Introduction to Playable Voxel-Shape Grammars

Abstract

A shape grammar is a collection of visually defined geometric rules that could be used to automate the generation of formal representations of designs for buildings, cities, products and more. We offer an extension of the shape grammar formalism based entirely on voxel space instead of vectors, which we used for the generation of schematic architectural designs. We describe a method using playability to increase human agency and designer control over the outcome of the generative phase of voxel-shape grammars. The method is presented with an implementation in the environment of Minecraft and employs three guidance mechanisms. To conclude we list a few considerations from our experience in the design of a playable, voxel-shape grammar and point to future work.

Full text

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Introducon to Playable
Voxel-Shape Grammars
1 Some voxel shapes in the language
dened by the voxel-shape
grammar shown in Figure 4, as
experienced by the users of the
grammar in Minecra. In the fore-
ground, an acvaon state for rule
1.
Anton Savov
DDU — Digital Design Unit
TU Darmstadt
Oliver Tessmann
DDU — Digital Design Unit
TU Darmstadt
1
ABSTRACT
A shape grammar is a collecon of visually dened geometric rules that could be used to auto-
mate the generaon of formal representaons of designs for buildings, cies, products and more.
We oer an extension of the shape grammar formalism based enrely on voxel space instead
of vectors, which we used for the generaon of schemac architectural designs. We describe a
method using playability to increase human agency and designer control over the outcome of the
generave phase of voxel-shape grammars. The method is presented with an implementaon in
the environment of Minecra and employs three guidance mechanisms. To conclude we list a few
consideraons from our experience in the design of a playable, voxel-shape grammar and point to
future work.

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INTRODUCTION
The ability of shape grammar generave formalism to capture
design intenons 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 eect upon
both experts and non-experts by leng them interacvely and
immersively explore design opons and learn by making. With
our shape grammar method we target use scenarios in the early
schemac design phase, when all stakeholders explore the rela-
onship between the elements of a project in an informal and
loose manner, oen in the form of massing models.
From very early on in the work we aimed to:
1. Oer user-friendly visual modelling of both the shapes in
the shape grammar, as well as the grammar rules, in order to
aord the expert users easy access to the tooling framework—
this was possible by redening the typically vector-based
shape grammars for a voxel space and using Minecra as the
implementaon environment.
2. Open the generave process to human agency in an inter-
acve, manageable and surmountable way—by making the
grammar playable, we could add direct parcipaon and
guiding mechanisms to the otherwise purely algorithmic
generave process.
We developed and tested an extendable framework imple-
menng playable, voxel-shape grammars in the Minecra
environment. This paper presents:
• a denion of playable, voxel-shape grammars (Secon 3.1);
• test cases at urban and building scales (Secon 4);
• three types of guiding mechanisms that experts could use to
control the play-driven generave process (Secon 5.3).
PROBLEM STATEMENT
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 soluons or
quickly generate two-dimensional representaons of designs
with desired formal qualies (Sny and Gips 1972; Sny and
Mitchell 1978; Chase 2002). The applicaon of shape grammars
consists of mostly two acvies:
1. designing the grammar, which consists of shapes and rules;
2. iterang mulple mes through the rules to generate designs.
The second acvity maintains the usefulness of shape grammars
as a design tool, subject to their implementaon as automated
systems run by a computer (Ruiz-Monel et al. 2013). However,
shape grammars have been mostly vector-based (Sny 1980;
Woodbury 2016), and the shapes generated with grammars are
only notaonal graphs or abstract 2D composions. (Marn
2006; Sny and Mitchell 1978; Duarte 2005). This poses two
main challenges in the aempt to use them as design tools:
1. computer implementaons of shape grammars are dicult to
dene;
2. computer-automated generaon of shapes with shape gram-
mars is dicult to explore and control.
Computer Implementations of Shape Grammars are
Difficult to Define
An important aspect of a successful shape grammar implemen-
taon is that the users are able to model the shapes and rules
themselves.
Usually, shape grammars have been dened in a closed, expert
coding environment with an interface dened solely for the
purposes of the shape grammar. Therefore, a potenal 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
address it:
Currently though, there are few computer implementaons that
are praccable for students or praconers. Most do not have
interfaces that make them easy for nonprogrammers to use.
More eorts have gone to computaonal problems than to inter-
face ones. Implementaons of simple, restricted grammars that
are visual and require only graphic, nonsymbolic, nonnumerical
input are needed. (Knight 1999)
We address this by implemenng 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 relaon to the voxel shapes they model—and subse-
quently iterate through in the game world—creates an immersive
percepon for a one-to-one architectural scale.
Computer-Automated Generation of Shapes with Shape
Grammars is Difficult to Explore and Control
Most exisng research on shape grammars uses a computer-au-
tomaon approach to the generave phase, leaving no control,
or very lile, mostly global control, to the designer during the

536
process of shape generaon. This has been done “as pencil-
and-paper execuon might be tedious and therefore useless for
the sake of discovering many new soluons.” (Ruiz-Monel et al.
2013). However, an automated generaon process is most oen
opaque and non-iterable—the user cannot inuence the result
while the process runs and is simply presented with an outcome.
Our method uses a combinaon of playability and guiding mech-
anisms to make the iteraon process more navigable.

SHAPE GRAMMARS

George Sny (1980) denes a vector shape as follows: "A shape
is a limited arrangement of straight lines dened in a cartesian
coordinate system with real axes and an associated euclidean
metric.” In a similar manner let us dene voxel shape as a limited
arrangement of voxels in a discrete voxel grid and an associated
euclidian metric (Figure 3).
A voxel-shape will dene all further terms we nd in Sny's
“Introducon to Shape and Shape Grammars” (1980), but for the
discrete voxel space instead of connuous cartesian vector space.
For example, a scale operaon 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. Rotaons
would go only in 90 degree increments and so on. A less strict
denion, allowing real number scale factors and rotaon, is
also possible, but it would need a post-processing voxel detailing
roune, such as marching cubes, and thus introduce unnecessary
complexity for the current purposes of the method (Marais and
Crumley 2012).
The original shape grammars formalism uses vectors that are
simple representaons 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,
consisng of shape and symbols, used as a matching mask for
the grammar rules. The marker symbols in vector space shapes
are notaonal. In our voxel shapes we use voxels with special
aributes for markers (Figure 3).

Shape grammars perform computaons with shapes in two steps:
a recognion of a parcular shape and its possible replacement.
Rules specify the parcular shapes to be replaced and the
Savov, Tessmann
3
2
4
2 The original graphic denion of
shape grammars as it appeared in
the 1980 paper “Introducon to
Shape and Shape Grammars.”
3 A vector shape as dened by Sny
and Gips 1980 and a voxel shape as
dened in this research.
4 Graphic denion of a sample
voxel-shape grammar and some
of the shapes in the language it
denes.

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5
5 Sample playable voxel-shape
grammar (le: rules, right: inial
shape)—besides the voxels’ state,
the rules take into account also the
player's posion.
6 Generaon 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
inuence their decisions.
6
7

538
8
9
8 The urban scale voxel-shape
grammar from IBA_GAME has rules
that place pre-designed buildings.
9 A schemac design for a residenal
building created using a voxel-
shape grammar with 6 rules.
manner in which they are replaced. (Willis 2012)
A shape grammar is dened by rules and an inial 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
2).
For the shape rules’ implementaon in voxel space we dene 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 dened in
vector form and only the generated shapes—aer the iteraon 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 sll novel, as the enre
grammar is dened and iterated in voxel space.
Friedman and Stamos (2013) introduce the noon of a voxel
grammar in their work on procedural tree generaon. However,
their grammar denion 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 dened directly
in terms of […] shapes” (Sny 1980). Our implementaon here
suggests that the enre voxel-shape grammar (shapes and rules)
is dened 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 dened in
secon 2.
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 addional step in the generave iteraon 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 posion.
Diering from shape grammars, where the generaon is auto-
mated and each step of the iteraon produces the condions
for the next, playable voxel-shape grammars require that every
iteraon needs to be iniated 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).
Savov, Tessmann

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On the other hand, player decisions could be inuenced by a
guidance mechanism. A guiding mechanism is dened by the
author of the grammar and is able to encode a design intenon
or expert knowledge. A well-dened 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 inuence their decisions (Figure 7).
EXPERIMENTS AND CASE STUDIES
We are tesng the concept of playable voxel-shape grammars
in the project 20.000 BLOCKS. Our implementaon consists of
a Minecra version with the ComputerCra mod and a set of
custom scripts which drive rule detecon, player/goal tracking
and results export. See Savov, Buckton, and Tessmann (2016)
and www.20000blocks.com for further details on the project.
We invesgated 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 possibilies 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 Variaons based on shape rotaons 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 residenal, mul-apartment buildings. Three teams
of architects and engineers used our implementaon of playable
voxel-shape grammars and dened components of the buildings
within the grammar (Figure 9). Each variaon had up to 16 shape
rules and was played by aendees of the conference.
MINECRAFT IMPLEMENTATION OF PLAYABLE

Based on our two-year experience with this ongoing project, we
oer the reader the following thoughts on voxel shapes, voxel-
shape rules and guidance mechanisms.

Design
The abstracted modelling environment with a voxel size of 1 x 1
x 1 m could be liming. However, since our aim is to generate
schemac architectural designs, this level of abstractness works
in our favour.
Walkability
An important requirement in order to achieve an immersive
experience in the generave phase—i.e., in the play phase—is
that the resulng structures are walkable for players, so they can
reach the newly added markers, otherwise the iteraon process
is blocked. That means that in both urban or building scales, all

540
11
12
possible sequences of the grammar’s shape rules need to create
a walkable combinaon when placed.
Color Coding
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 dierent.
Furthermore, with larger sets of rules, such as in IBA_GAME,
where we used six types of rules with 2–4 variaons each, a
color coding of the types of rules helps the player learn the
grammar faster.
Rotation Options
As we are operang in a strict orthogonal voxel grid, we had four
possible rotaons 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 rotang of the shapes, i.e.,
the masking shapes that are modelled in the grammar rules are
absolute in size and orientaon. Due to the discrete quality of
a voxel space, scaling and rotaon 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 acvator block on which a player steps to acvate the
detecon of a masking shape they had built around it (Figure
5);
2. the extension block, which is a marker that replaces the ac-
vator block upon successful detecon.
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 populang the
design space with too many scaered, independent struc-
tures. That means some shapes in the grammar act as seeds,
for example the shape represenng a house in IBA_GAME,
and others as extensions, for example the shapes represenng
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 vercally
proporoned windows and enclosed;
2. a green resource -> shapes are lighter, with horizontally
proporoned 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 resulng shape,
with the same behavior during the iteraon process, but with
dierent design qualies.
Markers in a Grid or Freely Spaced
When designing the playable voxel-shape grammar, the expert
needs to make sure that all rules are spaally compable 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
Savov, Tessmann

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to regulate, across our team, how and when secons of a shape
rule could overlap with another (Figure 12). This saved the work
of having to try all combinaons separately.
Another strategy, which avoids the rigidity of using a grid, is for
the shapes to come with the markers in a posion that allowed
for the making of stepped structures and richer designs in spaal
terms. To avoid too many unwanted overlaps, new structures
only grow from exisng 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 acvate a grammar rule with it
and so gain the rewards given by the rule. We used playability as
a generave force and at the same me as a control mechanism
over the outcome. Ruiz-Monel 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 intenon into the
playable voxel-shape grammars, we tried three types of guidance
mechanisms: a quantave game-goal system; liming choice
with the shape design; and performance-based feedback.
Quantitative Guidance Mechanism
We used a so goal system that qualitavely guided the growth
as dierent players chose to go for dierent goals. For example
in IBA_GAME we dened four server-wide goals: collect the
most green points, build the most buildings, build the tallest
structure, build as many dierent 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 variaon.
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 Liming player choices with design.
Le: With a rule that allows users
to stack the same house over itself,
the most ecient 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 ecient
way of gaining height points is to
criss-cross houses.
14). Each voxel-shape rule in the grammar rewards the player
dierently 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 lile eort 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
(Figure 13).
Performative Guidance Mechanism
While sll in the early works in terms of seamless integraon, we
tested a guiding system based on structural analysis. It exports
the model to Grasshopper every me a rule is acvated, runs an
analysis roune 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 Sensive Assembly, documented in Savov, Tessmann, and
Nielsen (2016), where this type of feedback loop is described in
more detail.
CONCLUSIONS AND FUTURE WORK
We presented an extension to the shape grammar formalism
for voxel spaces, which we used for the generaon of schemac
architectural designs. We described a method using playability to
increase human agency and designer control over the outcome
of the generave phase of voxel-shape grammars. At the end we
shared a few thoughts on the design of a playable voxel-shape
grammar in Minecra.
13

542
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 interpretaon
and analysis for their architectural potenal without further
transformaon or translaon steps.
Furthermore, the method allows for the integraon of design and
fabricaon. An addional reason to use voxel-shape grammars
instead of vector-shape grammars is to come one degree closer
to embedding material specicaon rules in the grammar (Rossi
and Tessmann 2017; Sny and Gips 1971).
Challenges
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 bolenecks to increasing parcipaon:
1. The need to download and use a customized Minecra
version, which reduces the number of potenal players. We
are looking for ways to implement the grammar logic enrely
on the server side so that players can parcipate with a
Vanilla (unmodied) Minecra client.
2. Closed server access: currently the data collecon requires us
to run the server ourselves. We are exploring opons to let
users run their own Minecra server with the map and save
results in the cloud.
Future Work
The research could benet from the following future
developments:
• A generave visualizer, which could simulate a game being
played so that a designer can capture some of the most
common conict/bugs in advance, like mismatching shapes
and broken walkability, without having to play the game over
and over again.
• Implemenng automated rules that would not need the user’s
input at every generave step. There needs to be a beer
balance between the eects of the player’s intenons and
the generave rules over the nal designs. To address this, in
some cases, when the right condions occur, the grammar
rules might allow for several iteraon steps to happen auto-
macally one aer the other, in the form of a bonus eect or
what Sanchez (2015) denes as synergies.
• The collected data (grammar denions plus the generated
shapes) can be used to train a machine learning algorithm to
generate either grammar sets or schemac designs.
The test game can be downloaded at: www.20000blocks.com.
ACKNOWLEDGEMENTS
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:
Steen Bisswanger, Ben Buckton, Theo Gruner, Jörg Hartmann, Thomas
Valenn Klink, Sebasan Koerer, 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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IMAGE CREDITS
Figure 2: George Sny, 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 iniated the plaorm “20.000 Blocks" as a means for
collaborave 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 savov@dg.tu-darmstadt.de
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 Quantave guidance mechanism in the form of four goals: greenest, tallest, densest, most diverse neighbourhood.