Michael J. OstwaldDepartment of Architecture Faculty of Architecture, Building and Design, University of Newcastle University Drive, Callaghan, NSW 2308 AUSTRALIA
This paper focuses primarily on architectural appropriations of fractal geometry to briefly describe more than twenty years of "fractal architecture" and to identify key trends or shifts in the development, acceptance and rejection of this concept. The aim of this paper is to provide an overview for both architects and mathematicians of the rise and fall of fractal architecture in the late twentieth century. The present paper has three clear limitations or provisions which define its extent and approach. Firstly, it does not question the validity of any specific claims from either architects or mathematicians even though there is evidence to suggest that claims made by both sides are debatable.[1] Secondly, the paper is concerned only with conscious attempts to use fractal geometry to create architecture. A number of prominent examples of historic buildings which exhibit fractal forms have been proposed by both architects and mathematicians. For the purposes of this paper these proposed fractal buildings, including various Medieval castles, Baroque churches, Hindu temples and works of Frank Lloyd Wright or Louis Sullivan, are not considered to be a consciously
created fractal designs even if they display an intuitive grasp
of fractal geometry. For this reason, the origins of conscious
fractal architecture cannot have occurred until after fractal
geometry was formalised by Benoit Mandelbrot in the late 1970s
even though Georg Cantor, Guiseppe Peano, David Hilbert, Helge
von Koch, Waclaw Sierpinski, Gaston Julia and Felix Hausdorff
had all studied aberrant or mathematically "monstrous"
concepts which are clear precursors to fractal geometry. A final
provision for this paper is concerned with the relationship between
fractal geometry and the sciences of complexity. While mathematicians
and scholars have valued fractal geometry in its own right, architects
have generally valued it more for its connection to Chaos Theory
and Complexity Science. This is because contemporary architects,
like many historic architects, have little interest in geometry
or mathematics per se, but value geometry for its ability
to provide a symbolic, metaphoric, or tropic connection to something
else. Thus, for modern architects fractal geometry provides a
connection to nature or the cosmos as well as a recognition of
the global paradigm shift away from the views of Newton and Laplace.
For this reason, the vast majority of architects mentioned in
this paper view fractal geometry as an integral part of, or sign
for, Chaos Theory and Complexity Science.
But why appropriate scaling? The feedback mechanisms and fractal forms associated with order in seemingly chaotic systems are, for Eisenman, a means of destroying the stability of architecture and undermining the anthropomorphic orthodoxy that has sustained architectural theory since Vitruvius. Eisenman argues that,
Perhaps the culmination of Eisenman's fascination with fractal
architecture is the project
Scaling, self-similarity and self-referentiality are all present
in
It is ironic indeed that the remainder of their philosophical position is derived from a loose understanding of quantum physics, sub-atomic particle theory and natural systems theory.[25] Nevertheless, they are not alone in their attempts to deny any connection between their architecture and Complexity Science. Perhaps one of the reasons for this dramatic disavowal might be found in the growing number of satirical descriptions of the relationship between architecture and fractal geometry. Paul Shepheard suggests that in 1994 the constant quest for the new resulted in "a furor of nonconsensus" [26] in architectural theory. In order to illustrate the confusion of the time he provides five derogatory descriptions of un-named architectural role models. The first description, which appears to be a synthesis of Peter Eisenman, Daniel Libeskind and Morphosis, commences with a veiled insult.
Although Shepheard's description is strongly reminiscent of
Sorkin's 1991 critique of the "daffy postfunctionalist methodology
(form follows … anything!)" [28] -- a design
process that culminates in tracing the "outline of last
night's schnitzel" [29] -- it is the way in which the use
of fractal geometry in architecture starts to be associated with
caricature that is consequential.
At other times analogies are drawn, both by mathematicians
and by architects, that call upon the opposing body of theory
to submit to an array of duties, ranging from menial, pedagogical
roles to heroic, evidential ones.
Architectural Science: Past, Present and Future. (Sydney:
Department of Architectural and Design Science, University of
Sydney, 1993), 223-235; Michael J. Ostwald and R. John Moore,
"Fractalesque Architecture: An Analysis of the Grounds for
Excluding Mies van der Rohe from the Oeuvre." In A. Kelly,
K. Bieda, J. F. Zhu, and W. Dewanto, eds. Traditions and Modernity
(Jakarta: Mercu Buana University, 1996), 437-453; Michael J.
Ostwald and R. John Moore, "Icons of Nonlinearity in Architecture:
Correa - Eisenman - Van Eyck." In Vikramaditya Prakash ed.
Theatres of Decolonization: (Architecture) Agency (Urbanism).
Vol. 2 (Seattle: University of Washington, 1997), 401-422; Michael
J. Ostwald and R. John Moore, "Spreading Chaos: Hayles'
Theory and an Architecture of Complexity." Transition,
No. 52/53 (1996): 36-53. return to
text[2] Charles Jencks, [3] Benoit B. Mandelbrot, [4] Jean-François Bédard, ed. [5] In [6]Peter Eisenman, "Eisenmanesie." [7] Ibid., 14. [8] Charles Jencks, "Deconstruction: The Pleasures
Of Absence". in Andreas Papadakis, Catherine Cooke, and
Andrew Benjamin eds., [9] When examined in detail, from a scientific perspective,
the concept of "fractal architecture" is problematic.
See: Michael J. Ostwald and R. John Moore, "Fractal Architecture:
A Critical Evaluation Of Proposed Architectural And Scientific
Definitions." in Kan, W. T. ed., [10] Peter Eisenman, Moving Arrows, unpaginated. [11] Peter Eisenman, "Eisenmanesie", 70. [12] Aaron Betsky, Violated Perfection …, 146. [13] Peter Eisenman, "Eisenmanesie", 70. [14] Ibid., 71. [15] Anthony Vidler, . [16] Jacques Derrida and Peter Eisenman, [17] Peter Eisenman, "Eisenmanesie", 137. [18] See: Gilles Deleuze and Felix Guattari, [19] Cf. Alan Sokal and Jean Bricmont, [20] Ironically, as Jencks notes in a 1996 interview
with the author of this paper, Sorkin, who has expressed his
reluctance to affix the label of chaos theory on any work of
architecture for fear that it might be read as over fashionable,
should himself by 1993 be producing designs that are in part
inspired by his readings in complexity. Jencks states that "it
is completely and utterly rich that someone like Michael Sorkin,
who is now seven years later designing chaos cities, is claiming
that it is out of date. He should have had a little more insight
into himself, than to have denigrated the idea in other peoples
work and then done it. Come on - [21] Michael Sorkin, [22] Aaron Betsky, Violated Perfection … , 148.
[23] Gisue Hariri and Mojgan Hariri, "Architects'
Philosophy." [24] Ibid. [25] Cf. Gisue Hariri and Mojgan Hariri, "Villa,
The Hague: The Netherlands, 1992." [26] Paul Shepheard, [27] Ibid., [my italics]. [28] Michael Sorkin, "Nineteen Millennial Mantras."
In Peter Noever ed., [29] Ibid. [30] Alberto Pérez-Gómez, "Architecture
as Science: Analogy or Disjunction." In Cynthia C. Davidson
ed. [31] Ibid., 70. [32] Ibid. [33] Ibid. [34] Christoph Langhof, "Imagination is More Important
than Knowledge." [35] Paul-Alan Johnson, The Theory of Architecture: Concepts,
Themes and Practices (New York: Van Nostrand Reinhold, 1994),
242. [36] See for example the critiques of Peter Davey, Christian
Norberg-Schulz, Giles Worsley and Richard Weston; Peter Davey,
"The Architecture of the Jumping Universe." [Review.]
[37] Ushida, Eisaku. Findlay, Kathryn. [38] Ibid. [39] See: Ostwald, Michael J., "Fractal Traces:
Geometry and the Architecture of Ushida Findlay." In Leon
van Schaik ed., [40] Peter Downton, "The Migration Metaphor in Architectural
Epistemology." In Stephen Cairns and Philip Goad eds., [41] The architectural historian Crowe discusses Mandelbrot's
views on architecture in some detail as a means of explaining
a different way of appreciating patterns at multiple scales.
Crowe mostly reiterates Mandelbrot's assertions for architecture
without comment although he finally concludes that for Mandelbrot
"the presence of a natural sense of visual detail that relates
to scale may well explain why such buildings as prismatic glass
skyscrapers soon become boring to many people. This insight might
also be considered for our negative reaction to a building or
interior that has too much ornament and so appears to us as chaotic."
Cf. Norman Crowe, [42] Two papers by the author with R. John Moore published
in 1995 and 1997 are, to date, the most detailed works on the
topic. See: Michael J. Ostwald and R. John Moore, "Mathematical
Misreadings in Non Linearity: Architecture as Accessory/Theory,"
in Mike Linzey ed. [43] Alberto Pérez-Gómez, "Architecture
as Science …", 72. [44] Peter Coveney and Roger Highfield, [45] Stewart and Golubitsky in - Benoit B. Mandelbrot,
*The Fractal Geometry of Nature*(New York: W. H. Freeman and Company, 1982) - Jean-François Bédard, ed.
*Cities of Artificial Excavation: The Work of Peter Eisenman, 1978-1988*(Montreal: Canadian Centre for Architecture, 1994) - Aaron Betsky,
*Violated Perfection: Architecture and the Fragmentation of the Modern*(New York: Rizzoli, 1990) - Anthony Vidler,
*The Architectural Uncanny: Essays in the Modern Unhomely*(Cambridge, Massachusetts: MIT Press, 1992) - Jacques Derrida and Peter Eisenman,
*Chora L Works*, Jeffrey Kipnis and Thomas Leeser eds. (New York: The Monacelli Press, 1997) - Paul Shepheard,
*What is Architecture: An Essay on Landscapes, Buildings, and Machines*(Cambridge, Massachusetts: MIT Press, 1994) - Paul-Alan Johnson,
*The Theory of Architecture: Concepts, Themes and Practices*(New York: Van Nostrand Reinhold, 1994) - Norman Crowe,
*Nature and the Idea of a Man Made World: An Investigation into the Evolutionary Roots of Form and Order in the Built Environment*(Cambridge, Massachusetts: MIT Press, 1995) - Peter Coveney and Roger Highfield,
*Frontiers of Complexity: The Search for Order in a Chaotic World*(London: Faber and Faber, 1996) - Ian Stewart and Martin Golubitsky,
*Fearful Symmetry: Is God a Geometer?*(London: Penguin, 1993) - Carl Bovill,
*Fractal Geometry in Architecture and Design*
Nexus Network Journal.
Copyright ©2001 Kim Williams top of
page |
NNJ HomepageAbout
the AuthorComment on this articleRelated
Sites on the WWWOrder
books!Featured
ArticlesDidacticsGeometer's
AngleBook
ReviewsConference and Exhibit ReportsThe Virtual LibrarySubmission GuidelinesTop
of Page |