or artificial in the use of
fractals in architecture such the example shown below and this I maintain has
generally been the situation. By naive I would suggest that Eiffel Tower in
Paris. My contention is that the tower is made of many small trusses which have
been progressively scaled down to build the whole structure. But that this is
essentially two dimensional (Figures a, b)
(Figure 3-a) (Figure 3-b)
3) Is Fractal Geometry being used in conceptual design?
The Mathematical definition of a Fractal is “an object whose Hausdorff dimension is not an integer”
(http://homepages.uel.ac.uk/1953r/what2.htm). A
spiral is progressively Fractal in the way that the semi circle is scaled
up or down to create the form. Through except in very few cases e.g.
(Figure 4) an example of
the Fractal Tree
Frank Lloyd Wright in his later work (Palmer house, in Michigan) where he used
self-similarity form of triangles in the plan (Figure
A Plan of Palmer House, B self-similar triangles). Here fractal geometry was only used in two dimensions
as planning device. Where he used self-similarity form of triangles in the
plan, but that was not part of the consistent design methodology.
(Figure 5-a) (Figure 5-b) 
These attempts
have also not been very systemic, for example; in the twentieth century some
architects have researched or applied unconsciously the concept of
self-similarity.
4) How might Fractal
Geometry be used in conceptual design?
This paper will have a
philosophical context which is: how is the human intellect positioned
within the living and working environment? The issue that I will address
here is the generation of form in architecture design/urban design through
mathematical rules in general and fractal geometry in particular. This
would then be a result of an autonomous generation of form, as well as the
pre-ordering of a creation by using deliberate mathematical notation rather
than a naive and an unsystematic approach.
(Figure 6)
(An
elevation of staircase Source: J. F. Gabriel, Beyond the Cube page, 454)
City Tower Project
Philadelphia, PA; 1952-1957;
UNBUILT, by Louis Kahn
(Figure
7-a)
(Figure 7-b)
The connection between the above examples is that the
staircase which is designed for the purpose of human movement is structurally
formed on the transformation of triangles. Remarkably the unbuilt structure by
Louis Kahn uses the same concept. A further example is shown in the appendix-
see (Figures 10-a & b)
The conscious and methodical use of Fractal Geometry
in architecture can produce more than two dimensions, nevertheless to take it
into three dimensions it will be necessary to engage in ICAA and this is a
result of human occupation or human intellect as outlined above.
Human
activities, and the built environment can be expressed in terms of occupation
and the conflicts of aesthetics and human needs, the designer must resolve the issue
and satisfy these occupations. This in my opinion is a matter of Geometry. An appropriate example would be design
project set at the third year level for a law student residence in London. In
(figure 8a) is shown my initial conceptual drawing in three dimensions. It
represents a typical working design solution which most students would arrive
at early in design process (Figure 8b) is the same solution which has been
translated via the application of Fractal Geometry. This concept is now ready
for a potentially huge range of manipulation
(Figure 8a) (Figure
8b)
The Architect
is concerned with the whole rather than with the parts that is a synthesis.
Mathematics and in particular geometry is the language that can describe the
interface between the human behaviour and the built environment
In
conclusion the process of design in architecture is an equation, that has input
and output, the input could be behaviour and environment and the output is the
physical manifestation of many different forms, however the method is a
mathematical and fractal geometric language
Selected references:
Alison and Peter Smithson, The Charged Void: Architecture, 2001, (
Monacelli Press, Inc.)
Batty Michael, and P. Longley, Fractals Cities, 1994, (Academic
Press London)
Benoit B. Mandelbrot, The Fractal Geometry of Nature, nineteenth
printing, 2000, ( W.H. Freeman and Co. )
Bovill, C., Fractal Geometry in Architecture and Design. 1996
(Birkhäuser, Boston)
Broadbent Geoffrey, Design in Architecture: Architecture and the
human sciences, 1975, (John
Wiley & sons, Inc.)
Christopher Alexander, Notes on The Synthesis of Form, 1964,
(Harvard University Press)
Christopher Alexander r, The Nature of Order (2000, New York:
Oxford University Press).
Grabrel
J. Francois, Beyond the Cube, 1997, (John Wiley & sons, Inc.)
Issam
el –Said, Islamic Art and Architecture, The
System of Geometric Design , Edited by Tarek, El-Bouri & Critchlow,
1993, (Garnet Publishing Ltd.)
March, L. & Steadman, P. The Geometry of Environment, 1971,
(RIBA, London )
William I Mitchell, The Logic of Architecture, 1998, (MIT Press)
http://homepages.uel.ac.uk/1953r/thesis.htm
http://www.spongobongo.com/no9978.htm
http://www.iit.edu/~krawczyk/fract01.pdf
http://students.bath.ac.uk/ma1wgg/arc.htm
http://www.math.utsa.edu/sphere/salingar/fractals.html
http://caadria98.env.eng.osaka-u.ac.jp/pdf/425Emdanat.pdf
http://www.math.unipa.it/~grim/Jsalaworkshop
The
Sri YantraUsing 9 triangles with transform and intersect four point the down
centre with five point upper centre to from connection this is also
Fractal
The Second Arts building in
University of Bath
APPENDIX
(Figure 10-a) (Figure
10-b)
Axonometric
of second floor, shown connection to the way within the existing building, Luiz
Neto brede, Amanda Marshall from the book about ( the charged Void:
Architecture Alison and Peter Smithson)
This
building shown above is I believe anther good example of architects using
fractal geometry, in this case the concept is that of Geometric Progression
internality and in the external envelope
09 November 2004