c

Io

c

c

s

P

a

Y

E

.2

e

t:: :: -e

...--I_ .-

.

,i iii1

b

nninate Form

historical mathematical developments that preceded it, so t o o w i l l an ani­mate approach t o arch i tecture subsume t rad i t ional models of statics i n t o a m o r e advanced system o f dynamic organizations. Traditionally, in architec­ture, the abstract space o f design i s conceived a s an ideal neutra l space of Cartesian coordinates. In o t h e r design fields, however, design space i s con­ceived as an environment o f force and mo t ion rather than as a neutra l vac­uum. In naval design, fo r example, t h e abstract space of design i s imbued w i t h the proper t ies of f low, turbulence, viscosity, and drag so that t he fo rm of a hul l can be conceived in m o t i o n through water. Although the f o r m o f a boat hul l i s designed t o anticipate mo t ion , t he re i s no expectat ion that i t s shape w i l l change. An ethics o f m o t i o n nei ther implies n o r precludes l i te r ­a l mo t ion . Form can be shaped by t h e co l laborat ion between an envelope and the active context in which it i s si tuated. Wh i le physical f o r m can be defined in terms o f static coordinates, the v i r tua l force of t he env i ronment in which it i s designed contr ibutes t o i t s shape.The par t icu lar f o r m of a hul l stores mult iple vectors o f m o t i o n and f l ow f r o m the space in which it was designed. A sailboat hull, f o r example, i s designed t o pe r fo rm under mul t i ­ple po ints of sail. For sailing downwind, t he hul l i s designed a s a planing sur­face. For sailing in to the wind, t h e hu l l is designed t o heal, presenting a greater surface area t o the water. A boat hul l does n o t change i t s shape when it changes i t s d i rect ion, obviously, bu t variable points of s a i l a r e

incorporated in to i t s surface. In this way, topology al lows fo r n o t just the incorporat ion of a single moment b u t ra ther a mul t ip l ic i ty o f vectors, and therefore, a mul t ip l ic i ty o f t imes, i n a single continuous surface.

Likewise, the forms of a dynamically conceived arch i tecture may be shaped in association w i t h v i r tua l m o t i o n and force. b u t again, this does n o t man­date tha t the architecture change i t s shape. Actual movement of ten involves a mechanical paradigm o f mu l t i p le d iscrete posit ions, whereas v i r tua l move­ment allows fo rm t o occupy a mul t ip l i c i t y o f possible posit ions continuous­ly w i th the same form.

The te rm virtual has recent ly been so debased that it o f ten simply refers t o the digital space of computer-a ided design. It i s o f ten used interchange­ably w i th the t e r m simulat ion. Simulat ion, unl ike virtual i ty, i s n o t in tended as a diagram fo r a fu ture possible concrete assemblage bu t i s instead a visu­al substi tute. “V i r tua l rea l i ty ” might describe architectural design bu t as it i s used t o describe a simulated env i ronment it would be be t te r replaced by “simulated real i ty” o r “subst i tu te reality.” Thus, use of t he t e r m v i r tua l here refers t o an abstract scheme tha t has the possibi l i ty o f becoming actual­ized, o f ten in a variety o f possible configurations. Since architects produce drawings of buildings and n o t buildings themselves, architecture. m o r e than any o the r discipline, i s involved w i t h t h e p roduc t i on o f v i r tua l descript ions.

10

m i m a t e form

There i s one aspect o f v i r tua l i ty that arch i tects have neglected, however. and tha t i s the principle o f v i r tua l force and the dif ferential variat ion it implies. Arch i tectura l f o r m i s conventional ly conceived in a dimensional space o f idealized s t a s i s , defined by Cartesian f ixed-point coordinates. A n object defined a s a vector whose t r a j e c t o r y i s relat ive t o o the r objects, forces, fields and flows, defines f o r m w i t h i n an active space o f force and m o t i o n . T h i s shif t f r om a passive space o f stat ic coordinates t o an active space o f interactions implies a move f r o m autonomous pur i ty t o con tex tu ­a l specificity.2 Contemporary animation and special-effects software are just now being in t roduced as too l s f o r design rather than a s devices f o r rendering, visualization and imaging.’

The dominant mode fo r discussing mo t ion in arch i tecture has been the cin­ematic model, where the mul t ip l icat ion and sequencing o f static snap-shots simulates movement. The problem w i th t h e mot ion-p ic ture analogy i s t ha t arch i tecture occupies the r o l e of the stat ic frame through which m o t i o n progresses. Force and m o t i o n are el iminated f rom fo rm only t o be re in t ro ­duced, a f ter the fact o f design, through concepts and techniques o f opt ica l procession.

In contrast, animate design i s defined by the co-presence o f mot ion and force at the moment of formal conception. Force i s an init ial condition. the cause o f bo th mo t ion and the part icular inf lect ions of a form. For example, in what i s called “inverse kinematic” animation, the mo t ion and shape of a form is defined by mult iple interacting vectors that unfold in t ime perpetually and openly. W i t h these techniques, enti t ies are given vectorial propert ies before they are released in to a space dif ferentiated by gradients of force. Instead of a neutral abstract space fo r design, the context fo r design becomes a n active abstract space that directs form wi th in a current o f forces that can be stored as in for ­mat ion in the shape of the form. Rather than as a frame through which t ime and space pass, architecture can be modeled as a part icipant immersed w i th ­in dynamical flows. In addit ion t o the special-effects and animation industries, many o the r disciplines such as aeronautical design, naval design. and automo­bile design employ this animate approach t o modeling form in a space that i s a medium of movement and force.

Previous architectural experiments in capturing mot ion have involved the superimposit ion of simultaneous instances.The superimposition of a sequence of frames produces memory i n the form of spatio-temporal simultaneity.This idea o f an architecture in which t ime i s bu i l t in to form as memory has been a persistent theme throughout i t s history, but it was Siegfried Giedion in bo th Mechanization Takes Command ( I948) and Space, Time. and Architecture ( I 94 I ) who established these themes a s the pr imary concern of twentieth-century

11

mmate F o r i nninate F o r i

Flg”re I: Bucharerr urban dertgn compeurion xudy using particle mimauon flows to define variable deniirier a c r m s The site

Figure 2. Marcel Ouchamp. Nude Dercendmg (I Storrrorc. No 2 (1912) Ph#ladelph#aMuseum of

Art. Louise and Walter Arenrberg Coilecrton.

FlgUre 3 Umberro Eorrmni. Dynomlrm o f 0 Soccer Ployel (1913) Museum 01 Modern Art. N e w York,The Sidney and H a m e t Jilnls Col le ir~on

architectural theory and design.4 Giedion included bo th cubist and futurist approaches t o capturing mo t ion in form, using as examples the work of Marcel Duchamp (fig. 2) and Umber to Boccioni (fig. 3) . Giedion’s interpreta­t ion of these cubo-futurist experiments continues t o influence contemporary design and t h e ~ r y . ~In bo th approaches. mult iple static frames o f an object in t ime are captured and superimposed in the same space simultaneously, gener­ating a temporal palimpsest.

Another model o f indexical t ime i s associated w i t h Co l i n Rowe and hts dis­ciples. In Rowe’s text , “Transparency: L i tera l and Phenomenal,” co-authored w i th Rober t Slutzky, the idea o f a formal, o r phenomenal, transparency i s proposed along w i t h l i teral transparency.6 Phenomenal transparency I S the tracing o r impr in t ing of a deeper formal space o n a surface. Similarly, exam­ples o f formal o r phenomenal t ime include ”shearing,” “shifting.” and “rotat­ing” operations. Superimposed snap-shots o f mo t ion imply t ime as a phe­nomenal movement between frames o r moments. For instance. Kenneth Frampton’s descript ion o f Charles Gwathmey’s early w o r k as “rotat ionol” i s

one such example of t ime being used t o describe the movement between superimposed, formal moments.’ Ano the r example i s that o f the “troce.” a

t e r m that has emerged in the last twen ty years a s a graphical notat ion o f t ime and m o t i o n in architecture.* In such projects, a design process o f sequential formal operations i s recorded in the building’s configuration through co lors , alignments, imprints, addit ions and subtractions. One such example i s t he simultaneous presence o f mul t ip le h is tor ica l ground condi­t ions at a single moment . The intervals between the moments that are superimposed generate i r resolute condit ions which are explo i ted f o r the i r destabi l izing effect on the present.

In al l o f these indexica l responses t o t ime, a super impos i t i on o r sequence o f stat ic f o r m s i s p u t i n t o re la t i on such t h a t t h e v iewer resolves mu l t i p le states th rough t h e in i t ia t ion o f opt ica l m o t i o n . A l though f o r m i s t hough t in series and m o t i o n in these examples, movement is someth ing tha t i s added back t o t h e ob jec t by the v iewer .This involves a d ia lect ic def in i ­t i o n of m o t i o n tha t assumes tha t ma t te r i s i n e r t wh i l e o u r exper ience of it involves movement . Statics becomes t h e c o n d i t i o n o f m a t t e r w i t h o u t f o rce and dynamics becomes the cond i t i on o f m a t t e r acted o n by force. B o t h pos i t i ons assume tha t force i s someth ing wh ich can be added o r sub t rac ted f r o m mat ter .

The mode l i ng o f a rch i tec tu re in a conceptual f ie ld populated by forces and m o t i o n con t ras ts w i t h these previous paradigms and technologies o f f o rma l s t a s i s . Stasis i s a concept which has been in t imate ly l inked w i t h a rch i tec tu re in a t least f ive impor tan t ways, inc lud ing I ) permanence. 2 ) usefulness, 3) typology, 4) procession, and 5) ver t ica l i ty . However , stat ics does n o t h o l d an essential gr ip o n a rch i tec tu ra l t h ink ing as much a s i t i s

a lazy hab i t o r default t ha t arch i tects e i t h e r choose t o re in fo rce o r con ­t r a d i c t f o r lack o f a b e t t e r model. Each o f these assumptions can be t rans fo rmed once t h e v i r tua l space in wh ich a rch i tec tu re i s conceptual ­ized is mob i l i zed w i t h b o t h t i m e and fo rce . W i t h t h e example o f perma­nence, t he dominan t cu l tura l expectat ion i s t ha t bui ldings mus t be bu i l t f o r e t e r n i t y when in fact most bui ldings are b u i l t t o pers is t f o r on ly a s h o r t t ime. Rather than designing f o r permanence, techniques f o r obso­lescence, dismantl ing, ru inat ion, recyc l ing and abandonment th rough t i m e w a r r a n t exp lo ra t i on . A n o t h e r character is t ic o f stat ic models i s t ha t o f funct ional f ix i ty. Bui ldings are of ten assumed t o have a par t icu lar and f i xed re la t i onsh ip t o the i r programs, w h e t h e r they are in tersected, com­bined o r even f lex ib ly programmed. Typological f ix i ty, o f t h e k ind p r o ­m o t e d by C o l i n Rowe f o r instance, depends o n a closed stat ic o r d e r t o under l i e a family o f cont inuous variat ions. This concep t o f a discrete, ideal, and f ixed p r o t o t y p e can be subsumed by the mode l o f t he numer i ­cal ly c o n t r o l l e d mu l t i - t ype tha t i s f lex ib le , mutable, and d i f ferent ia l . Th is mu l t i - t ype , o r p e r f o r m a n c e e n v e l o p e , does n o t pr iv i lege a f ixed type

12

nnimate Form

b u t instead models a ser ies o f re la t ionships or expressions be tween a range o f potent ia ls . Similarly, independent in teract ing variables can be l inked t o inf luence one a n o t h e r t h r o u g h log ica l expressions def in ing t h e size, pos i t ion, ro ta t i on , d i rec t i on , or speed o f an ob jec t b y l o o k i n g t o

o t h e r ob jects f o r t h e i r character is t ics . This concept o f an envelope o f po ten t i a l f r o m wh ich e i t h e r a single o r a series o f i n s t a n c e s can be taken. i s radical ly d i f f e ren t f r o m t h e idea of a f ixed p r o t o t y p e t h a t can b e varied.

Finally. stat ic models u n d e r w r i t e the re t rograde understanding o f gravity as a simple. unchanging. ver t ica l force. Arch i tec tu re remains as the last refuge f o r members o f t h e f la t -ear th society. The relat ionships o f s t ruc tu re t o fo rce and gravity are by de f i n i t i on mu l t i p le and interrelated, yet architects tend to reduce these issues to w h a t i s s t i l l held as a centra l t ru th : t ha t buildings stand up vertically. In fact, there are mul t ip le in teract ing s t ruc tu r ­al pressures exer ted o n bui ldings f r o m many direct ions, including lateral w ind loads, upl i f t . shear, and earthquakes, t o name a few o f t he non-ver t ica l condit ions. Any one of these l i v e loads cou ld easily exceed t h e relat ive weight o f t he bui lding and i t s ver t ica l d e a d loads. The naive understanding o f s t ructure as pr imar i ly a p r o b l e m of the ver t ica l transfer o f dead gravity loads to the ground excludes, f o r instance, t he fact t ha t l ighter buildings have a tendency to upl i f t ; t h e main s t ructura l concern i n these cases is how t o te the r the roof . O f course arch i tects and s t ructura l engineers d o n o t ignore these o ther s t ruc tu ra l factors, b u t t h e pr imary percept ion o f s t ruc­t u r e has always been tha t it should b e vert ical. A reconceptual izat ion o f g round and vert ical i ty in l ight o f complex vectors and movements might n o t change the expediency and need f o r level f loors , bu t it wou ld open up pos­

sibi l i t ies f o r s t ructure and s u p p o r t t ha t take i n t o account or ientat ions o ther than the simply vert ical.

These concerns are not merely technical as architecture presently expresses also the cultural diagrams of stasis. Desp i te the popular concept ion among architects tha t gravity is a fact, t h e contemporary debates about theor ies o f gravity could in fo rm present discussions o f arch i tecture in the same spir­it tha t they have done i n t h e past. T h e h i s to ry o f theor ies o f gravity are extremely nuanced. fascinating and unresolved. Since the t i m e of S i r Isaac Newton, gravity has been accepted as the mutual relat ive a t t rac t i on o f masses in space. Given a constant mass, stabi l i ty i s achieved th rough o rb i t s ra ther than stasis. This d i s t i nc t i on be tween stasis and orb i ta l or dynamic stabi l i ty i s impor tant . In t h e case o f a single, simple gravity, stasis i s t h e order ing system through t h e unchanging constant force o f a g round point . I n the case o f a m o r e complex concept o f gravity, mutual a t t rac t i on gener­ates mot ion; s t a b i l i t y is t h e order ing o f m o t i o n i n t o rhythmic phases. In

1 4

nninate Form

t h e simple, stat ic mode l o f gravity, m o t i o n i s e l iminated a t t he beginning. I n t h e complex, stable model o f gravity. m o t i o n is a n order ing principle. Likewise, dtscreteness. timelessness, and f i x i t y are characterist ic o f stasis; mult ipl ici ty, change, and development are character is t ic o f stability.

These dif ferences are very apparent i n t h e t w o models o f gravity debated by Rene Descartes and G o t t f r i e d W i l h e l m Leibniz. Descartes iso la ted and reduced elements i n a dynamic system to t h e i r const i tu t ive ident i t ies to create a steady-state equation: he e l iminated t ime and fo rce f r o m the equa­t i o n in o r d e r to calculate a precise pos i t ion. Leibniz. on t h e o ther hand, examined components w i th in the i r contextual f ie ld o f influences and w i t h ­in a developing temporal cont inuum. By reta in ing the creative s t ructura l r o l e o f t ime and force, Leibniz determined t h a t a pos i t ion in space can on ly be calculated continuously as a vectora l flow.9 The name tha t he a t t r i bu ted to any provisional ly reduced component or p r im i t i ve element i s that o f t h e “monad.” W h e r e N e w t o n used calculus to replace the zero value o f stat ics w i t h a “derivative,” Leibniz fo rmula ted the concept o f t he “integral,” where w i t h i n any monad the re is a kernel o f t he w h o l e equat ion in the f o r m o f t h e variables. Any monad has t h e abi l i ty to un fo ld a “possible world.” Thus i n te ­gral calculus i s s t ructured o n a monad logic o f cont inuous rnu l t ip l ic i ty .The sh i f t f r o m a discrete mode l o f gravity as a fo rce tha t cou ld be e l iminated f r o m matter, to a concept of gravity as in tegra l and cont inuous with mass­es in space, involves a redef in i t ion o f space f r o m being neutra l and t imeless to being temporal ly dynamic. Once design is posed w i th in a Leibnizian m o n ­ado\ogical space, arch i tecture may embrace a sensibi l i ty o f m i c r o and macro contextual specif ici ty as a logic tha t can n o t be ideal ized i n an abst ract space o f f ixed coordinates. In such an abst ract act ive space, t he statics o f f ixed po in ts i n neutra l space i s replaced by the stabi l i ty o f vectors tha t bal­ance o n e another in a phase space.

I f arch i tecture i s to approach th is m o r e complex concept o f gravity, i t s design technologies should also incorpora te factors o f t ime and m o t i o n . T h r o u g h o u t t h e h i s to ry of arch i tecture, descr ip t ive techniques have impacted the way in which arch i tectura l design and cons t ruc t ion has been pract iced. In t h e eighteenth century, t he o r r e r y (fig. 4) came to represent n o t on ly t h e image o f t he machine b u t also the conceptual processes of a universe tha t is harmonical ly regulated as a c losed system of c i rcu lar o rb i t s a round radial center points. Because an o r r e r y uses f i xed radial points, any d iscrete m o m e n t i n t ime can be calculated as a f ixed po in t .The compass. l ike t h e o r re ry , has imphcbt in it a series of conceptual and discipl inary lim­i t s tha t are rehearsed with every arc tha t i s drawn. Events such as t h e advent o f perspective. stereometr ic pro ject ion. and o t h e r geometr ic tech­niques have extended the descr ip t ive r e p e r t o i r e o f arch i tectura l designers.

‘ 5

nntnate Farm

In ou r present age, the v i r tua l space w i th in which arch i tecture i s conceived i s now being rethought by the i n t roduc t i on o f advanced m o t i o n too ls and a

constel lat ion of new diagrams based o n the computer. The geometry and the mathematics that Leibniz invented t o describe this in teract ive, combi­natorial. and mul t ip l ic i tous gravity remain as the foundations f o r topology and calculus upon which contemporary animation technology i s based. There can be l i t t le doubt tha t t he advent o f computer-aided visualization has al lowed architects t o explore calculus-based forms f o r t he f i rst t ime.

The sequential cont inu i ty o f m o r e than t w o variables in teract ing w i t h one another poses a problem tha t only calculus can answer. F i rs t posed by Kar l Weierstrass. Charles H e r m i t e and Gosta Mittag-Lefler in 1885, the "n­

body" problem was later made famous by H e n r i Poincare in 1889. when he was able t o prove that no d iscrete so lut ion f o r such a problem could exist. The fundamental aspect o f this problem, re fe r red t o a s " the Poincare three-body problem." i s that t he tempora l and spatial pos i t ion o f enti t ies cannot be mathematically calculated fo r a fu tu re pos i t ion w i thou t sequentially cal­culat ing the posit ions leading up t o tha t moment . The mathematics o f f o rm and space that architects have h is tor ica l ly understood, involve mathemati­cal descript ions f rom which t ime has been el iminated. In the three-body problem however. t ime. o r m o r e p roper l y durat ion and sequence, are in te­gral t o the spatial relat ionships being calculated. Ano the r aspect o f this k ind of relat ionship in which th ree o r m o r e objects interact, i s t ha t they of ten produce nonlinear behavior.The me thod by which these problems can be calculated i s through a mathematics tha t i s sequential and continuous: thus the invent ion by b o t h N e w t o n and Leibniz of d i f ferent ia l calculus.

Although the mechanical, acoustic, and s t ructura l systems of bui ldings have been calculated and conceived using the t o o l s o f calculus, architects in f re­quently use calculus for t he design o f form. The fact t ha t arch i tecture i s so heavily dependent o n mathematics f o r the descr ip t ion of space has been a

Figure 4 Reproduction of the apparatus ~ o m m i s ­ rloned by Charles Boyle. 4 th Earl of Cork and Orrery. showing rhc relarive po,ririonr and motions of bodies m the solar ryrrern by balls moved by wheel-work Reproduction by Van C a r t Inrfrumenfr. In'

Figure 5 An elipre conrrrucced wirh four circler wlrh four radii The connecting lines between the radii become the points of

tangency where the comporlre curves change from bemg defined in relation to one radius 10 anorher

Figure b Plan derail of Borrornini'r sketch for "Quatrro Fontane" Church of Sa" Carlo. rhowing rhe use of complex comporire cuwes connruced out of linked regmenrr of ctrclei and spheres From Anrhony Blunr. VIIO e opere d# Bvrrmini (Rome Edifori Larema. 1983). 51

Figure 7 A ceiling derail of The cupola of B o r r o r n d r ' Quarrro Fomaoe" From Anrhony Blunt. Vflu r opere d! Borromini (Rome Edtfori Lareria. 1983). 51

stumbling b lock t o the use of m o t i o n and f l o w in the design process, as these ideas requi re tha t architects draw geometr ies whose underlying mathematics i s calculus. The too l s that arch i tects use to draw, such as adjustable trlangles and compasses, are based o n simple algebra. The preva­lence o f topolog ica l surfaces in even the simplest C A D software, along w i th the abi l i ty t o tap the t ime-and- force modeling at t r ibutes of animation sof t ­ware, presents perhaps the f i rs t oppor tun i t y fo r architects t o draw and sketch using calculus. The challenge f o r con tempora ry arch i tectura l t heo ry and design i s to t r y to understand the appearance of these too ls in a more sophist icated way than a s simply a new s e t of shapes. Issues of force. m o t i o n and r ime . which have perennial ly eluded arch i tectura l descr ip t ion due t o the i r "vogue essence," can n o w be exper imented w i th by supplanting the t rad i t ional too ls o f exact i tude and stasis w i t h too l s o f gradients, f lexi­ble envelopes, tempora l f lows and forces.1°

As architects have been discipl ined t o el iminate questions of f l o w and

m o t i o n f rom the r igorous descr ip t ion o f space, these qualities have been relegated t o personal taste and casual def in i t ion. Because of the present lack o f experience and precedent w i t h issues o f m o t i o n and force in archi­

16

m i m a t e farm

Figure 8 A spline wrface drawn with v e ~ i o r sf h x hang from potntr

Figure 9 The +me surface after being converted IO rr langular polygons

tecture, these issues migh t best be raised f r o m w i t h i n the technological

regimes o f t h e tools r a t h e r than f r o m w i th in arch i tectura l history." Through exper imentat ion with non-arch i tectura l regimes, architects may discover h o w t o engage t i m e and motion in design. T h e computer has already proven t o be useful as b o t h a descr ip t ive and a visualizing tool t o

architects, bu t t he i n t roduc t i on o f t i m e and motion techniques i n t o archi­tec tu re i s not simply a visual phenomenon. The visual qual i t ies of comput ­er-generated images may be i m p o r t a n t b u t it seems misguided to under­stand geomet ry in te rms o f style. The invent ion o f styl ist ic categories r isks the reproduc t ion o f the same spur lous comparisons o f m o d e r n arch i tecture t o boats and aircraft based o n t h e s imi lar i ty o f shapes. For instance, although geodesic domes o f t e n employ tr iangulated surfaces and some computer programs conver t vec tor surfaces to f ixed po in ts th rough the use of tr iangular polygon meshes (figs. 8 and 9 ) , it is a very shal low comparison t o equate architecture designed using topolog ica l surfaces to Buckminster Ful ler simply because o f t h e commonal i t y o f t r iangulated surfaces. ' 2

Nonetheless, t he re are d i s t i nc t fo rmal and visual consequences o f t he use of computer animation. For instance. t he most obvious aesthetic conse­quence is the shift f rom volumes defined by Cartesian coordinates to topo­logical surfaces defined b y U and V vec tor coordinates (fig. 12). Another obvious aesthetic byproduc t o f these spatial models is t h e predominance o f deformat ion and transformat ion techniques available i n a time-based sys­tem of f lexible surfaces (fig. 13). These are n o t mere ly shapes bu t the expression o f the mathematics o f t h e topolog ica l medium.

In addi t ion to the aesthetic and material consequences o f computer-gener­a ted forms, c o m p u t e r sof tware also offers capabilities as a conceptual and organizational t oo l . B u t because o f t he stigma and fear o f releasing c o n t r o l o f t h e design process to software, few arch i tects have at tempted to use the computer as a schematic, organizing and generative medium f o r design. The l imi ts and tendencies o f this tool. as a medium f o r design, must be clearly unders tood conceptual ly be fore they can be grasped by a systematic i n tu ­ition.1'

T h e r e are also some misconceptions about t h e r o l e o f computers i n t h e design process. A precious f e w arch i tectura l designers and theor is ts , Ka r l Chu and John Frazier being t h e most luc id among them. argue f o r t h e cre­at ive capacity o f computers t o faci l i tate genet ic design strategies. The

genetic, or rule-based, phenomenon o f computa t ion should not b e dis­counted. Yet a t t h e same t ime , genetic processes should n o t b e equated w i t h e i t he r intel l igence or nature. The c o m p u t e r i s not a brain. Machine intel l igence might best be described as tha t o f mindless connections. W h e n connect ing mu l t i p le variables, t he computer s imply connects them, it does not th ink cr i t ica l ly about h o w it connects. T h e present l imits o f connec­t ion ism are staggeringly complex, and t h e directness w i t h wh ich mu l t i p le ent i t ies can be re la ted challenges human sensibility. T h e response has been to a t t e m p t to develop a commensurate sensibi l i ty i n the machines them­selves; b u t t h e failures o f ar t i f ic ia l intel l igence suggest a need to develop a systematic human in tu i t i on about t h e connect ive medium, ra the r than a t tempt ing to bui ld cr i t ica l i ty i n t o the machine, Even in the most scienti f ic appl icat ions of computer simulat ions it is argued tha t f i r s t an i n tu i t i on must b e developed in o r d e r to recognize the nonl inear behavior o f computer simulations." Also, t he computer I S n o t nature. A l though it makes shapes tha t are tempora l l y and formal ly open to de format ion and inf lect ion, those shapes are not o rgan ic .The organic appearance o f what will la ter be dis­cussed as a system o f in teract ion and curv i l inear i ty i s a resul t o f organiza­t ional pr inc ip les based o n dif ferentials.The fo rmal organizations tha t resul t f r o m the sequential mathematical calculat ion of d i f ferent ia l equations are i r reducib ly open i n te rms o f t he i r shape. They are of ten i n te rp re ted as organic because o f t h e inabi l i ty to reduce these shapes to an ideal fo rm. In contrast , t h e reducib le , f i xed fo rms of s imple mathematics-such as spheres, cubes, pyramids. cones and cylinders-have a simplici ty and pu r i t y t ha t a l lows t h e m to transcend the i r fo rmal par t icu lar i t ies .

Instead o f approaching the computer as e i the r a bra in or nature, t he com­puter might be considered as a pet . Like a pet , t h e computer has already been domest icated and pedigreed. ye t it does n o t behave w i t h human in te l -

A n i m a t e form nn ima te Form

ligence. Just as a pe t introduces an element o f wi ldness to o u r domestic habits tha t must be con t ro l l ed and discipl ined. t he computer brings b o t h a degree o f discipline and unant ic ipated behavior to the design process. By negotiat ing the degree o f discipl ine and wildness, one can cult ivate an in tu­it ion i n t o the behavior o f computer-aided design systems and the math­ematics behind them.

There are three fundamental p roper t ies o f organization in a computer that are very dif ferent f r o m t h e character is t ics o f i n e r t mediums such as paper and pencil: t o p o l o g y , time. and p a r a m e t e r s . These th ree proper t ies should be discussed. beginning w i t h t h e principles o f topolog ica l entities, cont inu ing w i t h t h e impl icat ions tha t topolog ica l fo rms raise f o r t he rela­t ionship between t ime and shape. and concluding w i t h a discussion o f sta­t ist ics and parameters tha t can be s to red i n these t imed surfaces.

O n e o f t he f i rs t principles of topolog ica l ent i t ies i s t ha t because they are defined w i t h calculus they take t h e shape o f a mul t ip l ic i ty ; meaning they are n o t composed o f d iscrete po in ts b u t rather, they are composed o f a con­t inuous stream of relat ive values. Historical ly, baroque geometr ies o f corn­pos i te enti t ies, such as mu l t i p le radi i , have been c i t ed as mul t ip l ic i tous spaces. But t he idea tha t t he baroque p e r i o d anticipates topo logy in archi­tec tu re i s somewhat misplaced. There is a cr i t ica l dif ference between the discrete geometry of baroque space-a geomet ry o f mul t ip le points, and the cont inu i ty o f topology-a mu l t i p l i c i t y w i t h o u t po ints . W h e r e baroque space i s defined by mul t ip le radi i , a topolog ica l surface is defined as a f l ow that hangs f r o m f ixed points tha t are weighted. Al though baroque space i s

geometrical ly highly cont inuous and highly dif ferentiated, it does retain mul t ip le spatial centers. T h e cont inuous contours of baroque in te r i o rs are composed of segments o f mu l t i p le d iscrete radial elements (figs. 5 and I O ) . For example, i n Francesco Borromini ’s Quat t ro Fontane the complex o f pr imi t ive volumes i s tangential ly aligned t o produce a cont inuous surface, giving the space simultaneous dynamism and centra l i ty (figs. 6 and 7). The relat ionships between these radial pr imi t ives are o f ten o f bi lateral ly sym­m e t r y and always o f tangency.

Instead o f being defined by points and centers, topo logy is characterized by f lexible surfaces composed o f splines (fig. I I ) .These splines are or iented in an opposing U and V or ien ta t i on t o cons t ruc t surfaces composed o f curve ne tworks (fig. 19). Unl ike lines, splines are vectors defined w i t h direct ion. The vectors are suspended f r o m l ines w i t h hanging weights similar t o the geomet ry of a catenoidal curve. lS Yet un l ike a catenoidal curve, a spline can accommodate weights and gravit ies d i rec ted in f ree space. T h e points, or “con t ro l vertices.” f r o m wh ich these weights hang, and th rough which the

20

Figure 10. An example of a cornporire curve using the same logic of mgianal dcf,n,r,on and tangency a$ the elllple descrtbed Jn Figure 5 Each i e c ~ l o nof the composite curve I I defined by fixed radius The C o n n e ~ t t o nb e w e e n radlal Curve reg­

rnenrl occurs a t points of tangency that are defined by a line connecr~ngthe rad,, Perpendlculnr co rhere i I lner. r r ra~ghr l ine regrnenrr can be inserted between the radial CY~IOI.

4 P

A

21

mimate Forn

Figure 12 A spline surface that begins 21 1 twisted rnobiur band and 15 rrrerrhed and p i n e d along ~ f sedger to farm a rctlh,ter­recring rvrlace Enclosed v o l ~ m e farc mapped wirhin the rurlace by both the p n 8 n g and ~ncerrecringopeiatlons From Stephen Barr. Eiperfmcnfr 10 Topalory (NewYork Dover Publmrlonr. In? , 1964). 69

Figure 13 A rraniformatlon of a r8ng Into a cup through the flex8blIicy of 2 m g l e surface. From Stephen Barr. Cxpertmentr (0

Topology (New York Dover Publicattons. I nc , 1964). 4

spline f lows. are located in X.Y. Z coord inate space. F rom a sequence of con t ro l vert ices the d i rect ion and strength o f weights establishes a tension along the hul ls.Although the con t ro l vertices, hulls, and weights are defined in a point-based. Cartesian. space, the splines are no t defined as points bu t as f lows.The spline curve i s unl ike a l ine o r radius in that i t s shape i s no t reducible t o exact coordinates.The spline curve f lows as a stream between a constel lat ion o f weighted con t ro l vert ices and any pos i t ion along this continuous series can only be defined relat ive t o i t s pos i t ion in the sequence.The formal character o f a par t icu lar spline i s based o n the num­ber of con t ro l vert ices inf luencing a par t icu lar reg ion o f t he f low. For instance. a three-degree spllne (fig. 14) w i l l begin a t i t s r o o t and determine i t s in f lect ion between every th ree points in a series. A seven-degree spline curve (fig. 15) w i l l be defined by groups o f seven con t ro l vertices, thus appearing smoother. A two-degree spline (fig. 16) wi l l appear l inear because it lacks smooth cont inu i ty between con t ro l vert ices. Even though the con­t r o l vert ices remain constant in these examples, the par t icu lar shape changes due t o the degree o f relat ive def in i t ion o f the con t ro l l i ng points of the sequential f low. Similarly, w i thou t changing the pos i t ion of any one of

22

nnLnate Form

t h e con t ro l vert ices o r t he degree o f the spline. the shape wi l l be altered when the weight o r d i rect ion of any o f t he normals i s a l tered (fig. 18)

A change in any po in t d is t r ibutes an in f lect ion across regions of these ent i ­ties. Because splines are vector ia l f lows th rough sequences of points they are by def in i t ion continuous mul t ip l ic l t ies ra the r than discrete enti t ies. A mul t ip l ic i ty i s a co l lect ion o f components tha t i s ne i the r reducible t o a sin­gle ent i ty n o r t o a co l lect ion o f mul t ip le ent i t ies . A mul t ip l ic i ty i s neither one n o r many, but a continuous assemblage o f heterogeneous singularities tha t exhibits bo th col lect ive qualities o f con t i nu i t y and local qualities o f heterogeneity. In the use o f topology in design, these mul t ip l ic i t ies imply a

very d i f ferent approach t o locat ion. as the re are n o discrete points along a spline.

The t w o l inked principles tha t are central to the tempora l component o f topology are ( I ) the immanent curvatures tha t resul t f r o m the combinato­r ia l logic o f dif ferential equations and (2) t h e mathematical cause o f that curvature. Because topological enti t ies are based o n vectors, they are capa­ble o f systematically incorporat ing t ime and m o t i o n in to the i r shape as in f lect ion. Inf lect ion. o r continuous curvature i s the graphical and math­ematical model fo r the imbr icat ion of mul t ip le forces in t ime.The shift f r om l inear i ty t o curv i l inear i ty i s a feature o f con tempora ry mathematics and geometry tha t has been discussed e lsewhere. I6 Curv i l inear i ty i s a m o r e sophist icated and complex f o r m of organization than l inearity in t w o regards: ( I ) it integrates mul t ip le ra ther than single enti t ies, and (2) it is capable of expressing vector ia l a t t r ibutes, and the re fo re t ime and mot ion. Curva tu re in a tempora l env i ronment i s t he me thod by whtch the in terac­t i o n o f mul t ip le forces can be s t ructured, analyzed, and expressed.

The calculat ion of t ime as expressed through curvature i s possible w i t h cal­culus. which animates numerical snapshots a t an in f in i te speed, simulat ing t ime. Under ly ing all o f the contemporary an imat ion software i s a math­ematics o f the inf initely small in terva l which simulates actual mo t ion and t ime through k e y f r a m i n g . T h e s e t ransformat ions can be l inearly m o r p h e d o r they can involve nonlinear in teract ions through d y n a m i c s . These sequential t ransformat ions are possible because the formal enti t ies them­selves are described using f lexible topolog ica l surfaces made of vec to r splines rather than points.

An example o f curvature as a mathematical and in tu i t ive system can be explained by the situation o f a FrisbeeTM being chased by a running dog. There are at least three con t r i bu t i ng elements t o the path of the dog and i t s possible in tersect ion w i t h the pro ject i le . F i r s t , the FrisbeeTM has a vec­

23

,

j miinate Form

Cartesian space of neutral equi l ibr ium a s a m o r e active space o f mo t ion and f low.

1 The curvi l inearity which results f r o m these mul t ip le parameters has previ­ously been simplistically understood as a debased f o r m o f l inearity, bu t in fact, it i s the order ing of a dynamical system of dif ferential factors In the early par t o f this century, Scott ish zoolo log is t S i r D 'A rcy Thompson ana­lyzed variat ions in the morphology of animals using deformable grlds. which yielded curvi l inear lines due t o changes in f o r m (f ig 20) H e compared the curvature o f deformations in formal configurations t o the curvature of s t a ­

t ist ical data, such a s speed, temperature, and weight Thompson was one of t he f i rst scientists t o no ta te g r a d i e n t forces (such a s temperature) through d e f o r m a t i o n , i n f l e c t i o n , and c u r v a t u r e 1 ' These th ree terms a l l involve the registrat ion o f force o n f o r m Rather than th ink ing o f deforma­t ion as a subset o f t he pure. the t e r m deformat ion can be understood as a system o f regulat ion and o r d e r tha t proceeds through the in tegrat ion and resolut ion of mul t ip le in teract ing forces and fields

Where Thompson pioneered the analyses of deformat ion as an index of contextual forces acting o n an organism, in the late nineteenth century Etienne-Jules Marey pioneered the study o f curvature a s t he notat ion of bo th fo rce and t ime. Francois Dagognet described the p ro jec t o f Marey as

. . . showing whot one could leorn from a curve, which wos not merely o

simple 'reproduction.' I t wos from ond with the curve thot forces could ini­tially be colculoted. I t wos eosy to obtain the moss of the body os well os the speed i t was going (chronobiology); from this one could induce the force that had set i t in motion, the work expended to produce this oction. The tro-Jectory olwoys hod to be questioned ond interpreted. No t only were the slightest nicks and notches in the line due to certain foctors, but they enabled the determinotion o f resistances as well as impulses.'*

Marey was one o f the f i rst morphologis ts t o move f rom the study of f o rm in iner t Cartesian space, devoid of force and mot ion. t o the study of rhythms, movements, pulses, and f lows and the i r effects on fo rm These fac­to rs he termed "motor evidence" In his book Animal Mechonism he shifted his a t tent ion f rom the study o f in ternal pulses and rhythms t o the external movements of animals Unl ike Muybridge and others who also employed chronophotography techniques. Marey t r iggered the exposures w i th bo th pneumatic and electr ical sensors located o n the animals (f ig 21) This. along w i th his method of attaching t iny re f lect ing opt ica l disks al lowed Marey t o sequence the exposures w i t h rhythms of m o t i o n (f ig 22) Dagognet describes Marey as pursuing "movements not moments" in his continuous

26

nnimate Form

Figure 10. Study of the transformation of ~ r u i t a c e mcarapaces through che deformation of a flexible grid or " r u b b e r mar" by D ' A r c y Thompson F r o m

Thompson. On Growth and Form. The Complete Rcvircd Edition (New York Dover Publicarianr. Inc , 1992). 1057.

Figure 21 h e n n e - J u l e r Marey used pneumatic triggers. arnched IO

the ) o i n i ~of mimalr . co trigger camera exporvrer 8" rhythmic sequencer In this way, <he rhychm o f photographic instances were sequenced t o the movements of the animal. "Device for harnessing the plgeon to the revolvtng frame." from Marey, "Le Val der ol5e.Yx:' a5 a p p e a r s I "

F r a n ~ o t r Dagognet, Et,eme­ ]"le$ Marey A Parrioo for rhc Trwe (New York Lone Books. 1992). 85

o

-e n i m a t e Form

Figure 22- Marey used reflective optical dirks atrached to kc? painrr of the body co capture points of rnor~on In tho5 example of a horse walklng. the film i s expored a t a rata where rhe pa,nrs begln t o blur m o motton w a d s 'Osc~llartonrof the

~ ~ ~ ~ ~ ~ ~ .front limb of the horse walking:' from Marey."LeVoi der OII~IUX." I S appears ,n ~ ~ a ~ n ~ a~r~~~~~ ~ j U i e s M~~~~ A Passion for [he Trocc (New York Zone Books. 1992). 7s

data recordings. A f te r exposing rhythmic sequences o f images on a single plate, Marey would connect curved lines through these points t o describe a cont inu i ty across the snapshots (fig. 23). To b o r r o w a te rm used t o describe the behavior o f chaotic a t t ractors . Marey produced "phose por ­traits" by describing t ime as a cont inuous curv i l inear f low, ra ther than a

divisible sequence reducible t o discrete frames. This i s the cr i t ical dif fer­ence between Marey's traces of vector movement and the techniques of sequential traces. Marey's model f o r continuous t ime based o n the inf lec­t ion and curvature o f m o t i o n paths and f lows, i s akin t o computer anima­t ion.

In addi t ion t o these examples o f analyzing t lme. movement, and transfor­mation. another model that has been developed in conjunct ion w i th evolu­t ionary theories i s the idea o f t h e fitness landscape. W i t h the replacement of f ixed types by temporal ly organized phylogenetic t rees, came the model of the developmental landscape t o describe the space w i th in which organ­isms evolve. In mathematics the landscape model has been developed by Rene Thorn. in physics by Stuar t Kauffman and in developmental biology by Conrad Waddington. It in i t ia l ly appeared when Francis Gal ton described evolut ion in terms of a fitness landscape; whereby a surface represents an external environment across which a facetted sphere ro l led . The facetted sphere represents an organism w i t h i t s own in ternal constraints, and the

Figure 23 Mare7 would c o n n e ~ fcurved lines through there pomtr to dcrr r lbe a c y r v ~ l ~ n e a r contlnurty across the rnaprhotr "Orc~liarioni of the front i h b of rhe horse gaIlap8ng." from Marey. 'Le Vol des o,seaux,'' IS appears ~n Francotr Dagognec, Erreooe-Jules Marey A Parrian for the Trace (New York. Zone Books. 1992). 75

landscape represents i t s potent ia l pathways o f development. This concept o f a landscape o f development in formed Charles Darwin 's evolut ionary the­o r y o f speciat ion. Similar t o any landscape model o f organization i s an evo­lu t ionary o r developmental logic.

A landscape i s a system where a po in t change i s d is t r ibuted smooth ly across a surface so that i t s inf luence cannot be local ized at any discrete po in t . Splines are t h e const i tuent element of topological landscapes. Spllne surfaces have already been explained as vector sequences whose regions of in f lect ion produce singularities on a continuous surface. The slow undula­t ions that are bu i l t i n t o any landscape surface a s hi l ls and valleys d o n o t mobi l ize space through act ion bu t instead through implied v i r tua l mo t ion . The movement o f a po in t across a landscape becomes the co l laborat ion of t he in i t ia l d i rec t i on , speed, elasticity, density, and f r i c t ion of the object along w i t h the inf lect ions o f t he landscape across which it i s travel ing.The landscape can in i t ia te movements across i tself w i t h o u t l i teral ly moving.The inf lect ions o f a landscape present a context o f gradient slopes which are enfolded i n t o i t s shape.The condi t ion of or iented surfaces has been elabo­ra ted by Paul V i r i l i o and Claude Parent in terms o f "oblique" rnovement.19 Likewise. any obiect moving across a landscape has an in i t ia l condi t ion of speed and density that i s unfolded across the landscape, This co l laborat ion o f enfolding a con tex t and unfolding an obiect i s a tempora l , mobile, and

2a

i

combinatorial model for s tab i l i ty and organization. In this schema the object has actual force and mo t ion , where the landscape has virtual force and mo t ion s tored in i t s slopes.The slope o f a landscape i s a gradient of mot ion, direct ion. and t ime .A landscape also implies a geological time-scale of format ion in that although it appears stat ic a t any instant, i t s form is the p roduc t o f long historical processes o f development.This class o f landscape objects can be extended to include any f o r m f r o m which temporal devel­opment cannot be simply reduced. Topological surfaces that s tore force in the inf lect ions o f the i r shape behave as landscapes in that the slopes that are generated s tore energy in the f o r m of or ien ted rather than neutral sur­faces.

The ear l ier example of the boat hu l l i s i tself a micro-landscape fo r the movements s tored in i t s surface shapes, across which viscous water f lows. Similarly t he global f lows of the water and w ind present a macro-landscape fo r t he mo t ion of the boat t o f l o w through. O t h e r topological landscapes include isomorphic polysurfaces ( o r blobs), s k e l e t o n s ( o r inverse kine­matics networks) , w a r p s , f o r c e s , and p a r t i c l e s . Spline enti t ies are inten­sively influenced by the i r con tex t due t o the fact that they are defined by hanging weights, gravity, and force. For example, the weights and direct ions pul l ing o n con t ro l vert ices in space can be affected by gradients of attrac­t ive o r repulsive force in which the spl ine i s si tuated. Similarly, the weights of one spline surface can effect those o f another spline surface (figs. 24 and 25). These result ing structures are cal led blobs f o r the i r abi l i ty t o mutually in f lect one another and f o r m composi te assemblages. The blob i s an a l ter ­native example o f a topological surface exhib i t ing landscape characteristics although it does n o t look l ike a topography.These b lob assemblages are nei­ther mul t ip le n o r single. ne i ther in ternal ly con t rad i c to ry n o r unified. Thei r complex i ty involves the fusion of mu l t i p le elements in to an assemblage that behaves as a singularity wh i l e remaining i r reducib le t o any single simple organization. W i t h isomorphic p o Iys urfac es. "meta-clay," "meta-ba II," o r "b lob" models. the geometric ob jects are defined as monadlike primit ives w i th in ternal forces of a t t ract ion and mass. A b lob i s defined w i th a center, a surface area. a mass relat ive t o o t h e r objects. and a f ie ld o f influence.The f ield of influence defines a re la t ional zone w i th in which the blob wi l l fuse with, o r be inf lected by. o the r blobs. W h e n t w o o r more l inked b lob objects are prox imate they wi l l e i ther ( I) mutual ly redefine the i r respective sur­faces based on the i r par t icu lar gravitat ional proper t ies o r ( 2 ) actually fuse in to one contiguous surface defined by the in teract ions o f the i r respective centers and zones o f in f lect ion and fusion.

Because i t i s no t reducible t o any single simple order ing principle, a blob's fusion and unif icat ion are d is t inct f r o m a d iscrete to ta l i ty or whole. In the

Figure 24 Dirconnecred primiriver "red 10 compare an isomorphic polyrurface

Figure 15 isomorphic palyrurface with primitives fused info a m g l e surface

case of t he isomorphic polysurfaces, either a l o w number o f in teract ing components o r a regular d i s t r i bu t i on o f components w i l l yield a global f o r m tha t i s m o r e o r less simple. O n the o the r hand, a high number of com­ponents and an irregular d i s t r i bu t i on of those components yields a global f o r m tha t i s more o r less complex.The dif ference between simple and com­plex systems i s relat ive to the number o f in teract ions between compo­nents. In this schema, there i s n o essential dif ference between a m o r e o r less spherical format ion and a b lob.The sphere and i t s provisional symme­t r ies are merely the index o f a ra ther l o w level o f interactions. whi le the b lob i s an index of a high degree of in format ion, where i n fo rma t ion i s equated w i t h difference. Thus, even what seems t o be a sphere i s actually a b lob w i t h o u t influence; an inexact f o rm tha t merely masquerades as an exact f o r m because it i s isolated f rom adjacent forces.Yet, a s a blob, i t I S

capable o f f lu id and continuous d i f ferent ia t ion based o n interactions w i th ne ighbor ing forces w i th which it can be e i ther inf lected o r fused. In this way, complex i ty i s always present a s potent ia l in even the most simple o r p r im i t i ve o f forms. Moreover, it i s measured by the degrees o f bo th cont i ­nu i ty and dif ference chat are copresent a t any moment .

Like a natura l landscape that stores the h i s to ry of i t s geological format ion in i t s shape, these fused topolog ica l aggregates manifest the i r geological conglomerat ion o n a single surface. Time, force, and mul t ip l ic i ty const i tu te the f o r m of a geological landscape. This s t ruc tu r ing o f t ime and energy through curvi l inear inf lect ions i s characterist ic o f m o t i o n o r act ion geom­

31

nnmate F o r m

etry . These inf lect ions index b o t h the in ternal combinat ions and relat ion­

11

ships of elements and t h e i r deformat ion w i t h i n a larger contextual field. W h e n proposing t h e mode l o f an in ternal ly regulated s t ructure, there are

i t w o possibilities: t h e f i rs t approach posits an essential in ternal o rder that j can b e discovered through reduct ive analysis, t h e second i s a loose binding

i o f const ra in ts that can be real igned and reconf igured in a prol i ferat ive and evolut ionary manner. In t h e second category, t he in ternal o r d e r is bo th

b activated and made legible th rough t h e unfolding o f i t s o r d e r instigated by external forces. The relat ionship be tween a system o f in ternal constraints, such as skeletons ( inverse kinematic chains), part icles, or blobs and the c o n t e x t i n which they unfo ld is intensive. Just as a topolog ica l landscape o r an assemblage o f blobs s tores various at t ract ions and combinations in a sin­gle surface, so too can topolog ica l ent i t ies be mutual ly inf lected by the fields i n wh ich they are situated. For instance, t h e space in which a surface or surfaces are located can be assigned w i t h d i rect ional force which wi l l in f lect t he normals o f a surface, thus inf lect ing the shape o f the surface based on t h e relat ive pos i t ion to the p o i n t f r o m which the force i s emanat­ed. The f ield in which fo rms are defined i s not neutra l b u t can be populat­ed by a var ie ty o f in teract ing forces wh ich establish gradients o f influence in a model ing space. Gradient shapes are areas tha t d o n o t have dist inct con tours or edges bu t are instead defined by dissipation f r o m points of emission. These gradients are n o t measured based o n points or coordinates bu t on fields. Like a tempera ture map tha t measures the continuous and gradual change o f force across a f ield, these fo rce gradients d o n o t have edges or contours. The spatial con tex t w i th in which surfaces and splines are conceived then i s also animate ra the r than stat ic.

Th is possibi l i ty o f an animate f ield opens up a m o r e in t r icate relat ionship o f f o r m and f ield than has been prev ious ly possible. Rather than an enti ty being shaped only by i t s o w n in ternal definit ion. these topolog ica l surfaces are in f lected by the f ield in which they are modeled. I f an ent i ty i s moved in space, i t s shape might change based o n t h e pos i t i on w i th in gradient space even though t h e def in i t ion o f t he en t i t y remains constant. Thus, the same en t i t y dupl icated identical ly b u t in a d i f ferent gradient space might have a d i f ferent configuration. A sequence o f identical ent i t ies located in a series th rough a gradient space wou ld const i tu te b o t h a self similari ty and a dif­ference based o n the characterist ics of the gradients and h o w they were pos i t ioned. This relat ionship between a fo rce and the ob jec t which stores tha t f o rce in i t s f o r m i s reminiscent o f t he insight made by H e n r i Bergson in his bbok, Mat te r and Memory, in which he argues f o r a nondialect ical understanding o f the relat ionship be tween substance and energy.20 Bergson argued tha t mat te r could n o t be separated f r o m the h is tor ica l process of i t s becoming.

32

mimate f o r a

Contemporary theor ies o f organic form, evolut ion, muta t ion and vitalism. as defined as the developmental unfolding o f a s t ruc tu re in a gradient

environment o f influences, might be in format ive to the discussion o f t opo l ­ogy, t ime, and parameters as they apply t o arch i tectura l design. Such discussions o f organic processes o f ten involve non-dialect ical relat ion­ships between mat te r and in format ion, f o r m and t ime , and organization and force. This resistance to t rea t form. t ime , and motion discretely is equivalent to what might be understood as an organic t rad i t ion. The thread o f “anorganic vitalism“ tha t runs f r o m Leibniz th rough Bergson and Gil les Deleuze cou ld underwr i te such a discussion, wh i l e replacing the i r natura l essentialism w i t h a revised cybernetic concept o f t he machine as a feedback device tha t creates hierarchy and organization. O n e of

the best possible models o f “anorganic vitalism” is t h e p ropos i t i on o f “fused assemblages” p u t f o r w a r d by Lynne Margul is. T h e malor revision t o concepts o f ho l ism tha t Margul is in t roduces is f r o m a predetermined ident i ty t o ident i t ies o f becoming. Margulls fo rmula ted the evolut ionary hypothesis tha t micro-organisms evolve t h e i r complex i ty b y i nco rpo ra t ­i ng simpler organisms i n t o larger mul t ip l ic i t ies t h a t become capable o f reproduc t ion as a singularity.2’ Thus, organisms are seen as previously f ree l iving co lon ies of organs that become a fused singularity. I n her schema, the re i s l i t t l e dif ference between a single body and an ecology o f organisms, as b o t h exp lo i t one another’s funct ions and machinic behav­iors th rough feedback and exchange. A body, Margul is suggests, is t he fused assemblage o f an ecosystem operating w i t h a high degree o f cont inu­i t y and stability. There i s n o essential s t ruc tu re t o such an assemblage tha t one can uncover or deduce, a t e i ther t h e macro or m i c r o scale. It is a logic of d i f ferent la t ion, exchange, and assemblage w i t h i n an environment o f gradient influences. The form, or shape, m o s t o f ten c i ted in reference t o such an environment i s t ha t o f the landscape.The epigenetic landscape is a theoret ica l and analyt ic device used t o descr ibe the relat ionship between an evolving fo rm, or organism, w i t h i n i t s developmental field, or environment.

Producing a geomet r ic f o r m f r o m a dif ferential equat ion is problemat ic w i t h o u t a dif ferential approach to series and repet i t ion. There are t w o kinds o f series: a discrete, or repet i t ive series and a continuous, or i tera­t ive series. In a cont inuous or i terat ive series, the dif ference between each object in the sequence i s c r i t ica l and individual t o each repet i t ion. If t he dif ference I S t h e p r o d u c t o f t h ree o r m o r e variables, and if those th ree variables are unrelated, t h e n the change be tween each i t e ra t i on w i l l be nonl inear in i t s s t ruc tu re and it w i l l there fore be d i f f icu l t to p red ic t w i t h absolute prec is ion. Each step is thus dependent o n the precise posi­t i o n of each o f t h r e e or m o r e variables; meaning tha t t h e fu tu re pos i t ion

33

I flnLmate Form

o f the i terat ive se r ies cannot be calculated outside o f t he s e r i e s itself. In an incremental, discrete series, t he dif ferences that accompany each repe­t i t ion are linear and reducib le .The en t i re in f in i te s e t o f possible futures of t he series can be calculated in advance w i t h a simple mathematical equation. In the case of t he cont inuous series such exact definit ions a r e impossible t o determine at the beginning, a s the beginning i s no t an origin bu t merely a po int of depar ture.The fu ture possible posit ions of a cont in­uous series must be thought o f as a cont inuum rather than as an enclosed infinity. This points t o the impor tan t d is t inct ion between the inf inite and the continuous. t w o terms which are of ten casually conflated. Difference and repet i t ion, when thought o f in a cont inuous rather than discrete man­ner, mandate a thinking in durat ion ra the r than in points.

This difference i s crucial t o an understanding of the spatial difference between the inf inite and t h e cont inu0us.A cont inuous series can be " inf ini­tized." o r reduced. through " i terat ive reduction," leaving a single, ideal type. In this method, a l imi ted set o f var ia t ion i s organized in a series so that its continuous differences can be progressively eliminated, leaving a discrete type that can then be in f in i te ly extended. This me thod o f i terat ive reduc­t i o n can be at t r ibuted t o Edmund Husserl. as it i s central t o his invention o f phenomenology.

M o t i o n and t ime are similarly taken away then added back t o architecture. Arch i tectura l space i s in f in i t ized by removing mo t ion and t ime through i terat ive reduction. They are then added back typical ly through phenome­nology. The dynamic concept o f arch i tecture, however, assumes that in any fo rm there a r e inf lect ions that d i rec t m o t i o n and provoke and influence the forces moving through. over, under and around surfaces. The fo rm i s t he site for the calculat ion o f mul t ip le forces. This i s the case in the example of the sailboat, where o n the hull's surface mul t ip le points of s a i l are calculated and resolved in the f o r m itself. The percept ion of the hull does n o t require the resolut ion o f mul t ip le vectors of movement as those vectors are s to red in the object i tself as potent ia l energy o r f low wi th in a gradient f ie ld of forces. Moreover, the pr imary method of experiencing these vector effects i s n o t opt ica l o r through aesthetic contemplation bu t instead through per formance. The vector f lows that are calculated and stored in the shape o f the hul l can be unfolded through bo th aesthetic analyses and use. Perhaps the best precedent fo r the unfold­ing of curved space i s evident in the concept o f Frederick Keisler's "endlessness" along wi th Ado l f Loos's concept o f t he "raurnplan" f rom which it was derived while Kiesler was work ing in Loos's office.22 Although a

discussion of the counter t rad i t i on o f modern endless space versus the canonical modern t rad i t ion o f in f in i te space i s n o t possible here, the

3 4

nncnate Forb

difference f rom the m o r e classical and reduct ive models of modern fo rm should be recognized.

The best model fo r t he discussion o f non-reducible forms o f mo t ion might be t o r e t u r n t o the model o f the landscape o r the obl ique ground, where mo t ion i s s to red in the gradient slopes o f a surface across which an oblect moves, Here the potent ia l m o t i o n o f an obiect across a surface i s s tored in a v i r tua l manner a s fu ture potent ia l energy. To re tu rn t o the force discus­sions, t he inf luence o f a gradient space o f force and energy i s bu i l t i n t o the spline ne tworks through t h e in f lect ion o f the i r normals. A landscape i s a ground that has been in f lected by the h is tor ica l f lows o f energy and move­ment across i t s surface. These historical forces manifest a geological f o r m of development tha t i s in f lected and shaped by the f lows that have moved across i t . These slow t ransformat ional processes resul t in forms which are or iented w i t h mo t ion , bo th t h e v i r tua l mo t ion of the i r h i s to ry and the actu­al mo t ion they in i t ia te through the i r slopes and val leys.This animation o f slow f o r m w l t h the h is tor ica l processes o f gradual geological becoming i s a paradigm of m o t i o n and t i m e that renders substance v i r tua l ly animated and actually stable. Rhythmic mo t ion i s manifest in stable-oriented f o r m rather than in l i teral ly moving oblects. In the words o f Hans Jenny,

. . . Nature reveals an abundance ofsculptured forms, and all of them, i t must be remembered, are the result o f vibration. If the tame ceases, the mass 'freezes.' Looking at these vibrational effects, i t would b e no exaggeration to speak of a true magnetocyrnatics with i t s own dynarnakinetic morphology. Experiments like this based on pure empiricism stimulate the plastic imagina­tion and develop the power to feel aneselfinto a space permeated by farces.13

The w o r k o f Hans Jenny in the 1950s and 1960s i s undoubtably the best example o f the study o f h o w oscillating, f luctuating. gradient fields of forces can produce n o t on ly pat terns bu t forms. The pr imary theme tha t runs through Jenny's wr i t ings about these experiments i s the continuous charac­t e r between the forms produced and the fields f rom which they emerged. For example, Jenny argues tha t in the case o f "the vibrational field i t can be shown that every pa r t is . in the true sense, implicated in the whole."24 H is experiments consisted o f t he effects of vibrat ions o n a par t icu la te concrete medium. The concrete forms he studied were in an env i ronment where v ibrat ion and wave phenomenon were inherent t o the system of f o r m gen­erat ion and evolut ion. He gave these structures the name "cymatics" mean­ing the "characteristic phenomenology o f vibratianol effects and wave phenom­enon with typical structural patterns and d y n a r n i c ~ . " ~ ~In general, Jenny p io­neered the use of viscous par t ic le f lows on plates that were bo th vibrat ing and magnet ized. H i s techniques var ied f r o m t h e study of i r o n f i l l ings o n

35

RnLnate Fora

Figure 26 and 27. A sequence of flowable miis through a vibrational mqgnetic field by Hans Jenny "There figurer show [he p l o r t ~poltern ef morcmrntr dirploycd by (I ferromagnetic moss m ~1 mqnetic field under the influence of wbmtions. The mass flows m rhe mopnct~cspore ond reflects ID c~nfig~rmioni. It wrrther, r e a n up, m d ttrctchcr out bur olwayr 8" 0 wdy that rcflerrr Ihe ~ i f ~ o t i o nm the mopetic field (11 that porndar time,'' From Jenny,"01 2 of Cymoticr. Wove Phenomenon Vibrdionol Effect% Harmonic Osrdottoor with their ltruaurc. Kmeticr ond Dynamm. (Barel- Basiliur PTCII. 1974). 62

Figurer 28 and 29: Jenny's description of the formarion of there formr i n magnetic space taker the language of architectural I ~ T Y L ­

ture a s he mentions borh archer and walls. "Under other cond11mns there are upfoldmgr which rise up IO form archer There i r r ~ ~ t u r e i tower up and tend 10 flow d o n g a path. Then they thrust out ogoin inlo rpace. ond m the tnterplay between the cshcrron of the mars ond the map­nelir force they spread, grow thm, and peter out. Farms tower up displaying the configuration wrought by mopnettc force and o ~ c i l l ~ f i o nLarge leaflike wollr toke rhope ond sway l o ond fro m the mognelic field." Jenny. Cymatirr. 61

plates t o the sandwiching o f f luids between v ibrat ing glass plates. Jenny also used mo t ion pictures t o capture the movement o f these forms wi th in the magnetic pathways of osci l lat ing fields. His method was t o study the mo t ion sequences of the forms ra the r than t h e i r stat ic form. Previously, part icles o f fil ings and other materials were t rea ted as discrete elements that would f o r m a pat tern that was co inc ident w i t h t h e geometry o f t he plate. By in t roducing viscosity t o the par t ic les thus forming a continuous semi-solid f low, Jenny was able t o study t h e shaping o f f o r m in f ree space rather than in two-dimensional pat tern only. By varying t h e Reynolds numbers of these part icles suspended in a f luid, he was able t o develop an in tu i t ion in to the morphology o f forms w i th in magnetic fields. His studies involved the famil­iar use o f a vibrat ing plate tha t wou ld configure i ron filings i n t o patterns. Added t o this influence was the presence o f magnetic fields t o impose polar patterns o n the filings.These forces were then thought o f in terms of per i ­odic excitement by bo th the v ib ra t i on osc i l la t ion and the changing pos i t ion of the magnet. Thus the forms tha t emerged were studied bo th in the i r f o r m and in the ways in which they w o u l d fo l l ow the magnetic pathways. The play between t w o types o f fields, magnetic and vibrat ional, produced form. The character o f these forms were persistence and continuity, but, unl ike discrete reducible forms, they remained continuous w i th the fields w i th in which they were generated. Rather than making shapes through the famil iar operations of a scu lptor o r arch i tect , through d i rec t manipulat ion

36

Figurer 30 m d 3 I: "There marwr h a r e solidified under wbro­tton The relief IS complicated m ~ l r u c t u r e

beroure eorh of the yorr0UI stage5 O f Con­

~ t e n c ythe moss hor porrcd throuph whde solidifying hor left 11s imprint There ore imge billow-like farmotioor ond tiny w r m

klcs. W O V E t r o m ru<ceedtog one another, ond sudden chonger m the dvecrmo of flow I t i s 01 8 f the 'hirtory' o f the process hod been recorded 8 0 tronsverre ond looptuda­no1 foldr.There IS 0110 0 tendency for 0 lot­trrework of folds t o tokc shape." jenny. Cymmcr. 63

3 7

Rninate Form

of mater ia l f o r example, Jenny modulated f o r m th rough oscil lating frequen­cies and parameters. Jenny sculpted f o r m th rough the adjustment o f osci l ­l a t o r s w i t h o u t for fe i t ing his in tu i t ion to a machine intell igence. The shi f t f r o m sculptural techniques o f whi t t l ing, carving, chipping, and scraping mater ia l to the modulat ion. oscil lation, and v ib ra t ion o f part ic les does n o t mandate t h e rel inquishment o f creat iv i ty t o machinery. Instead. it suggests t h e creat ive manipulation o f a f l o w o f parameters i n t ime.

The use o f parameters and statistics f o r t h e design o f f o r m requires a m o r e abstract, and o f ten less representat ional o r ig in f o r design.The shape of s t a ­t istics, or parameters. may yield a cul tural ly symbolic form, yet a t the beginning, t h e i r ro le i s m o r e inchoate. A r e t u r n t o the discussion o f the o r r e r y migh t supply t w o terms: the “concrete ossembfoge” and the “abstract muchine.” F o r example, i n Etienne-Louis Boullee’s Cenotaph t o Newton, the o r r e r y operates as b o t h an abstract model and as a sign. The orrery, i n the sense t h a t it represents the movements and organizat ion o f a centered and harmonical ly regulated universe, i s a concre te assemblage. To the degree t h a t it i s a diagram f o r central ized harmonic regulation, l ike a compass, it i s an abstract machine. The diagram f o r the o r r e r y can be seen to circulate among many inst i tut ional and symbolic regimes w h e r e it takes on many meanings. As a statement o f central ized regulation, however, i t s abstract per fo rmance i s consistent, Any abstract machine, such as an orrery, can be u n d e r s t o o d as b o t h a technical statement and as a signifier. Ne i ther i t s rep­resentat ional n o r i t s technical s t ruc tu re can be unders tood independently. The di f ference between i t s abstract and representat ional roles can be loca ted precisely a t the m o m e n t it crosses the technological th resho ld f r o m being a diagram t o a concrete assemblage. The use of the t e r m abstract ion here i s n o t intended to be confused w i t h the pur is t o r modern n o t i o n of visual abstraction. I n those instances abstract ion involves an aes­t h e t i c reduc t ion t o f ixed fo rmal essences th rough the paring away of dif­ferences. An al ternat ive concept of abstract ion, one tha t i s m o r e generative and evolut ionary, involves prol i ferat ion, expansion and unfolding.This marks a shi f t f r o m a modern is t n o t i o n o f abstract ion based o n f o r m and vision to

an abs t rac t ion based o n process and movement. I n o r d e r t o define such a

diagrammatic regime, it is perhaps m o s t helpful t o c i te Michel Foucault’s te rms; “abstract machine” and “diagrom.” Gilles Deleuze has re fe r red to these t e r m s as “asignifying concepts.” By def in i t ion, an asignifying concept i s ins t rumenta l be fore it i s representat ional . This mode l depends o n the pre­cise d i s t i n c t i o n be tween “linguistic constructions” and “statements.” Linguistic construct ions, such as propos i t ions or phrases, can always be a t t r i b u t e d t o part icular referents. Statements, o n the o t h e r hand, are n o t in i t ia l ly l inguistic b u t are machinic processes.26 F o r instance. the sequence o f le t te rs Q, W, E, R,T,Y i s d is t r ibu ted o n a t y p e w r i t e r o r computer key­

39

aninate Form

II

.o

board t o produce words.The logic o f the i r sequential d is t r ibu t ion i s based o n the cont ro l o f the speed a t wh ich one can potent ia l ly type words i n the English language. There i s no single sentence o r w o r d t h a t tests this distr i ­bu t ion b u t rather an indef in i te series o f exist ing and fu tu re words. Because there i s an open series t h e system must be characterized as indefinitely structured. The keyboard is an actual machine, or concrete assemblage, because it i s technological. Bu t t h e d is t r ibu t ion o f i t s le t te rs on keys in space i s a v i r tual diagram, o r an abstract machine. Statements such as these are machinic techniques, discursive concepts, o r schemata t h a t precede the representational and linguistic effects they facil i tate. Signifiers are n o t rejected b u t delayed toward t h e moment tha t they are “found at the inter­section of different systems and are cut across by the statement acting in the role of primitive function.”27 Linguistic construct ions are merely postponed, n o t abolished, and a regime o f abstract, schematic statements are seen t o preempt and sponsor them. From t h e part icular discursive fo rmat ion o f mult ip le, diagonally intersect ing statements, some f o r m o f expression emerges. Through the in te rac t ion of a mul t ip l i c i t y of abstract statements, signifiers emerge in a m o r e dynamic manner than mere representational effects might.The shift f r o m linguistic models t o the pro l i fe ra t ion o f asig­nifying statements marks what Deleuze te rms a move f r o m the “archive” t o the “diagram.”28 The move f r o m linguistic construct ions t o statements, o r m o r e proper ly f rom meaning to machine, i s a necessary shi f t i n sensibility if one i s t o tap the potent ia l o f abstract machines such as computational m o t i o n geometry and time-based, dynamic force simulations.

This shift i s the pr imary explanat ion f o r t h e apparent alliance between cer­ta in aspects o f Deleuze and Foucault’s discourse and many contemporary architects now weary of representat ional cr i t iques spanning f r o m stylistic postmodernism to deconstruct ion. I n Deleuze’s in te rpre ta t ion of Foucault’s c r i t ique o f panopticism, concre te archi tectural f o r m i s t ransformed i n t o abstract machinic instrumentality. Techniques, as opposed t o technology, become an expression of cul tural , social, and pol i t ical re lat ions ra ther than as an essential power. The effects of abstract machines tr igger the forma­t i o n o f concrete assemblages when the i r v i r tua l diagrammatic relationships are actualized as a technical possibil i ty. Concre te assemblages are realized only when a new diagram can make them cross the technical threshold. It i s the already social diagrams tha t select the new technologies. It i s in the sp i r i t o f the abstract technical statement ye t to become concrete that topologies, animation and parameter-based model ing are being explored here. In o rder t o br ing these technologies i n t o a discipline tha t i s defined as the s i te o f translation f r o m the v i r tua l i n t o the concrete, it i s necessary tha t we f i r s t interrogate the i r abstract s t ruc tu re . W i t h o u t a detailed under­standing o f the i r performance as diagrams and organizational techniques it

i s impossible t o begin a discussion o f t h e i r t ranslat ion i n t o archi tectural fo rm.The availabil ity and rap id colonizat ion of archi tectural design by com­puter-aided techniques presents the discipline w i t h ye t another oppor tun i ­t y t o b o t h r e t o o l and re th ink i tsel f as it did w i t h t h e advent o f stereomet­r i c p ro jec t ion and perspective. If there i s a single concept tha t must be engaged due t o the pro l i fe ra t ion o f topological shapes and computer-aided tools, it i s tha t i n the i r s t ruc tu re as abstract machines. these technologies are animate.

I

i

! '

T h i s p r o j e c t has been made p o s s i b l e i n p a r t

t h r o u g h t h e g e n e r o u s s u p p o r t o f The G r a h a r F o u n d a t i o n

f o r t h e R d v a n c e n e n t o f t h e H u m a n i t i e s

Published by Princeton nrchitecturat press

37 ~ a s tseventh street. NeY rork. N e W rork 10003, u 5 R

0 '999 w e $ Lynn ISIN 1-56898-083-3

n l t rLghts reserved 04 0 3 0 2 01 0 0 99 4 3 2 I

Prrnted and bound in chLna

N O p a r t o f this book or t o - n o m nay b e reproduced in any lanner uithout urrtten perlrssion fron the publrsher eacept in

the context of revLeus

Library of conqrorr catstoqinp-in-Publication nata:

Lynn. Greg nniiate Form I Greg Lynn

P cm ISBN 1-56896-083-3 [hardcover)

I Lynn, Greg--rnhtbtttons I ritle

N R 7 3 7 L9784 1998 720' rz'z--dczi 98-10076

project rditor: rherese uelly

sook Design: ores Lynn, utrrka narlsson, ueather noberqe, m d r e a s Froech

CO-ROI Design and production: nndreat FrOeCh. Dieter ~ a n s s e n , td welter

set in: g i l l sans. platelet

Photo credits: Jefferson fttinger (nrtirts space] nndreas Froech [uenie onstad] 111 Hotden lrokohana study nodet] oavtd Joseph Inrtists space] Gordon nLppinq (Henle onstad) nannes strassl (stereotithopraphy)

fvery reasonable attempt has been made to identify omners o f copyriqht Errors or OiiSsLons u r t l be corrected in subsequent editions

*' - ._2--:.-rh - .\i

4

I

c o n t e n t s B n i m a t e F o r m 8

~ r t i s t sspace r n s t a l l a t t o n 44

A r t i s t s s p a c e i n s t a l t a t t o n D e s i g n 62

c a r d i f f Bay o p e r a House 82

p o r t A u t h o r i t y Gateway 102

Yokohama p o r t T e r m i n a l 120

HOUSe P r o t o t y p e cn t o n g I s l a n d 142

~ e n t eo n s t a d i n s t a l l a t t o n o e s t g n 164

~ e n t eo n s t a d r n s t a l l a t t o n 184 A

c r e d i t s 203

P r o j e c t f l n i m a t t o n s Co-Ron