BLACK BOX: Ar cula ng Architecture’s Core in the Post-Digital Era 1
Reyner Banham consistently cri cized architectural design
for its mysterious mode of opera on and superﬁ cial incor-
pora on of new technologies. In early works, he claimed that
the avant-garde only adopted an aesthe c of the industrial
revolu on, while preserving the academic composi on as
an implicit design method1. Later, he depicted the modus
operandi of architecture as a black box2, “recognized by its
output, though unknown in its content”3. In this polemic anal-
ogy, architecture has nothing to do with the quality of the
built environment; it is an exercise of an arcane, privileged
and unspoken aesthe c code, inculcated in the studios and
gloriﬁ ed in the dra smanship of architectural drawing.
In this black box hypothesis, computer-aided design and the
binary logic of the computers would represent a “probably
fatal blow”4 to the mys que of Architecture. Coincidentally,
its original publica on in 1990 was followed by a digital turn
in architecture5. This turn invoked a paradigm shi in design
educa on and prac ce, marked by the emergence of compu-
ta onal design models and a new conceptual vocabulary6. In
the 1990s, architects started to manipulate digital geometry
with the new CAD, modeling and anima on so ware, chal-
lenging the limits of tradi onal architectural representa on.
In the following decade, programming was rediscovered by
designers with scrip ng languages and the rise of graph-
based parametric editors integrated in CAD systems. The use
of algorithms in design required the externaliza on of the
instruc ons for design genera on, moving the designer away
from the autographic domain of architectural drawing and
fracturing the black box.
However, the incorpora on of computa onal techniques in
digital prac ces did not promote the type of ra onality in
design and educa on aimed for by Banham. As in the past,
the claims of technological shi were saturated by aesthe -
cal disputes. Associated with digital fabrica on and new
advancements in architectural geometry, the computa onal
methods supported a new repertoire of non-standard forms
that were developed in research pavilions and, eventually,
applied to the design of the building surfaces, components,
and envelope. Prac cal architects intertwined design meth-
ods and aesthe c for the digital architecture.7 Even speciﬁ c
technologies, such as anima on or parametric modeling,
were assimilated as a blend of method and design content.8
In this sense, the dra smanship associated with architectural
drawing was replaced by digital varia ons.
This recurrence of techno-ideological feuds in architecture
is related to the socializa on of the aesthe cal code and for-
ma on of the professional behavior, in par cular with the
prominence of the “design crit in the architectural school
studio”9. The studio culture is reminiscent of the Beaux Arts,
where students were educated by the guidance of one or
more experienced architects, who cri que their solu ons 10.
In this se ng, design success is measured by sa sfying the
expecta ons of the circle of educated “patrons”. Despite
the aesthe c and technical diﬀ erences, the ﬁ rst digital edu-
ca onal experiences, such as the paperless studios, also
revolved around the explora on of an aesthe c agenda of
Notwithstanding, the studio, being a well-established and
tested educa onal se ng, in face of new technologies estab-
lishes a problema c rela on between design method and the
expecta ons of the cri c. For instance, it is usual to adopt
pre-deﬁ ned computa onal workﬂ ows and plug-ins as a plat-
form to explore a certain design agenda. This se ng comes
with the cost of immediacy and bias, as there is no me to
inves gate the poten al of computa on for design beyond
the agenda and toolbox provided by the studio.12
PEDRO VELOSO, DR. RAMESH KRISHNAMURTI
Carnegie Mellon University
BLACK BOX: Ar cula ng Architecture ’s Core in the Post-Digital Era2 3
Table 1: Computa onal schemas and techniques for GS and space
Table 2: Recent concepts associated with GS and computa onal design.
This rela on is even more cri cal in face of design automa-
on and Ar ﬁ cial Intelligence (AI), which have long been
encroaching on the territory of architecture. AI acquired new
momentum with the recent wave of deep neural networks,
which succeeded in automa ng ac vi es such as pain ng
style transfer, playing go, medical imaging, speech recogni-
on, face recogni on and synthesis. Not surprisingly, Mario
Carpo’s response to this momentum was the announcement
of a new digital turn for architecture 13. This me, the turn is
based on the computa onal logic of search and the availability
of big data14, resul ng in a movement from the non-standard
forms and smooth surfaces to a focus on voxeliza on and the
genera on of form with search and simula on.
The complex rela on between the terms computa on and dig-
ital is crucial for the future of design educa on. Computa on
strictly refers to the use of algorithms or models to perform
opera ons on symbolic representa ons. For example, com-
puta onal design methods use these algorithms and models
to represent, analyze and synthesize design alterna ves. In
contrast, the term digital has been used ﬂ uidly to describe
a certain cultural condi on or state of being related to the
advent of diﬀ erent informa on technologies. Design beneﬁ ts
from historical and philosophical interpreta ons of the inﬂ u-
ence of these technologies on our society and environment.
However, pursuing legi mate expressions of the digital with
restricted computa onal schemas prevents the access to a
more general knowledge on computa onal logic and struc-
tural changes in design prac ce.
While computa on logic can address diﬀ erent aspects of
architecture, in this paper we focus on the synthesis of forms
and spa al pa erns. A proper knowledge base of compu-
ta onal synthesis can be developed based on genera ve
systems (GS) − systems that can generate design alterna ves
automa cally for a certain problem. While current digital
studios and programming textbooks focus on parametric,
NURBS and mesh modeling, GS comprehends a wider vari-
ety of techniques from diﬀ erent ﬁ elds and domains. Design
educa on would beneﬁ t from a systema c and historical
understanding of the diﬀ erent computa onal schemas avail-
able for GS.
The deﬁ ni on and systema za on of GS have been devel-
oped in computa onal design books15, courses, ar cles
and research conferences in Computer-aided Architectural
Design16 (CAAD). A brief review is given below.
Christopher Alexander’s understanding of “genera ng
system” is as a system composed of a kit of parts and com-
binatory rules that can generate many varia ons17. In his
structuralist view, all natural and ar ﬁ cial phenomena are
themselves systems generated by a speciﬁ c set of interact-
ing forces or rules.18 However, while natural systems are
adaptable to the interac on of forces, the built environment
requires ar ﬁ cial methods to capture the exis ng forces and
promote a global behavior based on their equilibrium. In
opposi on to conven onal design, which addresses this task
by intui on, Alexander categorized three methods to gen-
erate form based on forces
: (1) numerical methods, which
use linear op miza on of design variables to look for the
best form; (2) analog methods, which use a physical model
to represent the forces of the system and look for a stable
conﬁ gura on; (3) rela onal methods, which use diagrams to
represent the diﬀ erent forces of a system and fuse them to
generate the proper form.
William Mitchell wrote one of the ﬁ rst overviews of GS in the
ﬁ eld of CAAD20. His understanding of GS is as systems that
can produce a variety of poten al solu ons for a problem.
He proposed three general categories for GS that are simi-
lar to Alexander’s methods: (1) analogue GS are composed
of analogue elements that enable mechanical opera ons to
change the state of the system; (2) iconic GS are systems that
use movies, models, drawings, and geometric opera ons to
generate solu ons, (3) symbolic GS use symbols and compu-
ta onal data-structures to represent a solu on and rely on
arithme c and logical opera ons to change it.
While Alexander’s work focused on GS based on rela onal/
iconic GS21, Mitchell’s overview focused on symbolic GS to
produce spa al solu ons that meets certain speciﬁ ed criteria
automa cally – i.e., space planning. In contrast to Alexander’s
structuralist approach, Mitchell interprets symbolic GS with
classical AI concepts. Each GS operates with discrete steps.
Related designs that are visited in the computa onal process
are codiﬁ ed in a directed graph called state-ac on graph,
which structures the space of all possible designs and avail-
able opera ons for naviga on.22 The goal of GS is to nav igate
the set of solu ons in this state-ac on graph looking for a
subset of solu ons that sa sfy the design goals.
Mitchell23 and other researchers, for example Henrion24 and
Ligge 25, classiﬁ ed and described the solu on procedures of
symbolic GS for space planning. Most of their categories are
inscribed in two computa onal schemas: search and op mi-
z a o n 26, which were the main topics in Simon’s famous text
on a science of design27. See Table 1.28 29 30
Since the 1990s, not only metaheuris cs but also other com-
puta onal concepts, such as cellular automata and swarm
algorithms became part of architectural experimenta on,
which were explored in computa onal design books31.
Addi onally, architects also incorporated anima on, NURBS,
mesh and parametric modelers in their design toolbox. While
most experimenta ons departed from classical AI, eventu-
ally, techniques, such as search and dissec on, are revisited32.
In Table 2, we organize authors who try to capture the
diﬀ erent computa onal and mathema cal concepts associ-
ated with design. We combine (1) the pedagogical categories
for the teaching of GS proposed by Fischer and Herr33, (2) the
concepts iden ﬁ ed by Kolarevic to characterize the digital
morphogenesis34, (3) the digital models of design beyond
CAD systems described by Oxman35 and (4) the mathema -
cal concepts iden ﬁ ed by Burry and Burry36 in contemporary
design. We organize them according to the following sche-
mas: complex geometry and topology, packing and ling,
diagramming and data visualiza on, anima on, op miza on
and performance, parametrics, rule-based systems and com-
plexity. 37 38
Recent classiﬁ ca ons have moved away from the computa-
onal logic to focus on their source or the applica on domain,
indica ng the incorpora on of GS as a common prac ce for
architectural design. Oxman and Oxman39 provide six general
models of form genera on: (1) mathema cal: which exploits
mathema cal formulae for genera ve procedures; (2) tec-
tonic, which employs tectonic pa erns for form genera on;
(3) material: which uses tectonic and assembly pa erns,
BLACK BOX: Ar cula ng Architecture ’s Core in the Post-Digital Era4 5
state of the system is speciﬁ ed, naviga on is deﬁ ned by the
selec on and applica on of rules or procedures, manually or
automa cally, to change the state of the system in discrete
steps. The design space is neither explicit nor deﬁ nitely ﬁ nite.
See example in Figure 1, top.
This schema addresses problems structured as a graph or
a tree, which are composed of states (nodes) and available
ac ons (edges). The states are the nodes and the possible
construc ons or ac ons are the edges. Naviga on combi-
natorically explores valid states in the design space, which
contains “the set of all states reachable from the ini al state
by any given sequence of ac ons”43. In a search, the solu-
on is a sequence of ac ons from an ini al state at the root
to a desired state. In a traversal, the solu on is a systema c
way to access some or all the states. In a sampling, a solu on
is generated by following a single path deﬁ ned by a certain
probability or policy. Diﬀ erent algorithms organize the search
in diﬀ erent ways by using strategies to order the explora-
on, to evaluate the costs of the decisions or to check the
consistency of the diﬀ erent constraints of the problem. See
example in Figure 1, middle and bo om.
This schema deﬁ nes geometric en es and rela ons using
such as folding, braiding, kni ng and weaving, to generate
form; (4) natural or neo-biological, which employs biologi-
cal principles to generate form; (5) fabrica onal, which uses
exis ng pa erns of fabrica on for design genera on; and (6)
performa ve, which models physical data of the context as
the input for a genera ve process that sa sfy certain objec-
ves. This type of categoriza on reﬂ ects the ubiquity of GS
in diﬀ erent architectural approaches, which is also reinforced
by categoriza on of solu on procedures in speciﬁ c domains,
such as digital fabrica on with parametric modeling40.
The challenge in categorizing GS is that their underlying tech-
niques originate in diﬀ erent ﬁ elds, they overlap, or they apply
to mul ple domains of design. While pioneer classiﬁ ca ons
focused on the computa onal logic of the GS, recent ones
address speciﬁ c technologies, design inspira on or applica-
on domain in architecture. These recent approaches are
very produc ve for educa on and bring design to the center
of a en on. However, they limit the scope of GS to the status
quo and design instan a on – i.e., to a set of solu ons with
its own tested work ﬂ ows and tools.
In the opposite direc on, our framework recovers the idea
of computa on not as a tool for design, but as an alterna ve
logic of design. It does not focus on the representa on of the
design elements but on the high-level concepts that mediate
design and computa onal genera on: design spaces and nav-
iga onal strategies. Broadly speaking, design space refers to
the space of possible alterna ves that can be generated given
a certain formula on of the problem. Design naviga on refers
to the opera ons and control strategies that are available to
navigate between these alterna ves. In tradi onal prac ces,
designers use heuris cs to formulate and reformulate the
problem, building expressive design spaces and naviga onal
strategies to explore solu on candidates.41 In GS, the design
spaces and naviga on strategies are a consequence of its for-
mula on with speciﬁ c algorithms and models.
By focusing on computa onal logic with more abstract
categories, this framework comprehends both the exis ng
solu on procedures and the poten al incorpora on of recent
advancements in AI. The eight schemas of our proposed
framework are in Table 3.42
The schema is based on the existence of a discrete repre-
senta on, which can be geometrical or even alphanumerical,
that is sequen ally constructed by the applica on of rules
or procedures, which might require a certain shape or a cer-
tain rela on between shapes to be matched. Once the ini al
Table 3: A GS framework based on design space and naviga on
Figure 1: Construc ve schema. Top: unstructured construc ve schema
of the qGrowth grammar. Middle: qGrowth structured in a tree with a
greedy best-ﬁ rst search algorithm that orders the fron er based on the
Euclidean dis tance to a target. Bo om: ex ample of qGrowth generated by
sampling. It follows the target behind a wall (ellipse).
BLACK BOX: Ar cula ng Architecture ’s Core in the Post-Digital Era6 7
space is deﬁ ned by all possible conﬁ gura ons of a simula on,
given its ini al se ngs and the agents’ policies
The next two categories employ Machine Learning – a mul -
disciplinary ﬁ eld concerned with programs that automa cally
improve with experience – to search for the best hypothesis
about a given data, behavior or knowledge.44 They open the
possibility of learning GS from data.
To solve many learning tasks, researchers employ genera-
ve models, which a er having been exposed to a dataset,
“explicitly or implicitly model the distribu on of inputs as well
. More than simply learning how to perform a
certain task, they model how the data has been generated.
Thus, a genera ve model enables the sampling of synthesized
data based on the data distribu on that it learned for the
task. The design space is the space and domain of the input
vector, which is translated to a result by the learned mapping.
See example in Figure 4.
This schema is based on learning the ac ons of agents to cus-
tomize a GS. Among other approaches, it includes adap ve
agents46 and reinforcement learning47. The system learns a
policy (the probability of choosing the available ac ons in a
state) by combining simula on with evolu onary algorithms
or by exploring and exploi ng ac ons to maximize a reward
in an environment.
In prac ce, the schemas presented above can be combined
to form hybrid GS. By combining the diﬀ erent categories,
designers can develop a custom GS with a proper design
space and naviga on for their problems.
The post-digital should not be understood as an emerging
era, but as a cri cal a tude towards the fascina on or denial
of the digital. New formula ons of a digital zeitgeist48 or re-
mys ﬁ ca ons of the architectural representa on49 are both
short-sighted acts. In contrast, if we accept the ubiquity of the
digital, we can use computa on to explore complex spa al
pa erns and interac ons, addressing previously ungraspable
aspects of society and environment.
parameters and constraints through explicit func ons
deﬁ ned by the designer. The resul ng design space is explicit
in the parameter space. It comprehends all the geometrical
and numerical varia ons resul ng from all possible combina-
on of the parameter values, which can be done manually or
algorithmically, using stochas c or determinis c procedures.
This schema is based on the transforma on of a state by a
search for alterna ves that perform be er according to
a metric. The design space is the parameter space, where
parameter values describe all possible design solu ons. The
func on space contains the possible results of a single or
many evalua ve func ons applied to a solu on. The ﬁ tness
space is a one-dimensional space that translates the results of
the func ons to a single measurement of success. The com-
bina on of these spaces results in a representa on called a
ﬁ tness landscape that contains all the ﬁ tness value for all the
solu ons in the parameter space. Improvement procedures
can be solved by the applica on of calculii, op miza on
strategies or metaheuris cs. See hybrid example in Figure 2.
This schema is based on a discrete representa on, such as a
grid or a graph. In combina on, the states of the local units
characterize the global state. Once an ini al global state is
deﬁ ned, the rules or procedures aﬀ ect some elements of the
collec on, based on local states and neighborhoods, whilst
preserving the global characteris cs of the representa on.
The design space comprehends all possible varia ons of the
global representa on, considering the ini al state and the set
of rules applied over me. The examples of discrete simula-
ons are generally associated with mathema cal models of
urban or natural phenomena. See example in Figure 3.
This schema is based on a collec on of agents that sense, act
and interact. Each agent interweaves local evalua on of its
goals and ac ons on the environment − the space, ﬁ xed ele-
ments and the other agents – by the applica on of local rules
or procedures. Agents can have diﬀ ering levels of autonomy.
While simpler systems use basic reﬂ ex agents, more com-
plex systems have a program to evaluate and act. The design
Figure 2: Hybr id (2 + 4). Op miza on of ﬂ oorplans with Gene c algorithm
an d K DTr ee .50 Figure 3: Discrete simula on. Rules and example of Beady Ring.51
BLACK BOX: Ar cula ng Architecture ’s Core in the Post-Digital Era8 9
We would like to express our gra tude to the Brazilian
Na onal Council for Scien ﬁ c and Technological Development
(CNPq) for gran ng Pedro Veloso a PhD scholarship (grant
1 Reyner Banha m, Theory and Desig n in the First Machine A ge (The MIT
2 A black box is a s ealed device origin ally depicted in an ele ctrical engi-
neer proble m. The observer must de duce the behavior of a sea led box by applying
diﬀ eren t distur ban ces to the in put te rminal s and by o bserving th e result s.
3 Reyner Banh am, “A Black Box: The Secret Pr ofession of Architec ture,”
in A Cri c Wr ites: Sel ected Ess ays by Reyn er Banha m (Berkel ey: Unive rsi ty of
Californi a Press, 1999), 293.
4 Ibid., 298 .
5 Mario Carp o, The Digital Turn in Archit ecture 1992-2012 (Chichester:
John Wile y & Sons, 201 3).
6 Rivka Oxman, “ Theory and Desi gn in the First Digital A ge,” Design
Studies 27, no. 3 (2006): 229 –265; Rivka Oxman, “Digital A rchitecture as a
Challeng e for Design Pedagogy: Th eory, Knowledge, Model s and Medium,”
Design Stud ies 29, no. 2 (2008): 99–120.
7 Joseph R osa, Nex t Genera on Ar chitect ure: Fold s, Blobs , and Boxe s
(New York: Ri zzoli, 20 03); Pete r Zellner, Hybri d Space: G ener a ve For m and
Digital Arc hitecture (New York: Rizzoli , 1999); Branko Kolarevic, “ Digital
Morphogenesis,” in Architecture in the Digital Age: Design and Manufacturing
(London: Spo on Press, 2003), 12–28.
8 Greg Lynn, Anima te Form (New York: Princeton Arch itectural Press,
1999); Patrik Schumacher, “Parametricism as Style - Parametricist Manifesto,”
2008, h ps://www.patrikschumacher.com/Texts/Parametricism%20as%20Style.
Our own approach in this paper situates the logic and his-
tory of computa on as a way of designing and not as a tool
to express a digital condi on. In the same way that an algo-
rithm course in computer science might refer to canonical
algorithms as a base for new developments – without claims
for an algorithmic era –, canonical computa onal schemas
can provide a common background to support research on
GS. By exploring and hybridizing the diﬀ erent schemas, the
designer can navigate in the complex territory of computa-
on to look for novel design logics.
We introduced this framework in a mini course in our
ins tu on, addressing the ﬁ rst ﬁ ve schemas. In the end of
the course, the students had to choose a problem in their
domain (game, building, landscape, urban design, etc.) and
develop a GS to produce alterna ves of solu ons. We s ll
plan to extend it to a full course where we can discuss all
the schemas, incorpora ng the recent advancements in AI.
For a future objec ve, we intend to reﬁ ne and formalize the
categories and their rela ons into a book.
Figure 4 Genera ve learning: Deepcloud. Top: architec ture of auto -
encoder tr ained on a dataset of chairs. Bo om: chair series generated by
naviga on on the resul ng feature space.52
9 Banham, “A Bla ck Box: The Secret Profes sion of Architecture,” 294 .
1 0 Joan Drap er, “The Ec ole D es Beaux- Arts an d the Arch itectural
Prof ession i n the Un ited States: Th e Case of Joh n Galen Ho ward ,” in Archi tect:
Cha pter s in the His tor y of the Prof essi on, ed. Sp iro Kosto f (Ber keley: Un iver sity of
Californi a Press, 2000), 211; John F. Hab erson, The Study of Arch itectural Design
(New York: Norto n, 2008), 182.
11 Stan Al len, “T he Pap erless Stud ios in Cont ext,” in Wh en Is th e Digita l
in Architec ture? (Montreal: CCA and Sternb erg Press, 2013), 383–4 04; Bernard
Tschu mi, “The M aking of a Gene ra on: Ho w the Paper less Stu dio s Came About,”
in Whe n Is the Dig ital in Arc hitect ure? (Mont real : CCA a nd Sternb erg Pres s, 201 3),
12 For example, parametric design can be associated with NURBS and
mesh modeli ng to explore complex g eometry. If perform ance is part of the
agenda, plug-ins for op miza on or physics simula on are added. Whenever
some addi onal cus tomiza on is nece ssary, th e student s try to “ha ck” the avai l-
abl e tool box to sa sﬁ c e the desig n task.
13 Mario Carpo, The Second Digital Turn: Design Beyond Intelligence
(Cambridge: T he MIT Press, 2017).
14 Carpo’s percep on of technological change is legi mate, but his deﬁ ni-
on of a digital zeitgeist bas ed on the duality of “don’t sort; search” (Ibid., 23.) is
fragile. In hi s interpr eta on , the di screte l ogi c of comput ers and it s capaci ty to
operate with b ig data – which he refers to as p osthuman complexi ty (Ibid., 48.) –
is opposed to th e formulaic and compr essive logic of classi cal science. However,
many o f the techn iques th at Carpo us es to repre sent this logi c of compu ta on in
design (heuris c search, op miza on, cellular automata and simula on associ-
ated with FE M) are not di rec tly re lated to bi g data. Addi onally, c omputa on is
not op posed to c omp ress ion. The d iﬃ cult y of curren t (or even fu ture) comp uters
to dea l with larg e and con nuous st ate sp aces jus fy th e use of heur is cs and
func on approximators, such as deep neural net works, instead of brute-force
search or tabu lar methods. Carpo a lso opposes Calculu s to the discrete logic of
computa on and its capacit y to search (Ibid., 65–70.). However, not only Calculu s
can b e disc re zed for geo metry proc essi ng (see dis crete diﬀ eren a l geometr y),
but it is als o the base fo r backpr opaga on, a main tech nique to tr ain neura l
networks for big data analysis.
15 Gabri ela Celani and P edro Velo so, “The Inter sec o n of Theor y and
Technology: Computa onal Concepts Applied to Architectural Design since Late
198 0s - a Literatur e Review,” i n Fron ers of Sci ence and Tec hnolog y: Water
Availability, Automa on and Sensor Technologies, Digital Fabrica on (7th
Brazilian-German Conference, Campinas, 2017).
16 Gabrie la Celani and Pedro Veloso, “C AAD Conferences: A Bri ef History,”
Elec tronic Proc eedings o f 16th Inter na ona l Confer ence CAAD Fut ures 2 015. Sao
Paulo, July 8 -10, 2015., CAA D Futures, 2015.
17 Christopher Alexander, “Systems Genera ng Systems,” Architectural
Design 38 , no. 12 (1968): 605–10.
18 Georg Vrach lio s, “ How Form C ame abou t from Soc iety: Ch ristop her
Alexander o r About Architectu re as a Form of Culture and Str ucture,” in
Stru ctural ism Relo aded: Rul e-Bas ed Design i n Archit ecture a nd Urb anism
(Stu gar t: Axel Me nges , 2011), 61–6 8.
1 9 Christo pher Alexander, “From a Set of Fo rces to a Form,” in The Man-
Mad e Obj ect , ed. Gy orgy Kepe s (New York: Ge orge Bra ziller, 19 66), 9 6–107.
2 0 Will iam J. Mitchel l, Compu ter-Aid ed Archi tectura l Design (New Yor k:
Mason Char ter Pub, 1977).
21 Alex and er’s own wor k emphas ized the use o f rela o nal meth ods fo r the
synt hesis of fo rm, from the fus ion of fun c ona l diagram s to the deve lopmen t of
a language of s emi-autonomous r ule sets for design. Fo r a general understand -
ing of this trans i on, see: C hristop her Alex ander, Notes on th e Synthes is of Fo rm
(Harvard University Press, 1964); Christopher Alexander, A Pa ern Language:
Towns, Buildings, Construc on (Oxford University Press, 1977).
22 Mitchell, Computer-Aided Architectural Design, 46–48.
23 Ibid., 425–74.
24 Max He nrion, “Au toma c S pace- Planning: A Pos tmorte m?,” in
Conf erence Proceedi ngs (Ar ﬁ cial Int elligen ce and Pa ern Reco gni on in
Computer Aided Design, New York: North-Holland, 1978), 175–91.
25 Robin S. Lig ge , “Autom ated Fac ili es La yout: Pas t, Presen t and
Future,” Automa on in Cons truc on 9, no. 2 (2000): 197–215.
26 Whil e op miza on i s itself a form of sear ch, it is di ﬀ ere n ated fro m
cla ssical se arch met hods bec ause it doe s not expl ore a syste ma c pat h to a
solu on, but sp eciﬁ c no des/stat es, based on the ir ﬁ tnes s. This cr eates som e
ambigui es. For mo re detail s about cl assica l search a nd op miz a on, see ch ap-
ters 3 and 4 of Russ el Stu art J. and Pete r Nor vig, Ar ﬁ c ial Intel ligenc e: A Modern
Approa ch, 3r d ed. (Uppe r Saddle Rive r: Pre n c e Hal l, 2010 ).
27 “Th e Sci ence of De sign : Crea ng the Ar ﬁ cial,” in T he Scien ces of the
Ar ﬁ cial, 3r d ed. (Camb ridge: Th e MIT Press, 199 6).
28 Word crea ted by Henrion to desc ribe cer tain for mula o ns of spac e plan-
ning that comb ine cons traint sa sfac o n and goal op miza on .
2 9 Generate a nd test is a general search p aradigm based on the co mbina-
on o f a rand om gener ator and a te ster, wh ich ﬁ lte rs the sa sfying s olu on s. It
can b e con side red a proto typical op miza o n where the teste r is an objec ve
fun c o n that returns a B oolea n valu e or it can be s tructu red as a cla ssical s earc h,
if the g enerator rel ies on pre vio us gen era on s of solu ons. Mitchel l descri be it
as a problem -solving method for sp ace-planning a nd Simon use it as a general
strategy to dec ompose the design prob lem.
3 0 Mitchell de scribes shape gramm ars as a technique to formul ate the
problem (a synt ac c formul a on) and not as a sol u on proc edure. Th is dis n c on
is subtle, as the sh ape grammars can be d eveloped with shape inter preters or
with search strategies. However, shape grammars are canonical rule-based GS,
so we su bverted his or iginal clas siﬁ ca on and add ed them to th is table as a GS.
31 John Fraze r, An Evo lu ona ry Ar chitec ture, Arc hitect ural Ass oci a on
(Lon don, 1995); Paul Coat es and Rob ert T hum, Gen era ve Modelling (Un iver sity
of Eas t London , 1995) , h p://roar.ue l.ac.uk /948/; Pa ul Co ates , Programmin g
Architecture (London: Routledge, 2010); Kostas Terzidis, Alg orithmic Architecture
(Oxford: Th e Architectural Press , 2006).
32 Kosta s Terzi dis, Perm uta on Desi gn: Build ings, Tex ts, and Co ntexts
(New York: Routled ge, 2014).
33 Thoma s Fische r and C hris ane M. Her r, “Teac hing Gen era ve D esign,”
in Pro ceedin gs of the 4th Conf eren ce on Gene ra ve Ar t (Genera ve Art,
Politechnico di Milano University, 2001).
34 Kolarevic, “Digital Morphogenesis.”
35 Oxman, “T heory and Design i n the First Digital Age.”
36 Jane Bu rry and Mark Bu rry, The New Ma them a cs of Arc hitecture
(Th ames & Huds on Londr es, 2010).
37 Fischer and Herr combine diﬀ erent techniques under the category
“Algorithmi c genera on a nd gro wth”. We opt ed to divid e them acc ording to our
38 Kolarevic mixes diﬀ erent algorithms (gene c algorithms and L-systems)
und er the categor y gene c s. We opted t o divide them ac cording to ou r general
3 9 “Fro m Comp osi on to Gen era on ,” in Th eories of the Di gital in
Architec ture (New York: Routledge, 2014), 55– 61.
4 0 Lisa Iwamoto, Digital Fabrica on: Architectural and Material
Techniques (New York: Pri nceton Architectur al Press, 2009); Nick D unn, Digital
Fabrica on in Architecture (Laurence King Publishing, 2012).
41 Peter G . Rowe, Design Thinking (C ambridge: The MIT Press , 1987).
42 T his is an in i al a emp t to deﬁ ne a framewor k, so we mixe d general
meth ods, mod els and al gorith ms fro m diﬀ ere nt areas in our ex amples .
43 Russe l and Norv ig, Nor vig Pe ter, Ar ﬁ cial Intelli gence, 67.
44 Tom M. Mitchell, Machi ne Learning (Boston: McG raw-Hill, 1997), 2–15.
45 Chris topher M . Bishop, P a ern Reco gni on and Ma chine Le arning (N ew
York: Springer-Verlag, 20 06), 43.
46 John H. Ho lland, H idden Order : How Adap ta on Builds Comp lexity
(New York: Basic Books, 1995); John H. Holland, Signals and Boundaries: Building
Blo cks for Co mplex Ad ap ve Systems (Cam bridge: The MI T Press, 20 12).
47 Richard S . Su on a nd Andrew G . Barto, Rein forcem ent Le arning: An
Intr oduc on (Dra ), 2nd ed. (Cam bri dge: The MI T Press, 2018), h p://incomple -
48 Carpo, The Second Digital Turn; Mario Carpo, “The Post- Digital Will
Be Eve n Mor e Dig ital , Says Mar io Carpo,” Metr opolis , July 5, 201 8, h ps://ww w.
49 Sam Jacob, “A rchite ctu re Enters th e Age of Pos t-Di gital Dr awing,”
Metropolis, March 21, 2017, h ps://www.metropolismag.com/architecture/
architecture-enters- age-post-digital- drawing/.
5 0 Insp ired by Katj a Knecht and Rei nhard Kön ig, “Gen era ng Floor P lan
Layo uts with Kd Trees and Evo lu ona ry Al gorith ms,” in Proc eeding s of the 13th
Genera ve Art Co nfer ence (Gen era ve A rt, Mila n: Domus Ar genia Pub lisher,
2010), 238–253, h p://www.genera vear t.com/.
51 Bill Hillier and Julienne Hanson, The Social Logic of Space (Cambridge:
Cambrid ge Unive rsi ty Press, 1984), 55–6 4.
52 Ardavan Bidgoli and Pedro Veloso, “DeepCloud. The Applica on of
a Data -Driv en, Genera v e Model in D esign,” in Rec alibra on: On Impr ecision
and Inﬁ delit y. Proceedings of 38th ACAD IA Conference, ed. Phill ip Anzalone,
Marcella Del Signore, and Andrew J. Wit (ACADI A, Mexico Cit y: Universidad
Iberoamericana, 2018), 176, 180.