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Crystal Formations and Symmetry in the Search of Patterns in Architecture

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Nature is always full of patterns inspiring all the disciplines and especially architecture in many ways. Currently, with the advances in technology and growing interest towards nature-driven studies, retrieving information from nature has a new connotation in scales and dimensions including both living and non-living beings. In this study, it is aimed to explore the scales of nature from Nano to Macro and a holistic approach is embraced to cope with the complexity of nature and architecture. To understand these complexities, patterns in different forms and scales serve as valuable tools to decode and recode information from one domain to another through locating the order and how patterns exist in different and changing environments with respect to forces and the urge of the existence of the being.This research focuses on the behavior of crystal formation which can be observed both in biotic and abiotic nature to understand the order generating the patterns in nature and its adaptation into a different and changing environment. This information of crystallization has great potential for architecture in terms of spatial structures, new materials and introducing a novel lattice for freeform structures. In this study, the potentials, limits and possible contributions of crystal formation are stated for architecture in the search of symmetry and patterns.
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Crystal Formations and Symmetry in the Search of Patterns
in Architecture
Müge Kruşa Yemişcioğlu1, Arzu Gönenç Sorguç2,
Çağlar Fırat Özgenel3
1,2,3Middle East Technical University, Department of Architecture
1,2,3{mugek|arzug|fozgenel}@metu.edu.tr
Nature is always full of patterns inspiring all the disciplines and especially
architecture in many ways. Currently, with the advances in technology and
growing interest towards nature-driven studies, retrieving information from
nature has a new connotation in scales and dimensions including both living and
non-living beings. In this study, it is aimed to explore the scales of nature from
Nano to Macro and a holistic approach is embraced to cope with the complexity
of nature and architecture. To understand these complexities, patterns in different
forms and scales serve as valuable tools to decode and recode information from
one domain to another through locating the order and how patterns exist in
different and changing environments with respect to forces and the urge of the
existence of the being.This research focuses on the behavior of crystal formation
which can be observed both in biotic and abiotic nature to understand the order
generating the patterns in nature and its adaptation into a different and changing
environment. This information of crystallization has great potential for
architecture in terms of spatial structures, new materials and introducing a novel
lattice for freeform structures. In this study, the potentials, limits and possible
contributions of crystal formation are stated for architecture in the search of
symmetry and patterns.
Keywords: nature-driven, computational design, crystal formation, symmetry,
pattern
INTRODUCTION
Men always search patterns which bring order and
predictability into Architecture. Observing the
weather, recording the earthquakes, decoding DNA
are some examples of the quest for patterns. Ar-
chitecture since from Vitruvius search for order as a
way to achieve strength, harmony, aesthetics. Differ-
ent architectural styles with prominent features man-
ifested in the façades, structural systems, ornaments,
tiling, the use of materials and even spatial organi-
zations can be considered as the examples of how
patterns in architecture determine the design. Na-
ture is always full of patterns inspiring all the disci-
plines and especially architecture in many ways. Cur-
rently, with the advances in technology and grow-
ing interest towards nature-driven studies, retrieving
GENERATIVE DESIGN - Volume 2 - eCAADe 36 |121
information from nature has a new connotation in
scales and dimensions such as molecules, organelles,
cells, tissues, organs, and living beings, behavior, and
ecosystem (Zari, 2010). I n order to explore various di-
mensional patterns, nature reveals as an important
model, mentor and measure in architecture (Benyus,
1997) both living beings and inanimate part of it
as a whole. Since nature and architecture are dif-
ferent complex systems, finding patterns in nature
which represent the ordered behavior is highly ad-
vantageous to transfer information to architectural
domain. Moreover, locating the disordered behavior
according to force and formation provides a valuable
source to understand the adaptation of resultant pat-
terns into changing conditions. Although this adap-
tation is mostly seen as an imperfection of the exist-
ing pattern, it is also possible to acknowledge it as a
new kind of order with new symmetry rules and pat-
terns.
In the scope of this study which is presented as
a part of an ongoing Ph.D. research, it is aimed to ex-
plore nature in terms of new orders and resultant pat-
terns. Then the discussion of the broadened refer-
ence domain towards a holistic one including both
living and non-living beings is carried by focusing on
abiotic nature as a source of information. In this re-
spect case study is focused on the behavior of crystal
formation which can be observed both in biotic and
abiotic nature to understand the order generating
the patterns in nature and its adaptation into differ-
ent and changing environment. The information em-
bedded in crystallization has great potential for ar-
chitecture in terms of spatial structures, new materi-
als and introducing a novel lattice for freeform struc-
tures.
PATTERNS AND NATURE
Nature has always been source of inspiration and
information for science, mathematics, architecture,
engineering, and arts. Among the information em-
bedded in nature, symmetry and resultant patterns
which reflect the ordered and disordered behaviors
are prominent for these domains. Today, with the ad-
vents in technology and need for novel solutions for
new challenging tasks like economic, environmental
and social ones, researchers again gravitated towards
nature with new tools and perspectives. Among
these approaches, biomimetics is taking attention
with its methods, tools and exemplary studies.
Figure 1
Flow systems in
action: the delta of
the Lena River in
northern Siberia
(left) and a cast of a
human lung (right).
(A.
Bejan/Doubleday)
[url-1]
The extent of the current biomimetic studies in Archi-
tecture is mostly limited with the living natural world,
and this issue is explained by the urge of organisms
to survive, thrive and nurture in the environment that
they proceed their life (Dorfman, 2016). Moreover,
learning from the inanimate part of the nature is dis-
couraged in the scope of Biomimetic studies by call-
ing it “Geomimicry” and it is claimed that adapting
122 |eCAADe 36 - GENERATIVE DESIGN - Volume 2
living nature’s aspects to survive and thrive on Earth
is the only valuable strategy, although water, stars,
air, and rocks are counted as important substances of
“nature” (Biomimicry Institute, 2013).
As the Constructal Law introduced by Adrian Be-
jan claims that nature works with same physical laws
both for animate and inanimate nature (Bejan & Zane,
2012), it is seen that both animate and inanimate na-
ture reacts to forces of their environment in a sim-
ilar manner which architecture is also seeking for.
The exemplary study of Philip Ball shows that abiotic
subjects have great potential to understand, analyze,
predict and generate the built environment, and bi-
otic and abiotic nature is not that much different from
each other, and they form the ecosystem together
(Ball, 1999). As it is shown in Figure 1, the genera-
tion and growth of geographical formations and our
lungs behave similarly depending on the flow of wa-
ter and air and this can be explained by Geometric
Similarity which is one of the similarity types that can
be established between two different scales. These
similarities are described as “tree model” which is the
non-dimensional pattern based on fractal branching
according to the acting forces.
Learning from abiotic nature is not a new con-
cept in architecture e.g. the hanging structural
model of Antoni Gaudi and book of Bruno Taut de-
scribing a utopian city are still valuable examples
showing the potentials of understanding the role of
forces on the forms in architecture. In Taut’s unreal-
ized drawings and explanations, a new city and ar-
chitectural approach is proposed based on the ge-
ographical formations formed by the natural forces.
The drawings created between 1917 and 1920 shows
the influence of inanimate nature in his works, also
explains the crystal inspiration on Crystal Pavilion
(1914) (Gomel & Weninger, 2004). Both the utopian
drawings and the pavilion can be seen as the explo-
rations of the influence of environmental forces both
on nature and the architecture. Recently, Speck et.al.
proposed “Geology” as “geo-derived development”
and nature-derived development along with “Biol-
ogy” as a source of information that have potential
to contribute to design and engineering (Speck, et al.,
2017).
Hence, in the scope of this study, it is aimed
to broaden the extend of biomimetic studies by
re-introducing inanimate nature and well-known
natural forces with their lessons to be learned
and adapted to architecture. Approaching nature
through only living organisms is found to be under-
estimating the potentials of balance between ani-
mate and inanimate nature. It is also stated that inan-
imate nature along with natural forces has great po-
tential for architecture, since the contemporary ex-
amples are seemed to be limited with formal ap-
proaches like biomorphic ones. Thus, comprehend-
ing the natural system as a whole with all or related
relations and changes in time provides more informa-
tion to architecture then acknowledging only one in-
stance of a part.
It is a fact that each of the natural beings is a
complex system showing “a complicated mix of or-
dered and disordered behavior” (Johnson, 2009). In
understanding these complexities, patterns in differ-
ent forms and scales serve as valuable tools to de-
code and recode information from one domain to
Figure 2
(a) Cave of Crystals,
found in Mexico
[url-2], (b) Collage
of protein crystals
and viruses grown
in space (Credits:
NASA). [url-3], (c)
Examples of Crystal
structure of human
DNA (Manvilla, et
al.,2012)
GENERATIVE DESIGN - Volume 2 - eCAADe 36 |123
another. In nature it is not a surprise to find geo-
metrically well-defined patterns like hexagonal hon-
eycombs, spiral seashells, branching fractals of trees
and leafage, molecular distribution and lattice struc-
tures of crystals helping to define growth and gener-
ation. These patterns can be found in both two and
three dimensions in different scales. In order to un-
derstand the order in complexity and relate it with
architectural patterns, it is important to decode the
existing symmetries and how the resultant patterns
exist in different and changing environments with re-
spect to forces and the existence of the being.
Hence, considering the importance of the tan-
gible case studies in nature-driven research in archi-
tecture, in this study, the order of crystal structures
is examined to retrieve information for architecture
to learn from its adaptive capacity and order based
on the symmetry groups and elements. Crystalliza-
tion processes are chosen to understand the relation
between different behaviors in different scales from
nano to macro.
CASE STUDY: CRYSTAL SYMMETRY AS A
PATTERN
Crystal formations are observed as an important ex-
ample on how animate and inanimate nature should
be taken into account in a holistic way. Crystalliza-
tion process can be observed both in animate and in
animate nature as can be seen in crystal caves (Figure
2a), in proteins and viruses (Figure 2b) and in human
DNA and RNA (Figure 2c). The crystallization process
regulates the being’s growth, by either adapting itself
to the changes of its environment or fitting to new
ones which are also very prominent for adaptation
Figure 3
Drawings of unit
cell and Bravais
Lattices are
generated by the
authors. Twin types
are retrieved from
http://www.tulane.edu/
124 |eCAADe 36 - GENERATIVE DESIGN - Volume 2
Figure 4
Screenshot of the
developed
algorithm
simulating the
growth of crystals
based on unitcell,
growth rates,
twinnings and
defects. The
algorithm is
developed by the
authors.
GENERATIVE DESIGN - Volume 2 - eCAADe 36 |125
in architecture. In this vein, crystal polymorphism is
a very appealing trait with its capability to adapt to
various environments as well as preserving the inner
order.
Figure 5
Spinel Crystal
generated based on
unit cell and growth
Although polymorphic crystals have different habits
and costumes, the faces which grow as a response of
the environment providing the efficient solution for
the growth process will occur and the response of the
environment based on crystal defects and growth
rates based on the inner code of the crystal (Kang, et
al., 2014). This code, which can also be interpreted as
the genetic code of the crystal, regulates all the be-
havioral features of the crystal and can be explained
by means of symmetry operations of the unit cell and
the lattice structure (Bravais Lattice).
In this respect, to comprehend and provide an
information for various levels of architecture, a com-
putational model is developed based on the crystal
class, metrics regarding the unit cell (lengths {a,b,c}
and angles {alpha, beta and gamma}), growth rates
of faces according to local axise. Then, the model is
elaborated to generate a cluster with numerical data
such as the number of crystals, and number of twin
crystals if a twinning process is foreseen among the
most common defects in crystals. Also, considering
the unpredictable emergence location of initial crys-
tallization, a randomization seed is included to illus-
trate some of the potential configurations. Spinel
Crystal (Al2MgO4) is generated based on the Crys-
tallography Information File (CIF) data retrieved from
“crystallography.net”. One of the instances of the al-
gorithm showing the process can be seen in the Fig-
ure 3.
As a result of aforementioned analysis and sim-
ulation, the potentials of crystal study are revealed
with the adaptive features, the varied strength of
3-dimensional patterns, and force-driven formation.
The outcome 3d spatial pattern based on a unit cell
has great potential in terms of space filling, adapta-
tion and structural behavior. Decoded and recoded
pattern of Spinel crystal is shown in Figure 4.
The growth process of the crystals along with de-
fects such as intergrowth and twinning are promi-
nent in architecture with its unique characteristic
of repetition of the 3d pattern while adapting into
a different environment. The simple ordered pat-
tern underlining the complex structure of crystals
126 |eCAADe 36 - GENERATIVE DESIGN - Volume 2
is important for architecture to comprehend and
3-dimensional tessellations which can evolve and
grow in time. Also, various configurations of same
atoms revealing varied patterns show quite different
structural behavior, such as diamond and graphite.
Structural simulations show that these configura-
tions can also lead architecture to search for new 3-
dimensional structural patterns.
NEW PATTERNS FOR ARCHITECTURE
Architecture can learn from form generation from na-
ture and crystallization which is a process occur in
any ordered matter is a prominent source. The idea
of creating the form based on forces is not a recently
developed idea, contrary it is being discussed in the
last century which can be discussed on the quotation
from D’Arcy Thompson: “Form is a diagram of forces.
(Thompson, 1917)
Therefore, the formation process of crystals
which occur according to thermodynamic forces of
the environment provides a valuable lesson regard-
ing the force-form relationship to architecture. The
information transferred from crystals can be mapped
into many architectural scales i.e. materials, com-
ponents, structural systems, buildings and building
blocks etc. Transfer or information among different
scales is a problematic process, especially all the ther-
modynamic reactions in nanoscale are completely
different than macroscale. Therefore, there is a need
for a common ground which defines the similarities
between not only different scales, but also different
knowledge domains namely crystallography and ar-
chitecture.
CONCLUSION
This study constitutes the basis of a generic model
in search of extreme architecture. The main chal-
lenge in this study is to associate disciplines (which
are crystallography, chemistry, physics, mathemat-
ics, and architecture in this study) on a single case
study. Thus, regarding the interdisciplinarity of the
subject, a group of researchers from different fields
are contributed to provide a model and a method. In
the proposed model, crystal formation is explored in
various scales which are exhibiting different behav-
iors yet, contributing the existence of crystal struc-
ture by adapting into different environmental forces
and conditions. It shows that abiotic nature which is
mostly disregarded in the current studies can guide
architecture to exist in different conditions through
the principles of emergence and growth of crystal
structures. These principles are illustrated with the
example of a spinel crystal which is a part of abiotic
nature. Yet, it is possible to demonstrate similar be-
havior with a biotic example with respect to its own
order and symmetry conditions.
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128 |eCAADe 36 - GENERATIVE DESIGN - Volume 2
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Article
Full-text available
Over the last few decades, the systematic approach of knowledge transfer from biological concept generators to technical applications has received increasing attention, particularly because marketable bio-derived developments are often described as sustainable. The objective of this paper is to rationalize and refine the discussion about bio-derived developments also with respect to sustainability by taking descriptive, normative and emotional aspects into consideration. In the framework of supervised learning, a dataset of 70 biology-derived and technology-derived developments characterised by 9 different attributes together with their respective values and assigned to one of 17 classes was created. On the basis of the dataset a decision tree was generated which can be used as a straightforward classification tool to identify biology-derived and technology-derived developments. The validation of the applied learning procedure achieved an average accuracy of 90.0%. Additional extraordinary qualities of technical applications are generally discussed by means of selected biology-derived and technology-derived examples with reference to normative (contribution to sustainability) and emotional aspects (aesthetics and symbolic character). In the context of a case study from the building sector, all aspects are critically discussed.
Article
Frei Otto (1925 – 2014) is one of the most decorated architects in the 2nd half of the 20th century in the world. He built lightweight structures as the German Pavilion in Montreal 1967, the roofs for the Olympic games in Munich 1972 and numerous tents and shell structures. In his pioneering research he described the growth and form of natural structures in living and non living nature. This contribution highlights Frei Otto’s approach and works.
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The mammalian repair protein MBD4 (methyl-CpG-binding domain IV) excises thymine from mutagenic G·T mispairs generated by deamination of 5-methylcytosine (mC), and downstream base excision repair proteins restore a G·C pair. MBD4 is also implicated in active DNA demethylation by initiating base excision repair of G·T mispairs generated by a deaminase enzyme. The question of how mismatch glycosylases attain specificity for excising thymine from G·T, but not A·T, pairs remains largely unresolved. Here, we report a crystal structure of the glycosylase domain of human MBD4 (residues 427-580) bound to DNA containing an abasic nucleotide paired with guanine, providing a glimpse of the enzyme-product complex. The mismatched guanine remains intrahelical, nestled into a recognition pocket. MBD4 provides selective interactions with the mismatched guanine (N1H, N2H(2)) that are not compatible with adenine, which likely confer mismatch specificity. The structure reveals no interactions that would be expected to provide the MBD4 glycosylase domain with specificity for acting at CpG sites. Accordingly, we find modest 1.5- to 2.7-fold reductions in G·T activity upon altering the CpG context. In contrast, 37- to 580-fold effects were observed previously for thymine DNA glycosylase. These findings suggest that specificity of MBD4 for acting at CpG sites depends largely on its methyl-CpG-binding domain, which binds preferably to G·T mispairs in a methylated CpG site. MBD4 glycosylase cannot excise 5-formylcytosine (fC) or 5-carboxylcytosine (caC), intermediates in a Tet (ten eleven translocation)-initiated DNA demethylation pathway. Our structure suggests that MBD4 does not provide the electrostatic interactions needed to excise these oxidized forms of mC.
Published in the United States by Doubleday, a division of Random House, Inc., New York, and in Canada by Random House of Canada Limited, Toronto Benyus
  • Zane Bejan
Bejan, A and Zane, JP 2012, Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization, "Published in the United States by Doubleday, a division of Random House, Inc., New York, and in Canada by Random House of Canada Limited, Toronto Benyus, J 1997, Biomimicry: Innovation Inspired by Nature, Perennial
  • M Dorfman
Dorfman, M 2016, Nature Is Alive with Green Chemistry, Biomimicry 3.8
Romancing The Crystal: Utopias of Transparency and Dreams of Pain
  • Gomel
  • Weninger
  • Sa
Gomel, E and Weninger, SA 2004, 'Romancing The Crystal: Utopias of Transparency and Dreams of Pain', Utopian Studies, 15, pp. 65-91
Biomimetic design for climate change adaptation and mitigation' , Architectural Science Review
  • Zari
Zari, MP 2010, 'Biomimetic design for climate change adaptation and mitigation', Architectural Science Review, 53, pp. 172-183