PARAMETRIC DESIGN STUDIO NINA NOVIKOVA 2015

STUDIO AIR

2

ALGORITHMIC SKETCHBOOK CONTENTS

B1

B2

B3

B4

B5

TECHNIQUE ANALYSIS 36

43

LOOP_03 - CASE STUDY 2COMPLEXITY

MATRIXES

VARIATIONS

B6

B7

B8

PROPOSAL

BIOTHING REVISITED - CASE STUDY 1

MATRIXES 44

52

60

72

FORMFINDING (PROTOTYPING)

74

78

LEARNING OUTCOMES 90

ALGORITHMIC SKETCHBOOK

REFERENCES

91

93

3

PART B CRITERIA DESIGN

CONCEPTUAL FORMULATION + TECHNICAL DEVELOPMENT+PROPOSAL

The convenTional undersTanding of folding is as ThaT of a Technique ThaT defines edges, TessellaTes The connecTion poinTs beTween surfaces. folding is, in essence, a poinT of disTorTion on a plane, a poinT of sTress on a surface. This goes around To imply ThaT iT’s a Technique necessary To achieve any geomeTry. if we fold a square piece of paper, iT will become a Triangle, if we fold iT on pre-calculaTed seams, we’ll have paper models of plaTonic solids, and so on.

double agenT whiTe, an experimenTal sTrucTure consisTing of developable combinaTion of spheroids, explores how folding inTeracTs wiTh morphology of geomeTry and sur-face ouTlines where They meeT.

one of The consTraining parameTers of double agenT whiTe would have been To develop a surface ThaT allows for curvaTure wiTh angles ThaT would allow proTrusion, yeT flows inTo iTself smooThly. scored and folded lines serve as conTrol poinTs Through which The folding occurs.

Though mark fornes and aTelier calTer do noT dis-close The generaTive process, iT is plausible To as-sume ThaT There mighT have been Trials To opTimise The amounT and direcTion of said conTrol poinTs/lines so ThaT Their usage is effiTfrom sphere To sphere seam-lessly.

of course, wiTh enough scored lines and bending momenTs, The projecT would have achieved The perfecT specimen of smooTh edge and conTinuiTy – a symmeTri-cal plaTonic sphere ThaT holds a simplified sTrucTural uniTy. however ThaT would diminish greaTly from The sense of visual conTinuiTy and The language of mor-phology. an idea explored by roberT woodbury in his ‘how do designers use parameTric design’ is ThaT There’s a Typology of parameTer – in This case visible as The juncTure beTween elemenTs and The overlapping of Two direcTions of paTTerns and inTeracTion of double curvaTure (aimed To furTher The complexiTy of shape) – and The guidelines for acTual form – The size of The spheres, The degree of vaulT.

once condiTions aT which The shapes are conjoined and The relaTionships beTween differenT sizes of spheroids are esTablished, The rhyThm, The logical law by which folding as a Technique conTrols The bending poinT and juncTion, is derived. The shapes can Then be sTacked and reapplied over and over To creaTe a conTinuous surface and sTrucTural vaulTing over a span dicTaTed by independenT facTors – such as The siTe or insTalla-Tion space area and heighT, designaTed usage of space, and amounT of open large vaulTs required.

above: numerous spheroids (the Very Many)right: joints at the folds (Strabic)

4

TECHNIQUE EXPLORATION | FOLDING

A3. GENERATION

left - Andrasek’s conceptual research for Seroussi Pavilion (biothing)

5

once condiTions aT which The shapes are conjoined and The relaTionships beTween differenT sizes of spheroids are esTablished, The rhyThm, The logical law by which folding as a Technique conTrols The bending poinT and juncTion, is derived.

The shapes can Then be sTacked and reapplied over and over To creaTe a conTinuous surface and sTrucTural vaulTing over a span dicTaTed by independenT facTors – such as The siTe or insTallaTion space area and heighT, designaTed usage of space, and amounT of open large vaulTs required.

above: interior of the structure, showing the vault space (the Very Many)

left - Andrasek’s conceptual research for Seroussi Pavilion (biothing)

6

B1 - TECHNIQUE STUDY

7

FABRICATING COINCIDENCES

The da office (moma, 1998) was designed by nader Tehrani and monica ponce de leon of nadaa, and aims To deconsTrucT The main-sTream definiTion of facade and sTrucTure. This is, in essence, a developable surface held by iTself and column-like supporTs, draped over an exisTing building.

here The folding also is responsible for granTing The sTrucTure iTs sTrucTural qualiTy. The bend/fold lines and The TriangulaTion edg-es beTween The sTrips of sTeel creaTe sTress poinTs and give The verTical span some rigidiTy and sTabiliTy. sTrucTural columns Through which The folding is conTinued assisT This noTion. This makes The meTal sheeT boTh The sTrucTural componenT bearing iTs weighT, and The aesTheTic/decoraTive funcTion prescribed To The ‘skin’, Thus blurring The line beTween The Two (moma).

The definiTions of folding here are all achieved Through principles of compuTaTion – defining each individual ‘face’ of The sTrip as well as The sTrip iTself, perforaTing The surface To leT lighT Through, deTermining The overlap and scoring The edges.

The Technique of score and fold raTher Than bend under direcT sTress, or welded/bolT-ed joinTs challenges boTh The qualiTies of maTerials and percepTion of assembly. why go Through The lengTh of acTually folding The maTerial as opposed To imiTaTing The folding paTTern? The eliminaTion of joinTs prevenTs needing To apply addiTional maTerial and caus-ing Thicknesses aT each joinT, which in Turn leTs The folds To look more clean-cuT and ex-ecuTed wiTh much more precision. There’s also less risk of The meTal failing under sTress, seeing as some of iT is relieved by The scoring.

8

once again, There is a focus on conTinuiTy Through The shape, The facT ThaT The ‘folding’ seam is indeed The proces-sion of one surface inTo The oTher as opposed To disjoinT-menT and fracTure of The face.

B1 - TECHNIQUE STUDY

in The boTswana innovaTions hub (shop archiTecTs), currenTly in consTrucTion, This qualiTy spans Through The enTire building. The facade of each floor is one long sTrip ThaT disTorTs and morphs as iT’s sTreTched over The building and loops up and down. This kind of language uniTes The horizonTal panes of The building TogeTher, and The facT ThaT The folded surface creaTes a geomeTry brings The whole form closer To a developable para-meTric form as opposed To jusT The facade.

9

left - the folding visual effect achieved by the metal sheeting on the outside of the dA structure (NADAA) above - FInal render for Botswana Hub (SHOP architects)

10

B2

Evolo - Double Agent White (http://www.evolo.us/architecture/double-agent-white-in-se-ries-of-prototypical-architectures-theverymany/)

Galilee, Beatrice, ‘Office dA‘ for Icon Eye, (http://www.iconeye.com/404/item/3484-office-da)

Fetro, Sophie, ‘Mark Fornes, Double Agent White, Prototype d’ar-chitecture’ (http://strabic.fr/Double-Agent-White-prototype-d)

Fornes, Mark & the Very Many, ‘Atelier Calder: Double Agent White,’ (http://theverymany.com/12-atelier-calder/)

NADAA studio, Projects - MoMA 1998, NADAA official site(http://www.nadaaa.com/#/projects/fabrications/)

SHOP architects, Porjects - Botswana International Hub (hhtp://www.shoparc.com/projects/botswana-innovations-hub/)

REFERENCE

REFERENCE

11

BIOTHING REVISITED

seroussi pavilion by bioThing, previously menTioned in ‘biomimicry’, is a concepTual compeTiTion enTry ThaT focuses on auTomaTed inTeracTion beTween elemenTs, reacTion To presenT charges, self-organisaTion and morphologies of geomeTry To achieve new form.

Through a base seT of curves seT in differenT direcTions, There is a disTribuTion of poinTs ThaT will organise lineworks engaging wiTh each elemenT and self-organising as defined by aTTracTion/repulsion generaTed by The force fields.

The TecTonic applicaTion of folding in This case is explored in Two direcTions. The firsT is ThaT The process of creaTion of Three-di-mensional form from a flaT diagram of some-Thing akin To an organic maTTer is in a way unfolding, unravelling The geomeTry.

iT’s almosT like The linework creaTed in The x | y panes is being pushed from The edges To bend upwards and creaTe The liTTle pods. This is a very inTeresTing generaTive feaTure and provides a mix of conTrol over The iniTial inpuT for elemenT arrangemenT, and novelTy, an el-emenT of predicTabiliTy as There is no knowing how ThaT iniTial basis will disTorT and morph in response To changes made To The iTeraTion in case There are such.

second, There is a folding/bending sequence in The maTerialiTy and expression of said form. The pavilion model seems To consisT of Thin sTrips fixed TogeTher aT The common poinT – The very Top of The ‘domes’, and Then relying on folding and bending To creaTe The geomeTry. iT would be inTeresTing To observe whaT happens To each sTrip once The definiTion sTarTs To change.

12

MATRIX ITERATIONS

species 1a i a ii a iii

a vii a ixa viii

species: reverse b i

b ii

b iii

species: buTTerfly

c i

c ii c iii

12

a iii a iv

a v a vi

a ix a x a xi a xii

b iv

b v

b vi

c v c vi c iv

14

species 1a icurve counT coming off per charge* poinT increased 24 curves > 80 curves

a ii

‘umbrella’ curve counT

poinT decreased

24 curves > 7 curves

a iii

curve counT coming off per charge poinT decreased

24 curves > 4 curves

a vii

curve per poinT - 1 radius - 2.6 poinTs per curve - 50

a ix

curves per poinT - 7 radius - 0.8 poinTs per curve - 20fline lengTh - 100 > 50

a viii

curves per poinT - 24radius - 0.05 poinTs per curve - 20fline lengTh - 100 graph range disconnecTed

species: reverse b i curves per poinT - 24radius - 0.05 poinTs per curve - 20fline lengTh - 100 graph range - 1graph scaling facTor - -8

b ii

curves per poinT - 24radius - 1.234poinTs per curve - 5fline lengTh - 140 graph range - 100graph scaling facTor - -7x - y swapped on graph

b iii

curves per poinT - 16radius - 1.5poinTs per curve - 5fline lengTh - 300 graph range - 100graph scaling facTor - 10curve value reversed

*will be referred To as ‘umbrella’ curve for shorTness

**if a cerTain parameTer is noT menTioned, assume ibid or defaulT

species: buTTerfly

c icurves per poinT - 24radius - 0.05 poinTs per curve - 20fline lengTh - 60 graph range - 6graph scaling facTor - 30

c ii

curves per poinT - 30poinTs per curve - 20fline lengTh - 100 graph range - 61graph scaling facTor - -8decay - 0.888

c iii

curves per poinT - 30poinTs per curve - 20fline lengTh - 100 graph range - 60graph scaling facTor - -8decay - 0.1 anoTher iniTial curve added

MATRIX DEFINITIONS

14

a iii

curve counT coming off per charge poinT decreased

24 curves > 4 curves

a iv

curves per poinT - 4charge poinT radius increased 0.05 > 3

a v80 curves per poinT charge poinT radius increased 0.05 > 2.6poinTs per curve increased 5 > 50

a vi

6 curves per poinT charge poinT radius 0.05 > 2.6poinTs per iniTial curve 5 > 50

a ix

curves per poinT - 7 radius - 0.8 poinTs per curve - 20fline lengTh - 100 > 50

a xcurves per poinT - 24radius - 0.05 poinTs per curve - 20fline lengTh - 100 graph range - 1graph scaling facTor - -8

a xi

curves per poinT - 9radius - 2.60poinTs per curve - 50fline lengTh- 100 graph range - 10graph scaling facTor - -10

a xii

curves per poinT - 6radius - 0.5poinTs per curve - 50fline lengTh - 30graph range - 10graph scaling facTor - -10

b iv

curves per poinT - 24**poinTs per curve - 5fline lengTh - 500 graph range - 360graph scaling facTor - 8 curve value reversed graph changed - sTeeper

b vpoinTs per curve - 55fline lengTh - 150 graph range - 360graph scaling facTor - -7.6curve value reversed x y reversed

graph changed - close To edges, obTuse

b vi

pods changed graph drasTically changed curve

c vcurves per poinT - 30poinTs per curve - 20fline lengTh - 200 graph range - 60graph scaling facTor - -1.9decay - 5 exTra curve inTroduced cull paTTern To iniTial poinTs ffTf

c vi curves per poinT - 30poinTs per curve - 50fline lengTh - 130graph range - 2graph scaling facTor - -3decay - 5 anoTher iniTial curve added

cull paTTern ffTff

c iv

curves per poinT - 1poinTs per curve - 8fline lengTh - 300 graph range - 5graph scaling facTor - 23decay - 0.75

16

c vii

curves per poinT - 26poinTs per curve - 5fline lengTh - 300graph range - 9decay - 6.7gaussian graph graph scaling facTor - 9

c viii

idenTical To 27 excepT swiTched inTcrv boolean making curves closed

species: surface

d i curves per poinT - 5poinTs per curve - 5fline lengTh - 100graph range - 60decay - 1graph - sine 3.2 exTruded

roTaTion vecTor from sTarT To end of ‘umbrella’ curve roTaTed by 90 deg

d ii

curves per poinT - 8poinTs per curve - 8fline lengTh - 100graph range - 60decay - 1graph - sine 5exTruded

roTaTion vecTor from sTarT To end of ‘umbrella’ curve roTaTed by 45 deg

MATRIX ITERATION + DEFINITION

16

c ix

curves per poinT - 24poinTs per curve - 5fline lengTh - 100graph range - 5decay - x pane graph - sine -6inTcurve mulT. boolean fTTf

inTcrv Turn 300 deg.

c xcurves per poinT - 7radius - 0.5 poinTs per curve - 20fline lengTh - remapped aT -50 To 100graph - gaussian 10decay - z pane inTcurve mulT. boolean fTTf

inTcrv Turn 300 deg.

d iii

curves per poinT - 4poinTs per curve - 5fline lengTh - 300graph range - 9decay - 6.7gaussian graph graph scaling facTor - 9

d iv

curves per poinT - 5poinTs per curve - 5fline lengTh - 100graph range - 60decay - 1graph - sine 8.7roTaTion vecTor from sTarT To end of ‘umbrella’ curve roTaTed by 25 deg

lofTed

c x

c vii

b ii

c x

The inTroducTion of a cull paTTern allowed To creaTe an inTense visual dynamic and a less predicTable disTribuTion of charge poinTs, breaking aparT The circular geomeTry and becoming more seemingly chaoTic. having The aTTracTor poinTs shifTed closer To The cenTre really emphasises The difference in posiTioning depending on how far away iT is from said poinTs, demonsTraTes how each ‘pod’ warps as The charge effecT decays - a new sense of rhyThm and dynamic in iTself.

1) To be visually dynamic, ThaT is, To have The visual elemenTs producing a sense of rhyThm or movemenT, some sorT of fluxuaTion. iT is The dynamic and repeTiTion of unified yeT differing elemenTs ThaT make seroussi pavilion so aesTheTically pleasanT. 2) To reTain iTs aTTribuTes as a Three-dimensional shape. all geomeTry ThaT is noThing buT flaT sTrips will be eliminaTed as iT doesn’T have any sTrucTural or archiTecTural applicaTion. 3) plausable real-life applicaTion or sTrucTural suggesTion

SELECTION CRITERIA

This has been a succesful Trial of reversing The shape and sTarTing To Think abouT sTrucTural values. you can easily imagine someThing like a builT vaulT sysTem To creaTe an enclosure, wiTh The aTTracTor poinT circumferences being The cenTre of weighT Transfer. The idea of an enTire sysTem is favourable because iT shows how parameTric design can be beneficial - The deriviaTion can be ediTed To accomodaTe column Thick-ness avaliabiliTy, The need To sTrucTural elemenTs required eTc. in Terms of selecTion criTeria, iT is a very plausable 3d shape imaginable in real life; The degree of slope and variaTion of each ‘pod’ is inTeresTing and dynamic To some degree.

The case sTudy is firmply rooTed in poinT charge and aTTracTor poinTs so iT was exciTing To break aparT ThaT paTTern and produce a new arrangemenT. There is The aforemenTioned movemenT and rhyThm noT only in repeTiTions of lines buT also in how The individual shapes seem To crawl ouT and away from The iniTial frame of curves. This iTeraTion embraces alisa andrasek’s idea of no confined canvas To work wiThin - as The gh definiTion changes, The shape disTorTs and spreads.

here a whole new meThodology of pod sTrucTure has been defined, wiTh inTerTwining arches and closed curves. This is almosT reminiscenT of self-organisaTional meThods. The firsT choice criTeria indirecTly hinTs aT presence of a paTTern, and compared To The oTher iTiraTions, This is The mosT inTeresTing and prominenT change ThaT has been achieved in The paTTern. The pods are quiTe Three-dimensional and have Their presense as individual shapes, which one can imagine prefabricaTed and sTacked TogeTher To form a dynamic whole, so a plausabiliTy of real-life applicaTion emerges.

20

B3 CASE STUDY 2

loop_03

loop_03 is an insTallaTion by unibolo and alessio erioli of co-de-iT, compleTed in 2012. iT is a com-plex flux shape consisTing of a membrane sTeTched on a series of ribs - secTioned sTrips of maTerial ThaT flucTuaTe beTween being pulled inTo The cenTre or sTreTched away from iT.

iT seems To reply on a number of conTrol/aTTracTor poinTs To pinpoinT The curvaTure. The process of folding is occuring as The sTrip Travels and disTorTs Through each poinT, Thus creaTing curvaTures ThaT sweep Through a complex horisonTal paTh as well as TwisTing and shearing as iT undergoes The bends and changes in ampliTude and sTeepness of each curve.

The curvaTure is, of course, The main focus. alessi wriTes on his inTenT To express The curve as boTh sTrucTure and aesTheTic, focusing on connecTions and spaTial inTeraTions beTween sTrips and surfaces.

The consTrucTion drawings/design projecTs Tend To suggesT ThaT This is a number of developable surface on a single base, buT They are noT of a regular elongaTed recTangle shapes, and Their edges are noT linear.

someThing To especially consider would be how The curves are generaTed, how is each divided inTo poinTs, and how The poinTs are isolaTed from The resT To allow The useage of Them as a verTice for roTaTion. There is an inTeresTing disTorTion obseravle Through The enTire sweep, and noT limiTed To jusT projecTing upwards, across or sideways - each sTrip is fluid, con-sTanTly morphing. Though iT is suggesTed ThaT This is a reacTion To how The sTrip is TwisTed and manipuTaed, The algorihTm behind The paTTern and disTorTion seems quiTe difficulT To adress - This would be The second parT of The reverse engi-neering process.

21

PAPER ARCHITECTURE

a series of experimenTs bending a paper sTrip To see how iT reacTs under pressure.

a series of conTrol poinTs have been employed To experimenT wiTh geomeTry similar To The one of loop_03. To achieve The 3-poinT ribbon sTrucTure, which is whaT The case sTudy uses, boTh aTTracTor and repulse poinTs are in acTion - The ones in The cenTre are pushing The sTrips in, folding Them in To-wards The cenTre; The ones around The ouTer curves ensure The surface reTains The volume.

similarly, when a number of sTrips is combined, They share Their conTrol poinTs and an amounT of shearing along The z axis is added and shifTed as The Two pieces of geomeTry inTeracT wiTh each oTher as well as The pins

22

analysis of bending in the physical realm

more prominenT on a Thicker sTrip, The flaT Thin body of The sTrip is warping even when noThing is done aside from pinning iT down. folding occurs ThroughouT The enTire sTrip even when only Three conTrol poinTs are employed - in oTher words iT supporTs iTself in a cerTain curveaTure ThroughouT when The same kind of cenTralisa-Tion happens as in loop-03

similarly, The shape changes drasTically and drasTically moves in The x+y+z axis when The naTural edges are TwisTed.

23

approach: disTribuTing a number of charge poinTs as The cenTres of each ‘pod’, disTribuTing lines To define The shape and radius of each pod; using graph curvaTure To define The level of Three-dimensional proTrusion of The pods.

innovaTion: new shape and unprecedenTed form morphing from minimal parameTers seT by human; everyThing else is derived from a grasshopper definiTion. self-organisaTional principles conTrolled Through a seT of variables and definiion facTors, almosT akin To biomimicry.

aesTheTic: rhyThmic, reaching ouT, dynamic, ballanced, symmeTric (despiTe slighT assymTery), flowing, inTerconnecTed, harmonous, sensual, serene

parameTric design advanTages: unprecedenTed form, inTeresTing folding/bending momenTs ThaT are oTherwise impossible To conTrol

biothing - seroussi pavilion

24

co-de-it - loop_03

approach: exTruding base seT of geomeTry To creaTe a seT of curvaTures and developables ThaT will have sTruc-Tural inTegriTy Thanks To The Tension and sTress disTribuTed by This percise curvaTure.

innovaTion:usng a maThemaTic formula, a sine graph, To define The flowing geomeTry, To define scale and spacing; To employ algoriThms defined by curvaTure (sin, cos, tan) To seT The parameTers for an opTimal form. This engages boTh generaTive compuTaTion and human inTelligence To pick The mosT pleasanT ouTcome.

aesTheTic: dynamic, flowing, morphologic, unTangible, unconTained wiThin horisonTal and verTical panes, organic, fluid, cenTered, unconTained, eThereal

parameTric design advanTages: unprecedenTed form generaTion, combinaTion of maThemaTic logic and aesTheTic expression

sTrucTural sysTem: verTical loadbearing braces, supporTing ‘ribs’ fixed aT braces, fabric membrane draped over ribs.

25

reverse engineering sequence

* working drawings published by co-de-it suggest use of tangent graph mapper after this step** repeat or use series component to generate needed amount of curves (4 in this case)

*

26

loop-03

**

27

matrix iterationsspecies: headwaTers

a i a ii a iii

a vii a viii a ix

a xiiispecies: rafT

b i b ii

b vi b vii b viii

a iv a v a vi

b iv

a xi a xii

b iii b v

b ix b x b xi

a x

matrix definitions

species: headwaTers

a iswiTch graph charge To negaTive, flipping The curvaTure

a ii

run a sorT lisT on poinTs To change The order of poinTs for inTerpolaTion (unexpecTed ouTcome from command)

a iii

swiTch boolean of inTer-polaTed curve To false To creaTe open curves

a vii

grafTing The emerging poinTs and The

inTerpolaTed curve inpuT

a viii

increasing amounT of poinTs/graph range To 15, creaTing more full spans of The sine over The exTrusion

a ix

flaTTening emerging poinTs and The inTer-polaTed curve inpuT To creaTe one long sTrip

a xiii

drasTically increasing number of poinTs The very iniTial curve is divided inTo (ampliTude defaulT)

species: rafT

b i drasTically increasing number of poinTs The very iniTial curve is divided inTo (ampliTude defaulT)

b ii

shifTing ampliTude and increasing graph range, graph value and graph curvaTure iTself

b vi

drasTically increasing number of poinTs The very iniTial curve is divided inTo (ampliTude defaulT)

b vii

when new baseline curves are creaTed by scaling and moving, moving oc-curs across boTh The x and z vecTors; geomeTry conTrolled Through am-pliTude, graph range and graph

b viii

similar To 20 buT a cull paTTern is employed To organise individual cur-vaTures and have Two differenT graph funcTions exTrude form from desig-naTed baselines

a iv

grafT The inpuT for base-line curves To creaTe in-dividual sTrips – boolean To false To disjoinT The emerging geomeTry

a vflaTTening inpuT for baseline curves and emergenT poinTs from The ‘divide’ command - boolean aT false

a vi grafT The baseline curves – boolean aT True, closed curve

b iv

sTeeper graph, smaller inTerpolaTed curve angle, geomeTry mirrored aT end-poinTs of exTrusions To form a buTTerfly shape

a xi

grafTed, idenTical To 4 excepT shifTing The ampliTudes of boTh lisTs, increasing The inTerval beTween The Two

a xii

flaTTened, idenTical To 5 excepT drasTically increasing of boTh lisTs (from under 10 To 1000)

b iii

similar To 15, larger difference beTween am-pliTudes and a less sTeep graph + lesser range

b vlofT of species b xi, porTrayed direcTly below. conTrol Through lofT opTions opTimised for smooThness and flow

b ix

ssubsTiTuTing very ini-Tial geomeTry To an open crescenT-shaped curve, creaTing differenT kinds of ouTpuTs Than previously

b xsubsTiTuTing very iniTial geomeTry for a sTraighT line and Then organizing The exTrusions Through a ‘move’ command

b xi

same approach as 23; cur-vaTure conTrolled Through graph, graph range and num-ber of poinTs derived from iniTial line.

a xincreasing ampliTude of one lisT and bringing The ampliTude of oTher close To 0

32

MATRIX ITERATIONSspecies: skin c i

c ii

c iii

c vi c vii

species: hor + verTical d i

species: large marsupials e i

e ii

e iii

species: absTracTing folding

f i f ii

f ii

2

c iv

c v

c v

d ii d iii d iv

e iv

e v

e v

species: disinTegraTion

g i g ii

g iii

34

MATRIX DEFINITIONS

species: skin

c i reTurn To The iniTial sine sTrip; lofTing The line curves of one as op-posed To exTruding Them.

c ii

a seT of inTerpolaTed sine curves organized Through ‘move’ componenT and lofTed; Then TriangulaTed inTo a mesh

c iii

similar To c ii; u/v values of TriangulaTion paTTern changed To imiTaTe scoring paTTern

c vi

panelise meshes from exTrusions from Two curves (refer To original definiTion)inTeresTingly, sine curvaTure becomes more subdued

c vii

conTinue from , add exTrusion lines for a 3-dimenTional paTTern across single-line pan-el edges TriangulaTed inTo a mesh

species: hor + verTical d i reTurn To iniTial defini-Tion. increase iniTial divide counT and modify culling paTTer/separaTion To in-crease amounT of dips and proTrusions

species: large marsupials e iuse iniTial definiTion lunchbox To quad mesh run kangaroo simulaTor

apply unary forces y vecTor

e ii

simialr To e i buT posiTion via x y z vecTors

use move funcTion To posiTion in conTinuous dynamic manner

e iii

imiTaTing bending moTion in digiTal space using kangaroo hinge funcTion. base curva-Ture exTruded, converTed To Triangualr mesh and benT accordingly

species: absTracTing folding

f ichange base geomeTry To a series of line geomeTry ThaT expands by roTaTing and moving in The xz axis

sine range and poinTs

derived - 2

f ii

increase line counT. decrease movemenT angle and vecTor lenghT afTer reaching 90. increase range To 3; sTeeper sine

graph mapper

f ii

increase line counT. decrease movemenT angle and vecTor lenghT afTer reaching 60. swiTch To bezier graph mapper. re-duce inTerpolaTed curve angle To 1

2

2

c iv

similar To 27 buT wiTh a lofT creaTed from edges as defined by panelisaTion as defined in c iii, and Then once again plugged To TriangulaTe

c vflaTTened componenT for brep edges as used in c iv

creaTing a seT of winding curves

c vchange panel generaTion To lunchbox quad mesh; employ cull paTTern To presenT form as individual sTrips, using u/v counT nodes To conTrol sTrip size

d ii conTinue increasing amounT of division poinTs and dips while slighTly adjusTing ampliTude

d iii iniTial definiTion - maxim-ising sine graph mapper, range and angle To inTer-polaTed curve To accenT on verTical differenTiaTion

d iv

conTinue playing around wiTh significanT verTical dif-ferenTiaTion while reducing inTerpolaTed curve angle To 1, causing flaT planar sTrips folding akin To a hinge funcTion

e iv

increase The amounT of force applied; swiTch To quad mesh

lengThen span of simulaTion and perform simulaTion in 3 by moving The anchor poinTs Through ampliTude (rfer To iniTial def)

e vconTinue experimenTing wiTh hinge definiTion, drasTically increase apliTude, perform simulaTion in 7 sTeps

e vuse boolean false iniTial curve (open); conTinue experimenTing wiTh hinge definiTion

species: disinTegraTion

g ireTurn To iniTial definiTon - find sine curvaTure brep edges, lofT, divide surface, inTerpolaTe curve

g ii

iniTial definiTion undexTrud-ed curves - divide by equal poinTs, draw lines beTween corresponding poinTs, exTrude lines in x z vecTors

g iii

iniTial def unexTruded curves di-vide by equal poinTs, draw lines, exTrude using sine curvaTure as per inTial definiTion, use range disconnecTed from division poinTs To conTrol densiTy

g iv

divide unexTruded sine curvaTures

draw arches Through consequenT poinTs. rebuild curve wiTh angle of 3. fiT geodesic curves

exTrude in x z wiThouT sine wiTh x lengTh > z lengTh

g vdivide unexTruded sine curvaTures

draw arches Through consequenT poinTs. conTrol shaping, slope and frequency Through poinT counT

g vi

simialr To iv buT inTroduce shifT lisT To creaTe sTeeper curve and inTeresTing frequency. exTrude wiTh x lengTh = z lengTh

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selection criteria

1) To employ The mechanic of generaTing new geomeTry and form Through sine curvaTure in an aesTheTically pleasanT unprecedenTed manner ThaT can be expressed in an algoriThm and applied To a variable seT of parameTers. one can speculaTe ThaT The parameTers, such as The base geomeTry, The maximum verTicaliTy or horizonTaliTy and oTher fea-Tures, can be direcTly Taken from siTe and brief conTexT, Thus combining The power of generaTive compuTaTion design and The need To granT iT conTexTual and meTaphysical value and unique siTe relevance.

2) To have a sense of movemenT and rhyThm expressed Through iTs visual elemenTs, To possess a cerTain con-TinuiTy, as This is more plausible in a circulaTion device and would complemenT The creek flow nicely. sines roTaT-ing around a fixed cenTre poinT are aT a disadvanTage here because Their circumference becomes iTs own limiTaTion To said conTinuiTy. one can speculaTe ThaT The parameTers, such as The base geomeTry, The maximum verTicaliTy or horizonTaliTy and oTher fea-Tures, can be direcTly Taken from siTe and brief conTexT, Thus combining The power of generaTive compuTaTion design and The need To granT iT conTexTual and meTaphysical value and unique siTe relevance.

3) To explore negaTive and posiTive space, The dynamic of solid and void; To be perceivable as a 3-dimensional flux shape yeT noT be solid. This has been a feaTure inTerTwined wiTh The basis of generaTive design Through sine curvaTure - making flux form beyond The limiTaTions of generic panes and orienTaTions Through someThing ThaT is Technically noT a solid (The concepT of developable surfaces challenges The percepTion of plaTonic solids aT iTs core). Therefore, To keep This un-whole-ness, The exTrusions cannoT have immaculaTe presence, There needs To be a dynamic of posiTive and negaTive spaces. as poTenTial on-siTe applicaTion, This can be effecTive dealing wiTh issues idenTified in parT a, such as waver level variaTions and polluTion sweep. The openings leT waTer pass freely, and could funcTion as a filTering device akin To baleen.

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paper architecture

g v

b viii

c v

c v

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selected species

The rafT species comply wiTh deconsTrucTing The cenTring around one aTTracTor poinT, which was a firsT coming ouT of The loop-3 reverse engineering. sine curvaTure creaTes a repeTiTion of plaTes ThaT are almosT sorT of like a paThway in The middle; The repeTiTion creaTes a sense of flow and rhyThm in The geomeTry, like liTTle waves in Themselves. in Terms of Technical applicaTion, one can imagine an exTended sequence forming a paving or a bridge of sorTs.

There is someThing very expressive and moving in This parTicular shape, and The full asymmeTric curvaTure is aesTheTically pleasanT. poinT 3 is really challenged here because This iTeraTion above all presenTs a solid shape, a Three-dimensional presence; and ouT of all iT has The leasT surface coverage seeing as all expression of form is expressed Through The use of curve, no exTrusions or lofTs. Though The influence of The sine wave is sTill reada-ble in The iniTial form, The ouTcome of rebuilding arcs – The kinks, The radius and behaviour - was quiTe unexpecTed and exciTing.

The folding mechanic here is a kind of folding novel To bioThing and loop-3 – sharp, angular, pronounced. iT’s a sTark conTrasT wiTh The smooTh curvaTure of oTher iTiraTions and The original case sTudy, and would be of equal conTrasT juxTaposed wiTh The naTural environmenT of merri creek, buT perhaps The conTrasT would work To emphasise The rhyThmic, dynamic presence of The shape. The TecTonics of creaTing 3d form from bending a single piece of maTerial in differenT direcTions is quiTe inTeresTing; buT while This meThod of surface TreaTmenT can easily be used for all kinds of surfaces, iT lacks in The innovaTion/unprecedenTed behaviour deparTmenT.

This species has been selecTed because iT gives an impression of scoring a solid shape, of inTroducing openings inTo The whole as opposed To Trying To make up a flux shape from smaller elemenTs, in This Technique exTruded sTrips. There is also a more or less defined sysTem of longer, curvier elemenTs resTing on Top, and harsher arch-es of sTrips aT The boTTom, which makes one Think of sTrucTural frames vs exTerior expressive curvaTure, giving room To make speculaTions of real-life applicaTion of someThing like This.

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paper architecturevariations

1flaT plaTeaus of layers To conTrol heigh and horisonTal proTrusion as defined by broken singular round curve and generaTed by sine curvaTure

2overall shape derived from sine curvaTure from Two separaTe curves conTrolled Through The same funcTion; lines drawn Through poinTs and joined, Then exTruded To form 3 fold direcTions from one sTrip.

3sTrucTure of lines connecTed beTween poinTs of shape defined by sine curvaTure derived from Two separaTe curves conTrolled by separaTe funcTions.

wiTh The selecTion criTeria in mind, a number of variaTions have been produced. evolving from The ‘rafT’ species above all, a bridgelike sTrucTure comes To mind. The Techniques of sine curvaTure exTracTion drive The geome-Try generaTion, while a remaining quesTion is how To besT express The form ThaT resulTs.

The overall shape of The geomeTry is deTermined by The curvaTure derived from siTe analysis, buT The direcTion/degree of paralleliTy is also emergenT of keeping The selecTion criTeria in mind. The iTiraTions suggesT ThaT The less cenTrelised and closer To a sTraighT line The base geomeTry is, The more and more prominenT becomes The visual conTinuiTy of iT, a dynamic, a frequency.

40

4sTrucTure of lines connecTed beTween poinTs of shape defined by sine curvaTure derived from Two separaTe curves conTrolled by separaTe funcTions.

53d shape generaTed from individ-ual sTrips conTrolled Through sine curvaTure.

63d shape generaTed from individ-ual sTrips conTrolled Through sine curvaTure combined wiTh exTruding joined lines beTween The Two sweeping curves.

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B4 TECHNIQUE

formfidinging: transformation from curve to flux shape

The aim of These excercises was To TesT how a flaT 2-dimensional developable surface was capable of being presenTed as an unprecedenTed 3-dimensional flux shape Through The Techniques of bending and folding as explored in previous case sTudies 1 + 2.

doing This in boTh digiTal and analogue forms helps To furTher The undersTanding of how bending is generaTed.

The physical presence of ‘sTrip’ becomes de-fined, displaying The way iT responds To fixed poinTs, pressure and posiTion, how frequencies and repeTiTions of geomeTry occur naTurally.

42

B5 PROTOTYPING

formfinding: bending and folding

formfidinging: scoring. play of opening vs whole.

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prototyping: material in bending/folding

Metal wire - posesses saMe MalleaBility as paper But doesn’t Bend sMoothly, angles itslf to forM sharper foldsdoes not spring Back - shared quality with steel. structurally staBle More or less - holds its own weight

plastic strips - posess saMe MalleaBility as paper and More rigidity, needs to Be fixed into place seeing as it will seek to return to its original state. unstaBle - Barely holds its own weight, doesn’t have high stress perfor-Mance or potential for tension.

a nuMBer of prototypes froM found/recycled Material.

44

prototype : folding iteration 2

evaluates visual effect of vertical repitition and sectioning.

tests the ‘riB and exterior’ systeM seen in loop-3.

tests how the sine curvature can dictate shape.

45

45

site awareness - merri creek

stakeholders

key proBleM

secondary proBleMs

circulation across the creek that does not require aBstraction froM the natural landscape or distancing away froM this

resolving safety issues with illegal wading across the streaM

- every sighted unresolved path froM Bank to Bank

coMMunity - strong coMMunal value present

environMental concern - posters, cleaning Bees, awareness

natural environMent - flora & fauna, a nuMBer of ecosysteMs

- ceres environMental centre

awareness for ecology and nature present across all stakeholders

flooding - lack of staBle water level to refer to

pollution - present in the water and lower Branches.

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B6 PROPOSAL

47

proposal

The aim is To engage wiTh generaTive design principals previously explored. The use of sine curvaTure has proven iTself To be a Tool To creaTe new geomeTries and shapes ThaT are aesTheTically pleasanT, mirror The dynamics of The siTe, and can have an applicaTion To engage The Two banks and The waTerway by creaTing a bridging sTrucTure.

bending and folding To creaTe curvaTure means a variaTion in levels, making This Technique very applicable To a) be able To be placed in varying Topography such as The sTeep banks of merri creek, and b) acTively engage wiTh such siTe condiTions, The heighT and posiTioning of anchor poinTs ineviTably affecTing The geomeTry.

The sparse solidiTy of bending/folding shapes, The separaTion of The shape inTo sTrips and gaps beTween The sTrips as seen in boTh bioThing and loop -3 would creaTe a shape ThaT has qualiTaTive funcTions of Transparency and lighTness, very suiTable for a siTe ThaT is desired To be perceived as naTural and unTouched by The sTakeholders. fullness, harmony and wholeness of form produced.

The direcTion To formulaTe This proposal was as follows:

> To provide base curvaTure inspired by The creek flow iTself from one presumed bank To The oTher

> To generaTe a number of sine curvaTures wiTh individual graph mappers

48

> To experimenT wiTh The algoriThm parameTers To produce The mosT ideal iTeraTion. refer To pasT selecTion criTeria as well as fullness, harmony and wholeness of form produced. These are, of course, pure specu-laTion aT This poinT, beginning To inTroduce a funcTional logic ThaT would need To be solidified and refined over and over again before iT can be considered physically applicable.

There are Three shapes presenT, unique buT very similar. The lower sweep separaTes The body of The speculaTed bridge from oncoming waTers and currenTs, acTing as a breaker in case of flood-ing and a barrier for large parTicles of rubbish.

The middle curves, analogous on boTh sides, are The body of The bridge, and would be The main loadbearing elemenTs.

The ouTer curve is a visual counTerweighT To The oTher proTrusion and allows a smooTh TransiTion from arTificial proposal To waTerline.

49

proposal

The form expression Through layering individual elemenTs and creaTing a play of opening and whole resolves The Two secondary problems - in The case of flooding, waTer would be able To pass freely, wiThouT sTagnaTing or ‘dambing’. large elemenTs of polluTion, however, would geT caughT on The lower curves and make The cleaning process easier.

50

The locaTion on siTe has signs of acTiviTy and aTTempTed crossing where There currenTly isn’T a bridge. insTalling one here in parTicular Thus resolves demand for circulaTion aT The lower banks.

The curvaTure of The creek is Transformed inTo Three dimensional flux form Through The sine folding Technique

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bridge geometry

Top 1: 50

perspecTive secTion

52

elevaTion - souTh 1: 50

elevaTion - norTh 1: 50

secTion

53

54

first full prototype

aim of proToType

evaluaTe sTrips and curvaTure as a meThod of shape generaTion in The phsyical realm. seeing wheTher This combinaTion of sTrips is capable of being perceived as a solid flux form.

relaTively successful. proves ThaT sine curvaTure is a plausable Tool in generaTing geomeTry ThaT is flowing, rhyThmic and has emoTive expression. could have been a good exploraTion of maTerial behaviour.

explores posiTive/negaTive space - which is perceived as a whole? which sTrip be-comes absTracTed?

proToType weakness

fails To acknowlegde maTerialiTy and Therefore does noT provide wiTh an accuraTe esTimaTe of The shape each sTrip will Take.

scoring paTTern noT parameTric - defined by offseTTing curve, quiTe likely noT opTimal.

concepTual weakness - should be fur-Ther explored in Terms of Technique and meThonodology. The curvaTure and sTrip analysis proved To be a powerful form generaTor buT has liTTle value in Terms of maTerialiTy, form expression and TecTonics.

sTrucTure - an indusTrial loadbearing sTrucTure, The proposal needs To concider sTrucTural inTegriTy and load disTribuTion

55

resolving connections

bolT sysTems To hold sTrips TogeTher before The ribs. These are The aTTracTor poinTs ThaT help define angle of folding, Therefore a fixed poinT is imporTanT.

‘ribs’ - fixed solid elemenTs which define The posi-Tion, curve and order of each individual sTrip.

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resolving current stagnations

here’s someThing To consider before parT c commences...

maTerialiTy

each maTerial behaves differenTly, especially so if exposed To sTress (such as bending and folding pro-cesses) and load (ineviTable in a bridge sTrucTure). iT is Therefore fruiTless To esTimaTe capabiliTies To hold shape and obey by a cerTain direcTion/parameTer wiThouT an indicaTion of how a chosen maTerial will behave. sTeel seems an easy choice from The Top of one’s head buT There’s always environmenTal concerns and cosTs relaTed – perhaps There is a more efficienT opTion for maTerialiTy, such as Timber ThaT sTill per-forms well and lasTs for a long Time when exposed To waTer – maTerialiTy is a field worTh researching inTo before sTarTing parT c. once The choice has been made, maTerial performance will be evaluaTed and proToTyped properly, wiTh consideraTion for connecTions, scale differenTiaTions and TecTonics.

beTTer side connecTion and consideraTion of scale

There were significanT issues wiTh Topography difference and The degree of curvaTure creaTed, as well as The span grasshopper ouTpuTs compared To The disTance beTween The Two banks. direcT measuremenTs of The siTe would be exTremely useful, prompTing a siTe revisiT, and a new, more accuraTe definiTion may need To be produced.

form expression

while The currenT proposal has a very direcT correlaTion To The chosen Technique, iT does have iTs disad-vanTages and risks – ensuring maTerialiTy and sTabiliTy, ensuring safeTy concerns, accessibiliTy and being user friendly, gaining quanTiTaTive value as well as arTisTic expression and concepTual depTh. iT is possible ThaT The sine curvaTure as a shape generaTor can be expressed in differenT manners, such as The ‘disinTe-graTion’ species – having an inTeresTing form and employing a differenT or slighTly modified Technique To TranslaTe iT inTo archiTecTure. Through i do noT plan To make a definiTive shifT in This direcTion, iT may be worTh invesTigaTing if conTinuous issues and doubTs arise wiTh The currenT Theme.

sTrucTural inTegriTy

iT is crucial ThaT The proposal is given sTrucTural ground and regulaTion, or aT leasT proven ThaT iT can creaTe someThing so rooTed in engineering and undersTanding load and inTegriTy as bridges are. iT would be wise To refer To exisTing bridge sTrucTures, wheTher To obTain a beTTer undersTanding of loadbearing elemenTs and requiremenTs. eiTher way, | anTicipaTe looking aT new precedenTs and coming up wiTh some basis for sTrucTural plausibiliTy before parT c is on The way.

proposed bridge by laurent sant-val (amsterdam) combines sine curvature and need for structural elements (eVolo)

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learning outcomes iT was fascinaTing To see Things previously covered in parT a sTarT To emerge in my own work – generaTive design, The abiliTy To creaTe iTeraTions, The response of grasshopper ouTpuTs To changes forced on The parameTers.

The biggesT obsTacle and The biggesT achievemenT during parT b has undoubTedly been The Technical side of grasshopper. even The TransiTion from analogue meThodologies of Thinking To compuTaTional ones Took some Time To occur. for example, in my loop 3 reverse engineering, my iniTial idea was To imiTaTe The bending Technique of whaT i laTer discovered To be The sine curve Through kangaroo. while kangaroo is a powerful Tool for simulaTions and compuTaTional performances, This mindseT shows my iniTial lack of undersTanding of generaTive processes and growTh, and Trying To overcome The Task by imiTaTing analogue meThods. once The principles of creaTing a new form from someThing ThaT did noT previously exisT, Through morphing and disTorTion as opposed To compuTisaTion of exisTing maTTer and slighTly ediTing iTs sTaTe, iT was really exciTing!

once i goT around To undersTanding daTa sTrucTures and basic manipulaTions such as shifTing lisTs, sorTing lisTs, singling ouT iTems in a daTa Tree and The effecTs of grafTing and flaTTening, iT became much easier To conTrol geomeTry and gave me a loT more conTrol over everyThing i was doing. my experience wiTh grass-hopper has been very Trial-and-error, branching ouT for new resulTs and realisaTions Through Things i already knew, and sTrengThening my undersTanding of cerTain funcTions Through The applicaTion of such.

in Terms of archiTecTure and TecTonics, i admiT iT was a biT difficulT To TranslaTe The Technique To an acTual plausible idea or concepT, so There was a biT of whaT i refer To as ‘concepTual sTagnaTion’. playing around wiTh paper, plasTic and wire proToTypes was a valuable learning Tool To overcome This – iT felT like conducTing a dialogue beTween digiTal and paper spaces. iT helped me learn To envision Techniques applied To real life spaces and consTrainTs, and To projecT Them onTo my brief and ouTlined problems.

anoTher learning ouTcome has been ThaT of digiTal fabricaTion, undersTanding The consTrainTs and resources avaliable. whaT is imporTanT abouT fabricaTion and maTerialiTy is undersTanding real-life indusTry applicaTions as well as maTerial properTies and fablab faciliTies - for example The abiliTy To 3d prinT someThing does noT mean ThaT said someThing is a plausible efficienT direcTion; and The abiliTy To pres-enT form does noT always mean valuable proToTyping. iT’s imporTanT To know whaT exacTly you’re TesTing for, and whaT inaccuracies are evidenT in cerTain proToTypes (paper bridge...enough said...) i look forward To conTinuing To explore grasshopper Techniques and learning abouT TranslaTing compuTa-Tional ouTcomes inTo archiTecTural elemenTs in a way ThaT has meaning and significance in Terms of maTeri-aliTy and TecTonics.

Trying To imiTaTe sine curvaTure in rhino Through compuTisaTion, and Through ‘bending’ a circle in kangaroo. glad we’re pasT ThaT.

algorithmic sketchbook - weekly tasks

week 4 - image mapper - creaTes frequencies in geomeTries by evaluaTing conTrasT and colour depTh of an imporTed image. an inTeresTing sTraTegy To enhance a piece of geomeTry and render iT more inTeresTing, buT noT very powerful as a compuTaTional or generaTive Technique or specTrum for innovaTion.

week 5 - l-sysTems and recursive aggregaTion - generaTing geomeTry Through The means of repeTiTion and recur-rances. alThough achievable in boTh 3d and 2d form and a fascinaTing generaTive Technique, iT would be difficulT To find a sTrucTural applicaTion To These in real life. They dodo, however, possess unique aesTheTic qualiTies and make greaT paTTerns To analyse.

week 6 - kangaroo meshes - running a simulaTion To analyse how a mesh mighT behave exposed To various forces. produced some inTeresTing resulTs, especially playing around wiTh aTTracTor poinTs. This could be a valuable Tech-nique ouTside of sTudio air To assisT in evaluaTing The performance of cerTain elemenTs.

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B7 + 8

algorithmic sketchbook - generative process

various aTTempTs from The reverse engi-neering Task and Technique developemTn, feaTuring kangaroo bending, hinging and lofTs. differences in unfolding sequence depending on wheTher The mesh is Triangu-lar or square; forming weird kinks aT The aTTracTor poinT placemenT ThaT wouldn’T be Therer in paper space.

mosT of The generaTive process-relaTed skeTches are already presenTed in The maTrices and var-iaTions; oThers don’T differenTiaTe from Them much, so i’ve chosen To presenT The less success-ful inTerpreTaTions here. alThough noT of direcT relevance To The Technique, They were sTill a greaT learning Tool To The mechanics of kangaroo.

references

andrasek, alisa, ‘bioThing’, 2009, frac cenTre.

Evolo - Double Agent White (http://www.evolo.us/architecture/double-agent-white-in-se-ries-of-prototypical-architectures-theverymany/)

Evolo - Mixed Use Bridge for Amsterdam(http://www.evolo.us/architecture/mixed-use-bridge-for-amster-dam-laurent-saint-val/)

Fetro, Sophie, ‘Mark Fornes, Double Agent White, Prototype d’ar-chitecture’ (http://strabic.fr/Double-Agent-White-prototype-d)

Fornes, Mark & the Very Many, ‘Atelier Calder: Double Agent White,’ (http://theverymany.com/12-atelier-calder/)

Galilee, Beatrice, ‘Office dA‘ for Icon Eye, (http://www.iconeye.com/404/item/3484-office-da)

NADAA studio, Projects - MoMA 1998, NADAA official site(http://www.nadaaa.com/#/projects/fabrications/)

SHOP architects, Porjects - Botswana International Hub (hhtp://www.shoparc.com/projects/botswana-innovations-hub/)

Tedeschi, Arthuro, ‘Algorithm-Aided Design’, Edizioni Le Penseur (2014)

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