Introducon to Playable
1 Some voxel shapes in the language
dened by the voxel-shape
grammar shown in Figure 4, as
experienced by the users of the
grammar in Minecra. In the fore-
ground, an acvaon state for rule
DDU — Digital Design Unit
DDU — Digital Design Unit
A shape grammar is a collecon of visually dened geometric rules that could be used to auto-
mate the generaon of formal representaons of designs for buildings, cies, products and more.
We oer an extension of the shape grammar formalism based enrely on voxel space instead
of vectors, which we used for the generaon of schemac architectural designs. We describe a
method using playability to increase human agency and designer control over the outcome of the
generave phase of voxel-shape grammars. The method is presented with an implementaon in
the environment of Minecra and employs three guidance mechanisms. To conclude we list a few
consideraons from our experience in the design of a playable, voxel-shape grammar and point to
| DISCIPLINES + DISRUPTION
The ability of shape grammar generave formalism to capture
design intenons and expert knowledge is what interests us in
the pursuit of engaging non-experts in the architectural design
process. We base our work on this large eld of research and
present a novel extension to shape grammars, namely playable,
voxel-shape grammars that could have an enabling eect upon
both experts and non-experts by leng them interacvely and
immersively explore design opons and learn by making. With
our shape grammar method we target use scenarios in the early
schemac design phase, when all stakeholders explore the rela-
onship between the elements of a project in an informal and
loose manner, oen in the form of massing models.
From very early on in the work we aimed to:
1. Oer user-friendly visual modelling of both the shapes in
the shape grammar, as well as the grammar rules, in order to
aord the expert users easy access to the tooling framework—
this was possible by redening the typically vector-based
shape grammars for a voxel space and using Minecra as the
2. Open the generave process to human agency in an inter-
acve, manageable and surmountable way—by making the
grammar playable, we could add direct parcipaon and
guiding mechanisms to the otherwise purely algorithmic
We developed and tested an extendable framework imple-
menng playable, voxel-shape grammars in the Minecra
environment. This paper presents:
• a denion of playable, voxel-shape grammars (Secon 3.1);
• test cases at urban and building scales (Secon 4);
• three types of guiding mechanisms that experts could use to
control the play-driven generave process (Secon 5.3).
Shape grammars have been successfully used to encode aspects
of expert architectural knowledge, and thus help their users,
mostly designers, to explore a large set of design soluons or
quickly generate two-dimensional representaons of designs
with desired formal qualies (Sny and Gips 1972; Sny and
Mitchell 1978; Chase 2002). The applicaon of shape grammars
consists of mostly two acvies:
1. designing the grammar, which consists of shapes and rules;
2. iterang mulple mes through the rules to generate designs.
The second acvity maintains the usefulness of shape grammars
as a design tool, subject to their implementaon as automated
systems run by a computer (Ruiz-Monel et al. 2013). However,
shape grammars have been mostly vector-based (Sny 1980;
Woodbury 2016), and the shapes generated with grammars are
only notaonal graphs or abstract 2D composions. (Marn
2006; Sny and Mitchell 1978; Duarte 2005). This poses two
main challenges in the aempt to use them as design tools:
1. computer implementaons of shape grammars are dicult to
2. computer-automated generaon of shapes with shape gram-
mars is dicult to explore and control.
Computer Implementations of Shape Grammars are
Difficult to Define
An important aspect of a successful shape grammar implemen-
taon is that the users are able to model the shapes and rules
Usually, shape grammars have been dened in a closed, expert
coding environment with an interface dened solely for the
purposes of the shape grammar. Therefore, a potenal new user
of the shape grammar cannot rely on computer skills they already
have, and must learn new, advanced ones. The use of generic,
accessible and easy-to-use 3D-modelling environments to imple-
ment shape grammars has not been well explored. The following
18-year-old quote from Terry Knight states the problem rather
well, and unfortunately not much has happened since then to
Currently though, there are few computer implementaons that
are praccable for students or praconers. Most do not have
interfaces that make them easy for nonprogrammers to use.
More eorts have gone to computaonal problems than to inter-
face ones. Implementaons of simple, restricted grammars that
are visual and require only graphic, nonsymbolic, nonnumerical
input are needed. (Knight 1999)
We address this by implemenng our method for playable,
voxel-shape grammars in a popular and accessible 3D environ-
ment with more than 40 million worldwide users of all ages and
backgrounds: the game Minecra. The size of a user’s Minecra
avatar in relaon to the voxel shapes they model—and subse-
quently iterate through in the game world—creates an immersive
percepon for a one-to-one architectural scale.
Computer-Automated Generation of Shapes with Shape
Grammars is Difficult to Explore and Control
Most exisng research on shape grammars uses a computer-au-
tomaon approach to the generave phase, leaving no control,
or very lile, mostly global control, to the designer during the
process of shape generaon. This has been done “as pencil-
and-paper execuon might be tedious and therefore useless for
the sake of discovering many new soluons.” (Ruiz-Monel et al.
2013). However, an automated generaon process is most oen
opaque and non-iterable—the user cannot inuence the result
while the process runs and is simply presented with an outcome.
Our method uses a combinaon of playability and guiding mech-
anisms to make the iteraon process more navigable.
George Sny (1980) denes a vector shape as follows: "A shape
is a limited arrangement of straight lines dened in a cartesian
coordinate system with real axes and an associated euclidean
metric.” In a similar manner let us dene voxel shape as a limited
arrangement of voxels in a discrete voxel grid and an associated
euclidian metric (Figure 3).
A voxel-shape will dene all further terms we nd in Sny's
“Introducon to Shape and Shape Grammars” (1980), but for the
discrete voxel space instead of connuous cartesian vector space.
For example, a scale operaon on a voxel shape needs to have
an integer number for the scale factor—for example 2x—so that
it turns one voxel into a cube of eight voxels: 2 x 2 x 2. Rotaons
would go only in 90 degree increments and so on. A less strict
denion, allowing real number scale factors and rotaon, is
also possible, but it would need a post-processing voxel detailing
roune, such as marching cubes, and thus introduce unnecessary
complexity for the current purposes of the method (Marais and
The original shape grammars formalism uses vectors that are
simple representaons of architectural elements such as walls.
Because of its 3D nature, the proposed voxel-shape grammar
could be used to represent both elements (walls, slabs) as well as
massing volumes of a building’s or city’s elements.
An important aspect of shape grammars is the labelled shape,
consisng of shape and symbols, used as a matching mask for
the grammar rules. The marker symbols in vector space shapes
are notaonal. In our voxel shapes we use voxels with special
aributes for markers (Figure 3).
Shape grammars perform computaons with shapes in two steps:
a recognion of a parcular shape and its possible replacement.
Rules specify the parcular shapes to be replaced and the
2 The original graphic denion of
shape grammars as it appeared in
the 1980 paper “Introducon to
Shape and Shape Grammars.”
3 A vector shape as dened by Sny
and Gips 1980 and a voxel shape as
dened in this research.
4 Graphic denion of a sample
voxel-shape grammar and some
of the shapes in the language it
| DISCIPLINES + DISRUPTION
5 Sample playable voxel-shape
grammar (le: rules, right: inial
shape)—besides the voxels’ state,
the rules take into account also the
6 Generaon of a voxel shape using
the playable voxel-shape grammar
shown in Figure 5.
7 A guiding mechanism provides a
desirable advantage to the players
for their next moves and thus could
inuence their decisions.
8 The urban scale voxel-shape
grammar from IBA_GAME has rules
that place pre-designed buildings.
9 A schemac design for a residenal
building created using a voxel-
shape grammar with 6 rules.
manner in which they are replaced. (Willis 2012)
A shape grammar is dened by rules and an inial shape, and is in
essence a language of shapes. Shape grammar rules consist of a
mask shape on the le and a replacing shape on the right (Figure
For the shape rules’ implementaon in voxel space we dene a
voxel shape as a mask, containing at least one marker voxel and a
replacing voxel shape (Figure 4). A voxel-space 3D version of the
2D vector-shape grammar from Figure 2 is seen on Figure 4.
The use of shape grammars in voxel space has only been previ-
ously explored on two occasions. Marais and Crumley (2012)
presented an extension to shape grammars called voxel-space
shape grammars, in which the shapes and rules are dened in
vector form and only the generated shapes—aer the iteraon is
complete—are voxelized in a post-processing step. A more appro-
priate naming for their method would be voxelized, vector-shape
grammars. Our method is therefore sll novel, as the enre
grammar is dened and iterated in voxel space.
Friedman and Stamos (2013) introduce the noon of a voxel
grammar in their work on procedural tree generaon. However,
their grammar denion is not visual but numerical, and as such,
lacks many of the advantages of the original shape grammar
formalism which “… allows for algorithms to be dened directly
in terms of […] shapes” (Sny 1980). Our implementaon here
suggests that the enre voxel-shape grammar (shapes and rules)
is dened in a visual, user-friendly way.
As such, voxel-shape grammars would be easy to model but
would have all the problems of shape grammars dened in
To address the control and ease-of-use issue described in 2.2, we
introduce human agency in the form of game mechanics. It adds
one addional step in the generave iteraon of the grammar
rules—a player needs to place some of the markers in order to
complete a mask shape found in the rules (Figure 5). Besides
the voxel state, the rules in the playable version of voxel-shape
grammars also take into account the player posion.
Diering from shape grammars, where the generaon is auto-
mated and each step of the iteraon produces the condions
for the next, playable voxel-shape grammars require that every
iteraon needs to be iniated by a player, thus making conscious
choice (i.e., a design decision) an important part of the explora-
on process (Figures 1, 5, and 6).
| DISCIPLINES + DISRUPTION
On the other hand, player decisions could be inuenced by a
guidance mechanism. A guiding mechanism is dened by the
author of the grammar and is able to encode a design intenon
or expert knowledge. A well-dened guiding mechanism would
be integrated in the game and would in essence be a means to
provide a desirable advantage to the players for their next moves,
and thus could inuence their decisions (Figure 7).
EXPERIMENTS AND CASE STUDIES
We are tesng the concept of playable voxel-shape grammars
in the project 20.000 BLOCKS. Our implementaon consists of
a Minecra version with the ComputerCra mod and a set of
custom scripts which drive rule detecon, player/goal tracking
and results export. See Savov, Buckton, and Tessmann (2016)
and www.20000blocks.com for further details on the project.
We invesgated the use of playable voxel-shape grammars at
two scales. At the urban scale the shapes in the grammar repre-
sent pre-designed whole buildings (or mass models of buildings),
and the rules represent the possibilies for these buildings
to exist next to each other in a city. We tested this approach
between August 2016 and March 2017 in the IBA_GAME—a
20.000 BLOCKS version that we created for IBA Heidelberg,
where players can create small neighbourhoods. Hundreds of
these neighbourhoods form a new quarter for the German city
of Heidelberg. The game featured a voxel-shape grammar of 40
buildings of six types: houses; housing extensions; businesses;
science and tech spaces; gathering spaces; and public plazas
(Figure 8). It had 140 players who played it 820 mes. The shape
grammar rules went through about 10 major revisions in the
course of development.
10 Variaons based on shape rotaons for the HOUSE RULE (rule 2 from Figure 8) in the urban scale grammar.
At the building scale the shapes in the grammar could repre-
sent physical elements of a building, such as walls and slabs or
the massing of the volume a room or an area would take in the
building, while the rules represent the logic for those elements
to aggregate next to each other to form a building. To test this
approach we ran a SmartGeometry workshop in April 2016
focusing on residenal, mul-apartment buildings. Three teams
of architects and engineers used our implementaon of playable
voxel-shape grammars and dened components of the buildings
within the grammar (Figure 9). Each variaon had up to 16 shape
rules and was played by aendees of the conference.
MINECRAFT IMPLEMENTATION OF PLAYABLE
Based on our two-year experience with this ongoing project, we
oer the reader the following thoughts on voxel shapes, voxel-
shape rules and guidance mechanisms.
The abstracted modelling environment with a voxel size of 1 x 1
x 1 m could be liming. However, since our aim is to generate
schemac architectural designs, this level of abstractness works
in our favour.
An important requirement in order to achieve an immersive
experience in the generave phase—i.e., in the play phase—is
that the resulng structures are walkable for players, so they can
reach the newly added markers, otherwise the iteraon process
is blocked. That means that in both urban or building scales, all
possible sequences of the grammar’s shape rules need to create
a walkable combinaon when placed.
The points of possible further grammar growth need to be very
clearly visible to the player while in play. Therefore, the textures
of the marker voxels and the building blocks need to be dierent.
Furthermore, with larger sets of rules, such as in IBA_GAME,
where we used six types of rules with 2–4 variaons each, a
color coding of the types of rules helps the player learn the
As we are operang in a strict orthogonal voxel grid, we had four
possible rotaons for each shape rule in the grammar. We found
out that modelling them to be the same in behaviour, but only
similar in looks, decreases the rigidity of designs and introduces
visual complexity (Figure 10).
Thus far, we have not used scaling or rotang of the shapes, i.e.,
the masking shapes that are modelled in the grammar rules are
absolute in size and orientaon. Due to the discrete quality of
a voxel space, scaling and rotaon in free increments could be
detrimental to the readability of a shape’s design.
Features of the Rule System
Markers Placed by the Grammar
We used two types of marker voxels:
1. the acvator block on which a player steps to acvate the
detecon of a masking shape they had built around it (Figure
2. the extension block, which is a marker that replaces the ac-
vator block upon successful detecon.
Some of the grammar rules require the extension block in their
masking shapes. The extension block ensures that structures
grow out of themselves coherently instead of populang the
design space with too many scaered, independent struc-
tures. That means some shapes in the grammar act as seeds,
for example the shape represenng a house in IBA_GAME,
and others as extensions, for example the shapes represenng
commercial buildings in IBA_GAME (Figure 8).
Markers Placed by the Player
Player-placed marker voxels, i.e., resources, are in essence the
material with which the player “draws” or models the masking
shape. For example in IBA_GAME, we used two resources that
encode a set of meta design features into the voxel shapes:
1. an urban resource -> shapes are more solid, with vercally
proporoned windows and enclosed;
2. a green resource -> shapes are lighter, with horizontally
proporoned windows and more open (Figure 11).
When using both types of resources to build the same masking
shape, the player would expect the same type of resulng shape,
with the same behavior during the iteraon process, but with
dierent design qualies.
Markers in a Grid or Freely Spaced
When designing the playable voxel-shape grammar, the expert
needs to make sure that all rules are spaally compable with
each other and create a walkable design. Walkability can be
obstructed by unforeseen shape overlaps.
One strategy we enforced in the rules is growth along, or within,
the constraints of a three-dimensional grid. The markers were
always placed in a shape according to a grid of 9 x 9 x 8 blocks
(Figure 10). We also developed an in-house design style guide
| DISCIPLINES + DISRUPTION
to regulate, across our team, how and when secons of a shape
rule could overlap with another (Figure 12). This saved the work
of having to try all combinaons separately.
Another strategy, which avoids the rigidity of using a grid, is for
the shapes to come with the markers in a posion that allowed
for the making of stepped structures and richer designs in spaal
terms. To avoid too many unwanted overlaps, new structures
only grow from exisng ones (seeds), to allow us to detect rule
adjacency (Figure 9).
Features of the Guidance Mechanisms
We implemented playability in the form of an economy system:
if a player owns the resources and the territory needed to create
a masking shape, then they could acvate a grammar rule with it
and so gain the rewards given by the rule. We used playability as
a generave force and at the same me as a control mechanism
over the outcome. Ruiz-Monel et al. (2013) make the case for
control mechanism as means to guarantee feasible designs.
For the designer to be able to encode a design intenon into the
playable voxel-shape grammars, we tried three types of guidance
mechanisms: a quantave game-goal system; liming choice
with the shape design; and performance-based feedback.
Quantitative Guidance Mechanism
We used a so goal system that qualitavely guided the growth
as dierent players chose to go for dierent goals. For example
in IBA_GAME we dened four server-wide goals: collect the
most green points, build the most buildings, build the tallest
structure, build as many dierent buildings as possible (Figure
11 Two resources that describe a
set of metadesign features of the
voxel-shapes in the grammar. Le:
the green resource and the house
associated with it. Right: an urban
resource with its house variaon.
12 An extract from the design style
guide for the urban scale grammar
of IBA_GAME, which was devel-
oped and shared within our team.
13 Liming player choices with design.
Le: With a rule that allows users
to stack the same house over itself,
the most ecient way for a player
to increase their height score is to
stack them up. Right: If the voxel
shape, by design, prevents direct
stacking, the next most ecient
way of gaining height points is to
14). Each voxel-shape rule in the grammar rewards the player
dierently on all four metrics.
Limiting Choice with the Shape’s Design
If players pursue a so goal such as height, then they will aim
to build as high as possible with as lile eort and expense as
possible. To prevent the stacking of one and the same house on
top of itself, we designed the roof of the house so that players
cannot model the masking shape for a new house on top of it
Performative Guidance Mechanism
While sll in the early works in terms of seamless integraon, we
tested a guiding system based on structural analysis. It exports
the model to Grasshopper every me a rule is acvated, runs an
analysis roune on it, and then “reports” back the results to the
players by color-coding certain blocks of the structure (Savov,
Buckton, Tessmann 2016). We used a similar approach in the
project Sensive Assembly, documented in Savov, Tessmann, and
Nielsen (2016), where this type of feedback loop is described in
CONCLUSIONS AND FUTURE WORK
We presented an extension to the shape grammar formalism
for voxel spaces, which we used for the generaon of schemac
architectural designs. We described a method using playability to
increase human agency and designer control over the outcome
of the generave phase of voxel-shape grammars. At the end we
shared a few thoughts on the design of a playable voxel-shape
grammar in Minecra.
Potential Contribution to the Field
With our method architects can encode architectural logic and
principles in the grammars and easily modify them. The gram-
mars are volumetric and thus open to immediate interpretaon
and analysis for their architectural potenal without further
transformaon or translaon steps.
Furthermore, the method allows for the integraon of design and
fabricaon. An addional reason to use voxel-shape grammars
instead of vector-shape grammars is to come one degree closer
to embedding material specicaon rules in the grammar (Rossi
and Tessmann 2017; Sny and Gips 1971).
The method relies on players using the Minecra map to model
grammars and generate structures. Currently we have had 800
plays, 150 play structures, and 150 downloads. There are the
following bolenecks to increasing parcipaon:
1. The need to download and use a customized Minecra
version, which reduces the number of potenal players. We
are looking for ways to implement the grammar logic enrely
on the server side so that players can parcipate with a
Vanilla (unmodied) Minecra client.
2. Closed server access: currently the data collecon requires us
to run the server ourselves. We are exploring opons to let
users run their own Minecra server with the map and save
results in the cloud.
The research could benet from the following future
• A generave visualizer, which could simulate a game being
played so that a designer can capture some of the most
common conict/bugs in advance, like mismatching shapes
and broken walkability, without having to play the game over
and over again.
• Implemenng automated rules that would not need the user’s
input at every generave step. There needs to be a beer
balance between the eects of the player’s intenons and
the generave rules over the nal designs. To address this, in
some cases, when the right condions occur, the grammar
rules might allow for several iteraon steps to happen auto-
macally one aer the other, in the form of a bonus eect or
what Sanchez (2015) denes as synergies.
• The collected data (grammar denions plus the generated
shapes) can be used to train a machine learning algorithm to
generate either grammar sets or schemac designs.
The test game can be downloaded at: www.20000blocks.com.
The project 20.000 BLOCKS is led by Anton Savov and developed at the
DDU (Digital Design Unit, Prof. Dr. Oliver Tessmann) at the architectural
faculty of Technische Universität Darmstadt with the following team:
Steen Bisswanger, Ben Buckton, Theo Gruner, Jörg Hartmann, Thomas
Valenn Klink, Sebasan Koerer, Marios Messios, Lorena Müller, Max
Rudolph, Alexander Stefas, Alban Voss. The IBA_GAME version of 20.000
BLOCKS was made possibly through the partnership with IBA Heidelberg
and sponsored by Eternit GmbH.
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Design Systems.” Automaon in Construcon 11 (2): 161–72.
Crumley, Zacharia, Patrick Marais, and James Gain. 2012. “Voxel-Space
Shape Grammars.” In Proceedings of the 20th Internaonal Conference on
Computer Graphics, Visualizaon and Computer Vision, edited by Vaclav
Skala, Part I, 113–22. Plzen, Czech Republic: WSCG.
Duarte, José P. 2005. “A Discursive Grammar for Customizing Mass
Housing: The Case of Siza’s Houses at Malagueira.” Automaon in
Construcon 14 (2): 265–75.
Friedman, Sam, and Ioannis Stamos. 2013. “Automac Procedural
Modeling of Tree Structures in Point Clouds Using Wavelets.” In
Proceedings of the 2013 Internaonal Conference on 3D Vision, 215–22.
Seale, WA: 3DV.
Knight, Terry. 1999. “Applicaons in Architectural Design, Educaon and
Pracce.” Report for the NSF/MIT Workshop on Shape Computaon. Vol. 2.
Marn, Jess. 2006. “Procedural House Generaon: A Method for
Dynamically Generang Floor Plans.” In Symposium on Interacve 3D
Graphics and Games. Redwood City, CA: I3D.
Rossi, Andrea, and Oliver Tessmann. 2017. “Designing with Digital
Materials.” In Protocols, Flows, and Glitches: Proceedings of the 22nd
Annual Conference of the Associaon for Computer-Aided Architectural
Design Research in Asia, edited by P. Janssen, P. Loh, A. Raonic, and M.A.
Schnabel, 37–42. Suzhou, China: CAADRIA..
Ruiz-Monel, Manuela, Javier Boned, Juan Gavilanes, Eduardo Jiménez,
Lawrence Mandow, and José-Luis Pérez-de-la-Cruz. 2013. “Design with
Shape Grammars and Reinforcement Learning.” Advanced Engineering
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Simulaon Video Game.” In Real Time: Proceedings of the 33rd Internaonal
Conference on Educaon and Research in Computer Aided Architectural
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Grasl, Wolfgang El. Lorenz, and Richard Scharanek, 89–97. Vienna:
Savov, Anton, Ben Buckton, and Oliver Tessmann. 2016. “20,000 Blocks.”
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In ACADIA // 2016: Posthuman Froners: Data, Designers, and Cognive
Machines, Proceedings of the 36th Annual Conference of the Associaon
for Computer Aided Design in Architecture, edited by Kathy Velikov, Sean
Ahlquist, Maas del Campo, and Georey Thün, 24–33. Ann Arbor:
Savov, Anton, Oliver Tessmann, and Sg Anton Nielsen. 2016. “Sensive
Assembly: Gamifying the Design and Assembly of Facade Wall
Prototypes.” Internaonal Journal of Architectural Compung 14 (1): 30–48.
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Figure 2: George Sny, 1980
All other drawings and images by the authors.
Anton Savov works as a research associate at the Digital Design Unit
(DDU) — TU Darmstadt and is the founder of architectural studio
AWARE. He iniated the plaorm “20.000 Blocks" as a means for
collaborave architectural design and successfully partnered with IBA
Heidelberg to create the IBA_GAME based on it. Previously, Anton has
worked at Bollinger+Grohmann Ingenieure and taught at the Städelschule
Architecture Class. His work has been exhibited at the Venice Biennale,
MAK Center in Los Angeles, NODE Frankfurt and others. If you want to
get in touch, email to firstname.lastname@example.org
Oliver Tessmann is an architect and Professor for Digital Design at TU
Darmstadt. His research and teaching is located in the eld of computa-
onal design and digital fabrica on. A er receiving his doctorate from the
University of Kassel in 2008, he served as the director of the performa-
veBuildingGroup at Bollinger+Grohmann. From 2010 to 2012 he was Visi
ng Professor at the Städelschule Architecture Class in Frankfurt and, from
2012 to 2015, held the posi on of Assistant Professor at KTH Stockholm.
14 Quantave guidance mechanism in the form of four goals: greenest, tallest, densest, most diverse neighbourhood.