Michael J. Ostwald
"Fractal Architecture": Late Twentieth
Century Connections Between Architecture and Fractal Geometry
Department of Architecture
Faculty of Architecture, Building and Design, University of Newcastle
University Drive, Callaghan, NSW 2308 AUSTRALIA
For more than two decades an intricate
and contradictory relationship has existed between architecture
and the sciences of complexity. While the nature of this relationship
has shifted and changed throughout that time a common point of
connection has been fractal geometry. Both architects and mathematicians
have each offered definitions of what might, or might not, constitute
fractal architecture. Curiously, there are few similarities between
architects' and mathematicians' definitions of "fractal
architecture". There are also very few signs of recognition
that the other side's opinion exists at all. Practising architects
have largely ignored the views of mathematicians concerning the
built environment and conversely mathematicians have failed to
recognise the quite lengthy history of architects appropriating
and using fractal geometry in their designs. Even scholars working
on concepts derived from both architecture and mathematics seem
unaware of the large number of contemporary designs produced
in response to fractal geometry or the extensive record of contemporary
writings on the topic. The present paper begins to address this
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.
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. 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.
THE RISE OF FRACTAL ARCHITECTURE: 1978-1988
In 1977 the scientist
Benoit Mandelbrot's seminal work Fractals: Form, Chance, and
Dimension, the first English language edition of his 1975
Les Objects Fractals: Forme, Hasard et Dimension, was
published to much critical acclaim. Although Mandelbrot had published
some sixty-three papers prior to this date, the formal science
of Chaos Theory is widely considered to be defined by this work.
However, like the mythopoeic "death of modernism"
manifest in the demolition of Yamasaki's Pruitt-Igoe Housing
in 1972, this birthdate for Chaos Theory is contentious. What
is certain is that within Fractals: Form, Chance, and Dimension,
Mandelbrot not only combines his observations of the geometry
of nature for the first time but he also makes the first of a
number of well documented forays into art and architectural history
and critique. Specifically, Mandelbrot concludes his introduction
to the book with a discussion of architectural styles in an attempt
to differentiate between Euclidean geometry and fractal geometry.
In this discussion he states that "in the context of architecture
[a] Mies van der Rohe building is a scalebound throwback to Euclid,
while a high period Beaux Arts building is rich in fractal aspects."
While this is not the first instance of a scientist or mathematician
working within the sciences of complexity venturing into architectural
territory, it is nevertheless the first clearly recognised example
of the attempt to combine or connect architecture with fractal
Less than twelve months after the English
language publication of Fractals: Form, Chance, and Dimension
the architect Peter Eisenman exhibited his House 11a for
the first time. A few weeks later, in July of 1978, House
11a became a central thematic motif in Eisenman's housing
design produced during the Cannaregio design seminar in Venice.
Although this project was not publicly exhibited until April,
1980 it nevertheless marks the first widely published appropriation
by an architect of a concept from complexity theory. Specifically,
Eisenman appropriated the concept of fractal scaling - a process
that he describes philosophically as entailing "three destabilizing
concepts: discontinuity, which confronts the metaphysics
of presence; recursivity, which confronts origin; and
self-similarity, which confronts representation and the
House 11a, a
composition of Eisenman's then signature "L"s combines
these forms in complex rotational and vertical symmetries. The
"L" is actually a square which has been divided into
four quarters and then had one quarter square removed. Eisenman
viewed this resulting "L" shape as symbolising an "unstable"
or "in-between" state; neither a rectangle nor a square.
The three dimensional variation is a cubic octant removed from
a cubic whole, rendering the "L" in three dimensions.
Each "L" according to Eisenman represents an inherently
unstable geometry; a form which oscillates between more stable,
or whole, geometric figures. The eroded holes of two primal "L"s
collide in House 11a to produce a deliberately scale-less
object which could be generated at whatever size was desired.
This is exactly what Eisenman attempted for a competition for
housing in Venice. His Cannaregio scheme ignored the existing
fabric of Venice and sought rather to affirm the presence, or
absence, of Le Corbusier's unbuilt hospital plan for the site.
Through the creation of a fictional past, a false archaeology,
the proposal voids the grid of Corbusier's hospital leaving absence
in place of fictional presence. "These voids act as metaphors
for the subject's displacement from its position as the centered
instrument of measure. In this project architecture becomes the
measure of itself." Then Eisenman placed a series of identical
objects at various scales throughout the Cannaregio Town Square.
Each of these objects is a scaling of House 11a, the smallest
object being man height but obviously not a house, the largest
object plainly too large to be a house, and the house sized object
paradoxically filled with an infinite series of scaled versions
of itself rendering it unusable for a house. The presence of
the object within the object memorialises the original form and
thus its place transcends the role of a model and becomes a component
and moreover a self-similar and self-referential architectonic
component. House 11a is effectively scaled
into itself an infinite number of times forming a kind of fractal
In the twenty years
that followed Eisenman's publication of House 11a more
than two hundred architectural designs or works of architectural
theory have been published which have laid claim, in some way,
to aspects of fractal geometry or some related area of the sciences
of complexity. While Eisenman has produced more than a dozen
projects that have relied upon fractal geometry and its characteristics
a large number of international architects, including Asymptote,
Charles Correa, Coop Himmelblau, Carlos Ferrater, Arata Isozaki,
Charles Jencks, Christoph Langhof, Daniel B. H. Liebermann, Fumihiko
Maki, Morphosis, Eric Owen Moss, Jean Nouvell, Philippe Samyn,
Kazuo Shinohara, Aldo and Hannie van Eyck, Ben van Berkel and
Caroline Bos, Peter Kulka and Ulrich Königs and Eisaku Ushida
and Kathryn Findlay, have followed his lead. Two of Eisenman's
projects provide useful points of reference for fractal architecture
during this period.
Eisenman's 1985 project Moving
Arrows, Eros and other Errors (or the Romeo and Juliet
project) is a turning point in the development of concepts appropriated
from Complexity Science into architecture. At the core of the
generative methodology underlying this project is the process
of scaling. For Eisenman fractal scaling confronts
"presence, origin, and the aesthetic object"  in the
context of the site, the building program, and its means of representation.
While scaling is already present in various ways in Eisenman's
earlier projects it is in Moving Arrows, Eros and other Errors
that it takes on a greater importance. Betsky records that by
[u]sing a formula developed by the scientist Benoit Mandelbrot,
which determines the 'self-sameness' or autonomous replication
inherent in certain figures, [Eisenman] mapped plans of vast
territories over each other. This technique questioned architecture's
relation to a 'normal scale' and 'problematized' the concept
of human perspective.
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,
[f]or five centuries the human body's proportions have
been a datum for architecture. But due to developments and changes
in modern technology, philosophy, and psychoanalysis, the grand
abstraction of man as the measure of all things, as an originary
presence, can no longer be sustained, even as it persists in
the architecture of today. In order to effect a response in architecture
to these cultural changes, this project employs an other discourse,
founded in a process called scaling.
Moving Arrows, Eros and other Errors is the result
of a dual appropriation of fractal scaling and the narrative
structure of Romeo and Juliet; as drawn from three different
versions of the story by Da Porto, Bandello and Shakespeare.
The literary narrative is used by Eisenman to dramatise the meeting
of the "the 'fictional' and the 'real'" . In doing
so Eisenman attempts to deny the possibility of the origin of
a concept meeting reality and thereby destabilise a conventional
paradigm in architecture. In the same way Eisenman appropriates
fractal geometry to undermine the scale specificity of conventional
anthropomorphic architecture; another long unchallenged paradigm
in architecture. Anthony Vidler suggests that both of these attempts
In the complex process by which the Romeo and Juliet landscape
is generated, there is no sense of an aesthetic or even a natural
'origin' that gives it meaning. Rather, the forms are produced
in a seemingly implacable autogeneration of grids, surfaces,
and their punctuation that stems from an equally autonomous procedure
called by the author 'scaling.' Referring to the random and fractal
geometries of Mandelbrot, this method applies a notion of continuum
to all scales and all intervals between scales that represent
objects in nature, and produces new objects by virtue of their
The result is nothing stable, nor anything
preconceived; it exists as a complex artifact marked by the traces
of the procedures that generated it.
Perhaps the culmination of Eisenman's fascination with fractal
architecture is the project Choral Works, which Eisenman
designed with the assistance of the philosopher Jacques Derrida.
In Choral Works Derrida's seminal text on Plato's Timeaus
combines with the semiotic play upon Chora, Choral, etc., to
create a twin textual and formal (or geometric) example of a
fractal en abime. In this project, actually not a building
but a small garden, both time, in the form of precedents, and
space, as a dislocation of Le Corbusier's rediscovered Venetian
hospital, are self-referential and are present in a variety of
controlled iterations. Eisenman claims that
At each scaling [of the design] aspects of the changes
in time, changes in rivers, borders, etc. are introduced. Thus
reverberations occur not only in scale but in time, resulting
in self similar, but not self same analogies. It is as if there
were infinite reflections in an imperfect mirror.
Scaling, self-similarity and self-referentiality are all present
in Choral Works although now these operations have taken
on a more philosophical and less geometric presence. Choral
Works is less obviously derived from geometric iterations
than House 11a or Moving Arrows, Eros and other Errors.
It must be remembered that in the late eighties many philosophers
including Gilles Deleuze and Felix Guattari (whose works were
becoming widely influential at that time ) had appropriated
fractal geometry to explain complex and often unrelated concepts.
However, while architects enthusiastically embraced fractal geometry
in the early to mid eighties, this situation was to turn around
dramatically in the early nineties, although signs of a change
had started to appear much earlier.
THE FALL OF FRACTAL ARCHITECTURE: 1989-1999
As early as 1988 some
architectural writers were deriding their colleagues' obsessions
with Chaos Theory, nonlinear dynamics and fractal geometry. At
this time, Michael Sorkin, then architectural critic for the
Village Voice, opens his critique of the work of Coop
Himmelblau with an apologetic warning that he intends to resort
to a discussion of Complexity Science and fractals. Not only
does his manner suggest some latent embarrassment about the topic
but he even takes the unusual step of attempting to justify his
actions with the claim that they are relevant to the profession
- an argument that seems out of context given Sorkin's otherwise
aggressive approach. In Post Rock Propter Rock: A Short
History of Coop Himmelblau Sorkin declares that "[c]haos
may be a little overfamiliar nowadays, especially in its studied
inscription in architecture. However, the idea behind this latest
upheaval in physics does have real implications for us."
Barely two years later,
in 1990, Aaron Betsky described Eisenman's Biocentre at
the J. W. Goethe University of Frankfurt in terms of a conventional
geometric system that is corrupted by fractal geometry. "To
safeguard [the] architecture from disappearing completely
Eisenman then meshed fractal geometry with" Euclidean geometry,
"'infecting' one geometry
with an equally available
one."  Here fractal geometry is metaphorically
described as a form of virus or parasite inflicting architecture
- conventional Euclidean geometry is the antidote. Fractal geometry,
the source of the outbreak, is not necessarily critical to the
design; rather it is merely the most "available" of
a number of possible sources of "infection". The tide
had started to turn and the relationship between architecture
and the sciences of complexity was now increasingly viewed with
cynicism and suspicion.
By 1993 a few architects
were even starting to categorically deny any connection between
their design philosophy, Complexity Science and fractal geometry.
For example, the Iranian born graduates of Cornell University,
Gisue Hariri and Mojgan Hariri, open their 1993 manifesto for
architecture with the statement that "[w]e do not believe
in Chaos, we do not follow Trends, and we despise
Kitsch."  By highlighting these three terms
in italics Hariri and Hariri not only emphasise these concepts
at the expense of their argument, they also infer that Chaos
Theory and fractal geometry are merely a trend that, for them,
is equated with kitsch. Once they have carefully distanced themselves
from this perceived taint they feel that they can state the theoretical
position that governs their design work.
It is the intension [sic] of our work to bring together
in an equilibrium the Mind that disintegrates and categorizes
and the Soul that is in constant search for universal
unity of all things and events
Examples of this concept
The Unification of the Opposites can be found in modern
physics at the sub-atomic level where particles are both destructible
and indestructible; where matter is both continuous and discontinuous,
and force and matter are different aspects of the same phenomenon.
Life in general and Architecture in particular are like force
and matter intertwind [sic]. It is the events and the smallest
experiences in life that form Visions of architecture.
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. 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"  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.
Here is a man who scatters chaos on paper and talks about
randomness and fractional theory. He calls the scatter the plan
of a building. Anything will do--twigs purloined from a pigeon's
nest, notes transcribed from the Song of Songs--a scribble he
did with his eyes shut, like a shaman in a trance drawing in
the dust of the Nevada desert. His building is built. It appears
like a mirage in the wasteland of the city, a histrionic essay
of joints and materials. He claims the building is ambiguous-he
says it is like the chaos of modern life-he tells us all that
it is profound.
Although Shepheard's description is strongly reminiscent of
Sorkin's 1991 critique of the "daffy postfunctionalist methodology
anything!)"  -- a design
process that culminates in tracing the "outline of last
night's schnitzel"  -- it is the way in which the use
of fractal geometry in architecture starts to be associated with
caricature that is consequential.
By the time
Alberto Pérez-Gómez presented Architecture as
Science: Analogy or Disjunction at the 1994 Anyplace
conference in Canada, he had to make a deliberate effort to discuss
Chaos Theory and fractal geometry as a side-line or accessory
to the rest of his presentation on the differences between phenomenological
hermeneutics and theories of science. In this way he effectively
distances his argument from the taint of nonlinearity while judiciously
relying on it to support his position. Pérez-Gómez,
realising that what he is about to do is "unfashionable"
, commences his comments on fractal
geometry with the informal statement that before progressing
to the main theme of the paper he "would like to explore
the potentially fascinating consequences of Chaos Theory for
architecture. This [being] a popular topic these days."
 Pérez-Gómez's outline
of the paradigm shift associated with Chaos Theory and fractal
geometry is an exemplary model of accuracy and scholarship; he
has even read the key scientific texts. Yet, throughout the paper,
his description is laced with a delicate tracery of sarcasm and
wit. Chaos theory embodies "a formidable and exciting realization"
he states. "We have at last 'discovered' that the ancient
analogical assumptions that drove traditional architecture and
science were not merely foolish dreams."  Architects
are described as playing with these ideas, using them as a form
of authority to legitimise their actions and augment their philosophies.
"I cherish", he says, such "stories about a living
world and the life of minerals, about the body without organs,
about nature as a machine without parts."  The tone
of Pérez-Gómez's paper is difficult to dissect.
He clearly believes that fractal geometry and Complexity Science
have much to offer yet his manner is cynical, or at best, wistful.
In the same year, 1994, Christoph Langhof published
Imagination is more Important than Knowledge where he too apologises
for lowering the tone of a journal to discuss fractal geometry.
"Our world" he says, "- if you would excuse the
trendy word - is becoming more and more fractal."
 Why would people like Pérez-Gómez
and Langhof feel obliged to apologise for discussing geometry?
Perhaps the reason may be traced to the rapid growth of interest
in complexity. As Paul-Alan Johnson records, Chaos Theory may
have only been "formulated in the 1970s" but within
a decade it had become "a booming business"  world-wide.
Yet within architecture, it had shifted smoothly from being the
favoured theoretical influence of the early eighties, to being
the conceptual bête noire of the early nineties.
When in 1995 Charles Jencks belatedly published a
polemical call for architecture to model a new, cosmogenic or
fractalesque aesthetic, (a position that he had developed from
his study of the sciences of complexity) the critics were sufficiently
forewarned that they were able to respond with a flurry of damning
reviews. Perhaps this reaction was complicated
by the cult of personality surrounding Jencks, or maybe it was
justified. But the fact remains that his call for a fractal architecture
of complexity was not only savaged by the critics, it appears
to have been largely ignored by an architectural profession that
now considered fractal geometry dated.
first recorded reference to fractal geometry in architecture
barely fifteen years had passed before these once cherished concepts
had become anathema. However the cycle from enthusiastic acceptance
to almost complete rejection is not complete and signs have begun
to appear which suggest that a cautious re-acceptance of complexity
is occurring. In 1996 when Carl Bovill published his impressively
researched book Fractal Geometry in Architecture and Design,
a new stage in the ongoing curious and contradictory relationship
between architecture and complexity theory was reached. Bovill,
more than any other writer in architecture, immerses himself
in the mathematics of complexity. He argues that fractal geometry
is a powerful tool for architects, but a tool that has to be
used wisely. To date this understated work has been well received,
perhaps because its modest aims are well supported in the text.
Whether or not Bovill's research signifies a genuine resurgence
of interest is unclear at this time. Similarly not all architects
stopped designing fractal buildings.
the nineties the architectural firm Ushida Findlay produced a
series of highly inventive projects using Golden Sections and
fractal geometry (often in combination) to generate powerful
spatial forms. Their S Project, an urban master plan,
presents fractal geometry in a particularly compelling manner.
The S Project is a major transport interchange for Tokyo
located at the intersection of a number of arterial roads and
a rail line. The design explores the notion of "city as
house"; an idea given renewed currency by the realisation
that natural systems posses similar patterns at multiple scales.
It is this same realisation, that fractal geometry operates at
many scales, that is lacking in so many architectural works that
claim a fractal heritage. In many ways, because large scale landscape
features are amongst the most recognisable fractal forms, the
master plan is an obvious subject for the use of fractal geometry.
In the S Project, Ushida Findlay are able to propose a
fractalesque network that incorporates systems of "flow
and clustering" operating simultaneously at many scales.
Regardless of whether the design caters for road traffic or pedestrians
it provides a system that "can accommodate the innumerable
encounters of freely moving persons who drift throughout the
city."  Ushida Findlay describes the S
Project as a vessel designed to accommodate the "Brownian
movement" of people, cars, trains and information. The result
is "a new terrain - a new kind of topography"  that possesses
dynamic similarities at many scales.
For almost twenty years there has existed
an intricate, constantly shifting relationship between architecture
and fractal geometry. At times this dependence is diffuse, and
modes of theoretical transference are subtle, symbolic or semiological.
At other times wholesale appropriations of geometry take place
and large fragments of theory are pirated away from their originating
discipline and used opportunistically. As Peter Downton evocatively
dark nights knowledge is sometimes smuggled over
the difficult terrain at disciplinary borders by radical thinkers.
It is urgently introduced in clandestine meetings and infiltrated
by stealth into the mainstream of the discipline without the
blessing of the powerful upholders of conventional orthodoxy,
the high priests of the dominant paradigm.
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.
period of this interdisciplinary relationship few from one side
have commented on the other side's position. That is, few architects
have discussed the way in which architecture is used by scientists
and mathematicians working in the sciences of complexity and
conversely, even fewer scientists or mathematicians have noted
the way in which architects borrow scientific or geometric theories
from complexity. A small number of architectural writers, including
Peter Fuller, Charles Jencks, John Kavannagh, Paul-Alan Johnson
and Norman Crowe  are clearly aware that another side
of the relationship exists, that mathematicians have made incursions
into architecture. But only Pérez-Gómez
has even obliquely considered this relationship in a critical
sense, concluding deftly that "Mandelbrot's view [of architecture]
is hardly different from Prince Charles's opinion" and that
"the relationship between geometry and architecture imagined
by Mandelbrot and some of his architectural fans is thoroughly
classical, simply mimetic in the traditional sense." 
Examples of the obverse case, that is mathematicians realising
that architecture has appropriated from fractal geometry, are
even more uncommon. Only the scientist Peter Coveney and the
journalist Roger Highfield seem to be aware of, or willing to
remark on, the fact that architects are developing their own
interpretations of Complexity Science and fractal geometry. In
a brief survey in their 1996 book Frontiers of Complexity,
the Search for Order in a Chaotic World, Coveney and Highfield
comment on developments in the non-scientific fields that have
arisen from a study of complexity. They state, with some consternation,
that "[c]omplexity has offered a 'cosmogenic' cocktail -
the motifs of fractals, catastrophic theory, and chaos - that
has caught the imagination of architects." Their promising
footnote leads only to Jencks's The Architecture of the Jumping
Universe; a minimal recognition but nevertheless better than
These fragments of
history are pieced together here to give a brief overview of
the often tortuous alliance, the sporadic shifting from amour
to intrigue, that has characterised the relationship between
architecture and fractal geometry for more than twenty years.
The simple reconstruction offered here, while representative
of the major shifts in the relationship, is necessarily superficial.
Not all architects turned away from fractals in the early nineties
and, in the last five years, the signs of renewed enthusiasm
for complexity are chimerical at best. In time it might be possible
to tell which way the relationship will shift. Whether or not
it will mature and stabilise (the state wherein cross-appropriation
is mutually recognised) remains largely unclear. Similarly, while
this general history, which is woven from fragments, records
a reasonable overview of the changes that have occurred it can
not and will not suffice to explain all of the roles that fractal
geometry has been forced to play in architecture, or architecture
in fractal geometry.
 See: Michael J. Ostwald
and R. John Moore, "Charting the Occurrence of Non-Linear
Dynamical Systems into Architecture." In Simon Hayman ed.
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
 Charles Jencks, The Language of Post-Modern Architecture
(London: Academy Editions, 1987), 9-10. return
 Benoit B. Mandelbrot, The Fractal Geometry of
Nature (New York: W. H. Freeman and Company, 1982), 23-24.
return to text
 Jean-François Bédard, ed. Cities
of Artificial Excavation: The Work of Peter Eisenman, 1978-1988
(Montreal: Canadian Centre for Architecture, 1994), 54. return to text
 In Violated Perfection Betsky incorrectly
refers to Eisenman's Romeo and Juliet project, Moving
Arrows, Eros and other Errors, as being produced in 1976.
If this date were correct it would make the "Romeo and Juliet"
project the first instance of an architectural appropriation
from chaos theory, some twelve months before the English publication
of Fractals: Form, Chance, and Dimension. The real date of the
exhibition of Moving Arrows, Eros and other Errors is 1986 thereby
confirming Eisenman's House 11a (or the contemporaneous
design for Cannaregio housing) as the first widely published
instance of an architectural appropriation from chaos theory.
Cf. Aaron Betsky, Violated Perfection: Architecture and the
Fragmentation of the Modern (New York: Rizzoli, 1990), p. 146; cf.
Peter Eisenman, Moving Arrows, Eros and other Errors (London:
Architectural Association, 1986). return
Peter Eisenman, "Eisenmanesie." Architecture
+ Urbanism, Extra ed. (August 1988): 70. return
 Ibid., 14. return to
 Charles Jencks, "Deconstruction: The Pleasures
Of Absence". in Andreas Papadakis, Catherine Cooke, and
Andrew Benjamin eds., Deconstruction: Omnibus Volume.
(London: Academy Editions, 1989), 119-131. return
 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., Architectural Science,
Informatics and Design (Shan-Ti: Chinese University in Hong
Kong, 1996), 137-148. return to text
 Peter Eisenman, Moving Arrows, unpaginated. return
 Peter Eisenman, "Eisenmanesie", 70. return to text
 Aaron Betsky, Violated Perfection
, 146. return to text
 Peter Eisenman, "Eisenmanesie", 70. return to text
 Ibid., 71. return to
 Anthony Vidler, .The Architectural Uncanny: Essays
in the Modern Unhomely (Cambridge, Massachusetts: MIT Press,
1992), 130-131. return to text
 Jacques Derrida and Peter Eisenman, Chora L Works,
- Jeffrey Kipnis and Thomas Leeser eds. - (New York: The Monacelli
Press, 1997). It should be noted that Eisenman variously calls
the project "Choral Works" or "Chora l works"
(the latter being a Greek pun). Choral works is usually
the correct title for the project. Kipnis uses the pun instead
as a title for the book (not the project) because the book looks
at Greek philosophy as well as Eisenman's project. return
 Peter Eisenman, "Eisenmanesie", 137. return to text
 See: Gilles Deleuze and Felix Guattari, A Thousand
Plateaus: Capitalism and Schizophrenia. Trans. Brian Massumi.
(Minneapolis: University of Minnesota Press, 1987); Gilles Deleuze
and Felix Guattari, What is Philosophy? Trans. Hugh Tomlinson
and Graham Burchill. (New York: Verso, 1994). return
 Cf. Alan Sokal and Jean Bricmont, Intellectual
Impostures: Postmodern Philosophers' Abuse of Science, (London:
Profile, 1998). return to text
 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 - Mea Culpa. Often the
people who damn fashion are those who are about to be victims
" Cf. Michael J. Ostwald, Peter Zellner and
Charles Jencks, [An interview with Charles Jencks.] "An
Architecture of Complexity: Interviewing Charles Jencks."
Transition, No. 52-53 (1996): 28-35, quote on p. 29. return to text
 Michael Sorkin, Exquisite Corpse: Writings on
Buildings (New York: Verso, 1991), 346-7. return
 Aaron Betsky, Violated Perfection
return to text
 Gisue Hariri and Mojgan Hariri, "Architects'
Philosophy." Architecture + Urbanism, No. 274 Is.
7 (July 1993): 81. return to text
 Ibid. return to text
 Cf. Gisue Hariri and Mojgan Hariri, "Villa,
The Hague: The Netherlands, 1992." Architecture + Urbanism,
No. 274 Is. 7 (July 1993): 118-121; cf. Kenneth Frampton, "On
the Work of Hariri and Hariri." Architecture + Urbanism,
No. 274 Is. 7 (July 1993): 82-83. return
 Paul Shepheard, What is Architecture: An Essay
on Landscapes, Buildings, and Machines (Cambridge, Massachusetts:
MIT Press, 1994), 15. return to text
 Ibid., [my italics]. return
 Michael Sorkin, "Nineteen Millennial Mantras."
In Peter Noever ed., Architecture in Transition: Between Deconstruction
and New Modernism (Munich: Prestel, 1991), 111. return
 Ibid. return to text
 Alberto Pérez-Gómez, "Architecture
as Science: Analogy or Disjunction." In Cynthia C. Davidson
ed. Anyplace, (Cambridge, Massachusetts: MIT Press, 1995),
67. return to text
 Ibid., 70. return to
 Ibid. return to text
 Ibid. return to text
 Christoph Langhof, "Imagination is More Important
than Knowledge." Curtin University Architecture Document
(1994): 41. [my italics] return
 Paul-Alan Johnson, The Theory of Architecture: Concepts,
Themes and Practices (New York: Van Nostrand Reinhold, 1994),
242. return to text
 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.]
GSD News: Harvard University, Graduate School of Design
(Fall 1995): 40-41; Peter Davey, "The Scientific American."
Architectural Review, Vol. 198 No. 1183 (September 1995):
84-85; Christian Norberg-Schulz, "The Jumping Jencks."
Byggekunst: The Norwegian Review of Architecture, Vol.
77 No. 7 (1995): 399; Giles Worsley, "The Architecture of
the Jumping Universe." Perspectives on Architecture,
Vol. 2 No. 15 (July 1995): 18; Richard Weston, "A New Architectural
Style is Born-Again," Architects' Journal, Vol. 201
No. 21 (May 25, 1995): 52. return
 Ushida, Eisaku. Findlay, Kathryn. S Project Program.
Gallery MA Books. Tokyo. 1996. unpag. return
 Ibid. return to text
 See: Ostwald, Michael J., "Fractal Traces:
Geometry and the Architecture of Ushida Findlay." In Leon
van Schaik ed., Ushida Findlay, (Barcelona: 2G, 1998).
136-143. return to text
 Peter Downton, "The Migration Metaphor in Architectural
Epistemology." In Stephen Cairns and Philip Goad eds., Building
Dwelling Drifting: Migrancy and the Limits of Architecture.
(Melbourne: Melbourne University, 1997), 82. return
 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, 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), 119. return to text
 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. Accessory/Architecture. Volume 1. (Auckland:
University of Auckland, 1995), 69-80; Michael J. Ostwald and
R. John Moore, "Unravelling the Weave: An Analysis of Architectural
Metaphors in Nonlinear Dynamics," Interstices, Vol.
4 (1997): CD ROM. return to text
 Alberto Pérez-Gómez, "Architecture
", 72. return
 Peter Coveney and Roger Highfield, Frontiers
of Complexity: The Search for Order in a Chaotic World (London:
Faber and Faber, 1996), 339. return
 Stewart and Golubitsky in Fearful Geometry
also comment on appropriations from mathematics by architects
but they are talking about Euclidean geometry not fractal geometry.
See: Ian Stewart and Martin Golubitsky, Fearful Symmetry:
Is God a Geometer? (London: Penguin, 1993). return
FOR FURTHER READING. The following works cited in this article can be ordered
from Amazon.com by clicking on the title
- Benoit B. Mandelbrot, The
Fractal Geometry of Nature (New York: W. H. Freeman and
- 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
ON THE WWW
Spanky Fractal Database
Geometry of the Mandelbrot Set.
Pictures and Animations.
Fractal Geometry and Architecture
of Maryland Newsletter: Carl Bovill, Fractal Geometry in Architecture
fractals and architecture by Mark Jeffery
ABOUT THE AUTHOR
J Ostwald lectures
in architectural history and theory at the University of Newcastle
in Australia. He has written extensively on the relationship
between architecture and geometry. He is the book review editor
of the Nexus Network Journal.
The correct citation for
this article is:
J. Ostwald, ""Fractal Architecture": Late Twentieth
Century Connections Between Architecture and Fractal Geometry"
, Nexus Network Journal, vol. 3, no. 1 (Winter 2001),
Copyright ©2001 Kim Williams
Comment on this article
Sites on the WWW
Conference and Exhibit Reports
The Virtual Library