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6 Frontality, Rotation and the Whites

6 Frontality, Rotation and the Whites

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9.6 Frontality, Rotation and the Whites


viewers’ (2004: 49–51). This incompatibility between the architect or artist’s desire

to present their work in an idealised way, and the viewer’s incapacity to experience

it in this way, was interpreted as representing the ‘separation of the self and the

world’ (Golub 2004: 200). In contrast, it was thought that buildings which exhibit

rotation accommodate a ‘self’ that was part of the ‘world’, not idealised into a

single universal or normative-height, masculine viewpoint. In Five Architects,

Frampton describes rotation as ‘asymmetrical spinning’ (1975: 9) akin to Rowe’s

idea of ‘a building as an entity gyrating around horizontal (and vertical) axes’

(1996: 192). Rowe defines rotation as ‘architectural contrapposto’ which ‘presumes

a pictorial or a sculptural condition of permanent argument’ wherein the building ‘is

simultaneously static and is also set in motion’ (1996: 192). Frampton’s argument is

not that the works of the Whites all embrace the same approach to rotation, but

rather that they use different types of contrapposto to resist the frontal proclivities of

early Modernism. This could be reframed as the hypothesis that the designs of

Eisenman, Hejduk and Meier show a more consistent formal expression when

viewed from multiple perspectives than from a single perspective. If this hypothesis

is true, it should be measurable using a variation of the fractal analysis method

which compares frontal and rotational views.


The Analytical Method

This section of the chapter analyses rotational views of Eisenman’s House I,

Hejduk’s House 7 and Meier’s Hoffman House. While the previous section of the

chapter analysed the four cardinal elevations of these houses, this section compares

an additional twelve elevations derived from the sub-cardinal points, while continuing to employ an orthogonal viewpoint. Thus, for this purpose, elevations were

prepared of each house from the following orientations: north (N), north-northeast

(NNE), northeast (NE), east (E), east-northeast (ENE), east-southeast (ESE),

southeast (SE), south-southeast (SSE), south (S), south-southwest (SSW), southwest (SW), west-southwest (WSW), west (W), west-northwest (WNW), northwest

(NW) and north-northwest (NNW). The fractal dimensions of these forty-eight

elevations (thirty-six sub-cardinal and twelve cardinal) are then measured, graphed

and compared.

Eisenman’s House I Rotated

Eisenman states that House I ‘differed from the traditional idea of a formal essence’

because it has ‘no specific form … but rather could be considered as unformed

possibilities for organization’ (1999: 62–63). In terms of frontality and rotation,

such an ambiguous house might be difficult to analyse, which is probably what

Frampton means when he says that in House I ‘the play between frontalization and

rotation amounts to an ever present conflict which at no point is ever allowed to be


9 The Avant-Garde and Abstraction

Fig. 9.15 House I, results for four cardinal elevations plus twelve sub-cardinal elevations

Fig. 9.16 House I, west-southwest elevation (top) and northwest elevation (bottom)

resolved’ (1975: 9). The House I results are the least consistent of the three analysed

using rotation (Figs. 9.15 and 9.16). The first three cardinal elevations, north, east

and south, all provide low results, under D = 1.2835, and, apart from the ESE

result, all others are higher than these three cardinals. However, what might appear

to be a rising and falling pattern as the viewer rotates around the axis of the house—

from the north to the south moving in an anti-clockwise direction—then suddenly

changes, with further rotation towards the west. Between SSW and NNW the

9.6 Frontality, Rotation and the Whites


highest set of results 1.3893 < D < 1.4576 are found. Interestingly, this part of the

house is the ‘back’, in functional terms the private address, while the eastern

elevation, with the lowest overall score (D = 1.2458), is the public entrance, or

‘front’ of the house.

Hejduk’s House 7 Rotated

According to Stan Allen Hejduk’s architecture ‘does not fix the gaze of the spectator in a “face-to-face” confrontation, but multiplies and redirects the gaze’ (1996a:

94). At the heart of this cryptic commentary on Hejduk’s work is the contested

relationship between frontality and rotation. Frampton maintained in Five

Architects that the frontality of the ‘total mass’ of Hejduk’s architecture is ‘in

contrast to the rotation of its extremities’ (1975: 9). Allen rejects this position

maintaining that in order for a design to be read, ‘the basic orthogonality of the

cubic form must be maintained’ (1996a: 94). For Allen, each elevation in Hejduk’s

architecture ‘establishes, through the rectilinearity of its geometry, a condition of

frontality regardless of the viewer’s position’ (1996a: 94). This difference of

opinion, between Frampton and Allen, can be productively assessed in relation to

House 7.

The set of sixteen results for House 7 are all in a tight range (R[E%] = 6.87), with

the difference between the cardinal and sub-cardinal elevations being less than

±3.44 % (Figs. 9.17 and 9.18). The four cardinal elevations are marginally less

complex than their proximate sub-cardinal neighbours, with indirect angles of

viewing adding only slightly to the overall visual complexity. Thus, the fractal

dimension results for the rotation of House 7 describe the design as one which

doesn’t change markedly as it is viewed from different angles, echoing Allen’s

proposal that in Hejduk’s domestic architecture, every different rotational position

constitutes a variation of the same frontal faỗade.

Fig. 9.17 House 7, results for four cardinal elevations plus twelve sub-cardinal elevations


9 The Avant-Garde and Abstraction

Fig. 9.18 House 7, northeast elevation (left) and west-southwest elevation (right)

Meier’s Hoffman House Rotated

Meier’s Hoffman House was selected for this analysis because it features his first

exploration of the impact of diagonal planning, a development that seems to

directly address the ideas of frontality and rotation raised by Frampton. The

Hoffman House has intersecting 90° and 45° angled plans, (see the plan in

Table 9.7) with the siting and landscaping arranged so that the southeast elevation

is the most visible from the road, where it ‘appears as a three-dimensional

abstraction of interlocking geometries’ (Meier 1984: 35). The house is then

approached by way of a driveway from the south and, as the visitor circles the

building, the southeast faỗade becomes dominant again, before the entrance, in the

eastern faỗade, is nally reached.

The range of rotational results for Meier’s Hoffman House, while still comparable (R[E%] = 15.05), cannot be said to be in a close range, and they do not form

any clear pattern (Figs. 9.19 and 9.20). These fluctuating results may, however,

reflect Cassarà’s argument that in the Hoffman House, ‘frontality and rotation

confront one another …, simply syllabising the grammar and syntax of the construction’ (1997: 30). While not forming a distinct pattern, the results do show a

significant lowering in complexity to the southern extremities, where the elevations

face the approach path. Viewed in this way, as a visitor would experience the house,

its formal complexity increases when seen from the road (DE = 1.2759), along the

driveway (DE = 1.2777) and to the front door (DE = 1.3794). Rather than forming a

data set that reflects a regular house that has been rotated, this data is perhaps more

similar to the experience of the approach path studied in Chap. 8 on Frank Lloyd

Wright, but from an orthogonal exterior view.

9.6 Frontality, Rotation and the Whites


Fig. 9.19 Hoffman House, results for four cardinal elevations plus twelve sub-cardinal elevations

Fig. 9.20 Hoffman House, east-northeast elevation (top) and south-southwest elevation (bottom)

Deciphering Frontality Versus Rotation

As Frampton no doubt realised when he wrote his chapter for Five Architects, there

is no consistency in the way these designers approach the relationship between

frontality and rotation. Moreover, as many scholars have observed, the very


9 The Avant-Garde and Abstraction

concepts of frontality and rotation may be more appropriate for the criticism of art

or sculpture—objects typically viewed from fixed, external viewpoints—than

architecture. As Robert Somol suggests, terms such as frontality and rotation are

merely an ‘articulation of a series of dialectics’, exemplifying the ‘logic of contradiction and ambiguity’ (Somol 1998: 86–87). Rosemarie Bletter also takes issue

with Frampton’s argument, declaring that his terms ‘are too broadly defined’ (1979:

205) to be useful.

The results in this chapter show that the orthogonal views of Hejduk’s House 7

and Eisenman’s House I are generally less complex than the rotated views, but this

could be a by-product of the nature of any cubic building. When a cube is viewed

askew, its visual complexity is likely to increase by virtue of the compressed

version of the adjacent face now being apparent. In contrast, the results for the

irregular form of Meier’s Hoffman House do not isolate the cardinal views in the

same way. Overall, these three sets of results could be interpreted as implying that

Hejduk’s and Eisenman’s houses actually represent special types of frontality, while

Meier’s demonstrates rotation.

According to Bletter, Frampton argues that in ‘Hejduk’s projects the notion of

frontality and rotation is resolved, while in the work of Eisenman … and Meier the

intrinsic conflict of these two systems of organization remains’ (1979: 205). This is

true only if by ‘resolved’, Frampton means that Hejduk’s architecture, when viewed

through rotation, begins to create a single faỗade experience. In that sense,

Eisenmans and Meiers works are less resolved, although the latter’s work most

clearly demonstrates the impact of formal rotation in its elevations, and in the

former’s may, as Frampton also implies, be most evident in its interior qualities,

although this is something which cannot be tested using the present data.



There are several remarkable features in the data presented in this chapter, including

the incredible consistency of Meier’s early houses, which feature a composite range

of <5.34 % and for the optimal sub-set, <0.54 %. Given different sites, client needs

and budgets, Meier’s early houses display an unwavering commitment to a clear set

of aesthetic values and goals. Eisenman’s houses display a different but equally

notable set of characteristics. For example, in House IV the range between the set of

elevations was <0.66 % and for the plans <3.41 %, both of which are striking in

isolation, but the difference between the two is also <2.14 %. The equivalent difference between the average plan and elevation results for Eisenman’s House VI is

even less at <1.64 %. If ever a pair of houses could be considered abstract sculptural objects, capable of being turned on their sides while still resembling their

original states, then House IV and House VI are it.

Hejduk’s architecture is less consistent across the set of his five works, but

within specific houses, and especially when viewed under rotation, they exhibit

some equally significant characteristics. For example, the rotational analysis of his

9.7 Conclusion


House 7 illuminates a complex argument that has ebbed and flowed around his

work for several decades. What is so special about its rotational properties, when

his work seems to be the most orthogonal of the group? The answer is that the

characteristic complexity of his architecture remains stable as it is viewed under

rotation, being within a range of <5.02 %. We have interpreted this, in the context

of past critiques of his architecture, as implying the presence of a single underlying

elevation treatment, which is most visible through movement.

Fundamentally, the early houses of Eisenman, Hejduk and Meier privilege form

over other factors. These architects demonstrate that the visual appearance of a

house is not necessarily a function of its siting (orientation), address (approach) and

program (the types of spaces in its interior), moderated in minor and consistent

ways by the exigencies of materiality and style. Architectural expression need not

be representational or figurative, that is it need not be restricted to the application of

a conventional set of architectural elements such as columns and architraves, it can

also arise from the manipulation of form, using rigorously applied rules and


Chapter 10


Ten houses, five by Robert Venturi and Denise Scott Brown and five by Frank

Gehry, are the focus of this chapter. Venturi and Scott Brown collaborated on the

design of many iconic Post-Modern buildings and in this chapter we measure the

geometric properties of the Beach House, Vanna Venturi House, House in Vail,

House in Delaware and House on Long Island. The elevations and plans that we

reconstructed for the fractal analysis were derived from published archival drawings

and interpreted using photographs of the completed buildings (von Moos 1987;

Stadler et al. 2008). The second set of houses featured in this chapter are by

architect Frank Gehry, who gained world wide attention in the 1990s for his

titanium-clad biomorphic buildings. However, from the late 1970s to the mid 1980s

he designed a range of modestly scaled and eclectically styled works, including a

series of houses that are often regarded as being the link between Post-Modernism

and Deconstructivism. The five houses by Gehry that are examined in this chapter,

all designed for or built in California, are the Familian House, Gunther House,

Wagner House, Spiller House and Norton House. Published design and construction drawings were used as the basis for the analysis of Gehry’s work, along with,

for the unbuilt projects, photographs of presentation models (Friedman 2009; Dal

Co et al. 2003; Gehry et al. 1990).

This chapter commences with an overview of the Post-Modern movement before

examining the data derived from the ten houses. In the final part of the chapter, a

comparison is undertaken of the impact of faỗade permeability on the visual

expression of a set of the Post-Modern works by Venturi and Scott Brown and a set

of modernist designs by Le Corbusier. The purpose of this analysis is to look for

correlations between formal modelling (the shape of the design) and any openings

in that form (typically an expression of function). Because the relationship between

form and function was highly contested by both modern and post-modern

designers, this secondary approach offers a new way of examining this issue.

© Springer International Publishing Switzerland 2016

M.J. Ostwald and J. Vaughan, The Fractal Dimension of Architecture,

Mathematics and the Built Environment 1, DOI 10.1007/978-3-319-32426-5_10




10 Post-modernism


For a philosopher or cultural theorist, the era that saw the eclipse of Modernism was

simply known as ‘post-’—meaning ‘after’—Modernism, a description of a time

when change began to occur in politics, technology and economics (Harvey 1990;

Jameson 1990). In parallel with the ascendance of this political view of the world,

architects developed an alternative interpretation of the concept of Post-Modernity

which entailed the rejection of functionalism and a return to historicist, social and

cultural expressions and values. While the philosophical and the architectural

interpretations of post-modernity do have subtle and important similarities, for the

purposes of the present chapter, the concept is used in its architectural sense.

The origin of the architectural variant of Post-Modernity is conventionally traced

to Hudnut’s (1945) article ‘The Post Modern House’. However, the Post-Modern

movement only began to gain momentum in architecture in the 1960s and 1970s,

when criticisms of the modern-day city and Modern architecture were published by,

amongst many others, Jacobs (1961), Brolin (1976) and Alexander (1977). Today

Post-Modernism is regarded as a movement that dominated architectural production

and discourse from the 1960s to the 1980s. Its canonical texts include Robert

Venturi’s Complexity and Contradiction in Architecture (1966) and Venturi and

Scott Brown’s Learning from Las Vegas (1972). Charles Jencks wrote extensively

on the movement, defining key moments in its history and highlighting a growing

number of examples of its application in design. Jencks’s Adhocism: the Case for

Improvisation (Jencks and Silver 1972), Modern Movements in Architecture

(Jencks 1973) and The Language of Post-Modern Architecture (Jencks 1977)

documented and promoted this approach, raising its profile internationally. Along

with texts by Stern (1988) and Moore (2004), these works collectively encouraged a

generation of architects to reject functionalism and embrace humour, historicism

and a newfound respect for human culture.

One of the earliest completed Post-Modern buildings was Venturi’s modest

design for a house for his mother, the Vanna Venturi House. In the years that

followed, and in the aftermath of the publication of works by Venturi, Scott Brown

and Jencks, several exhibitions promoted the value of historic forms, symbols and

social patterns. For example, in 1975 The Museum of Modern Art in New York

mounted a major exhibition of drawings from the Beaux Arts School; a movement

explicitly rejected by Modernist designers for its ornate, impressionistic aesthetic.

The display of these nineteenth-century works in a venue that had long been

regarded as the bastion of contemporary values, polarised intellectual debate and

helped to legitimise a growing volume of Post-Modern discourse on the value of

history. In 1980 the Venice Biennale featured works by many Post-Modern

architects, further authorising a revival of interest in decoration, colour and whimsy.

Marvin Trachtenberg argues that at this time the Post-Modern ‘current strengthened

into a broad, irresistible movement, with most leading architects converted to its

cause’ (1986: 553). By the mid-1980s, Michael Graves and Robert Stern, both

ardent supporters of Post-Modernism, ‘sought to address popular taste in startlingly




pastel and boldly historicizing designs’ (Ghirardo 2003: 21), their work being

emblematic of the later flamboyant era of Post-Modern architecture.

Internationally, Arata Isozaki in Japan and James Stirling in Britain designed

major buildings with Post-Modern stylistic leanings and in the USA proponents of

the movement included Stanley Tigerman, Frank Gehry, Philip Johnson, Barbara

Stauffacher Solomon and the members of SITE (Alison Sky, Michelle Stone and

James Wines). In Europe, in a context which was more embedded in the values and

experience of historic architecture, a more socially informed and classically derived

variation of Post-Modernism was promoted by Leon Krier, Rob Krier, Hans

Hollein, Vittorio Gregotti, Giorgio Grassi, Ricardo Bofill, Aldo Rossi and Bruno


Despite manifest differences between the American and European approaches

that had been combined under the heading Post-Modernism, the two shared a

similarly critical view of the austerity of Modernism and Functionalism. The

Post-Modernists argued that ‘purism’ should be replaced with ‘pluralism’ and that

Mies’s maxim ‘less is more’ should be rejected in favour of Venturi’s ‘less is a

bore’. Post-Modernists sought to improve architecture and urban design by creating

forms which embodied meaning, allowed for messiness to thrive and respected

cultural diversity. Jencks summarized this position by observing that Post-Modern

architecture was pluralist and inclusive, offering ‘a resistance to single explanations,

a respect for difference and a celebration of the regional, local and particular’ (1992:

11). However, rather than denying its Modernist forebears, ‘it still carries the

burden of a process which is international and in some senses universal. In this

sense it has a permanent tension and is always hybrid, mixed, ambiguous, or …

“doubly-coded”’ (Jencks 1992: 11).

Jencks’ concept of ‘doubly-coded’ relates to the Post-Modern practice of

working with, or being aware of, multiple simultaneous levels of meaning. For

example, while admiring classical Greek and Roman architecture, most

Post-Modernists did not wish to replicate such works; instead, they set out to create

an ornamental pastiche of periods and places by applying iconic, identifiable

building elements to often blocky, pitch-roofed and otherwise more contemporary

building forms. Their historic formal references were also often simplified, lined

with large geometric swathes of colour, and containing architectural symbols and

signs that were arranged in contradictory combinations. The overall effect was often

intended to be ironic, although the satire was inevitably lost on the general public,

being reliant on a detailed knowledge of architectural history. This is the type of

double-coding that Jencks argues is central to the promise and appeal of


In hindsight, historians have described Post-Modernism as both a positive and a

negative force in design. For example, Gössel and Leuthäuser describe it as ‘superficial’ (2012: 485) yet simultaneously ‘a model for successful urban repair’

(2012: 488). Trachtenberg argues that the movement ‘embraced overt historicism,

garish symbolism, vivid ornamentation, and humble vernacular models’ (1986:

553) but was also ‘a dynamic, self-confident, new international “style” of surprising

breadth and depth’ (1986: 570). For much of the last two decades architecture


10 Post-modernism

schools internationally have tended to understate the significance of the

Post-Modern movement, deriding its failures while forgetting that beneath its often

irreverent surface, it served to reemphasize the importance of embedding social and

cultural symbols and values in our buildings and cities.


Robert Venturi and Denise Scott Brown

Denise Scott Brown met Robert Venturi in 1960 when she was teaching at the

University of Pennsylvania. They shared a passion for architectural theory and

social discourse and began to collaborate, preparing joint lectures and research.

Scott Brown was born in North Rhodesia in 1931, and began her architectural

studies in 1948 at the University of Witwatersrand in South Africa before moving to

London, where she completed her studies at the Architectural Association in 1952.

In London, Scott Brown was influenced by Alison and Peter Smithson and their

idea ‘that architects should design for the real life of the street and for the way

communities actually work’ (Venturi et al. 1992: 8). After graduating she travelled

and worked throughout Europe, England and South Africa until in 1958 she

enrolled in a master’s degree at the University of Pennsylvania, where her education was shaped by the teachings of the urban sociologist Herbert Gans.

Venturi was born in 1925 in Philadelphia and studied architecture at Princeton,

where under the tutelage of Donald Drew Egbert and Jean Labatut he developed ‘an

understanding of modernism in the context of history’ (Minnite 2001: 245). After

completing his master’s degree in 1950, Venturi worked for Eero Saarinen and

Louis Kahn. In 1954 he won the Rome Prize Fellowship and spent the next two

years touring Europe, studying Christian architecture of the fourth and fifth centuries, and ornamental architecture from the fourteenth to the eighteenth centuries.

He later stated that ‘I have always loved history, and if I hadn’t been an architect, I

would have been an art historian’ (qtd. in Barriere et al. 1997: 129). Venturi became

an associate professor at the University of Pennsylvania in 1964 and two years later

he published Complexity and Contradiction in Architecture, a book which has since

been recognised as a key theoretical underpinning for the Post-Modern movement.

In that work Venturi argues that a ‘valid architecture evokes many levels of

meaning and combinations of focus: its space and its elements become readable and

workable in several ways at once’ (Venturi 1966: 23).

In the years after the publication of Complexity and Contradiction in

Architecture, Venturi and Scott Brown began to teach at Yale. It was during this

period that they took a studio group to Nevada to observe the commercial architecture and signage of Las Vegas, an event that led to the production of their highly

influential book, co-written with Steven Izenour, Learning from Las Vegas (Venturi

et al. 1972). Their book argued for the importance of visual analysis as a tool for

developing a sociological understanding of the way space and form operate and

communicate. Amongst other provocative ideas contained in the book—like

praising car parking lots, signage and luxury casinos—Learning From Las Vegas

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