For several years, designers have given
their attention to self-formation progressions in nature to realize a more
possibilities in the way architecture can be organized. The pioneers in analog
form finding who I will be discussing in this paper are Antonio Gaudi and Frei
Otto. The results of analog experiments are aesthetically pleasing. However,
the Interesting and the sensation of this method lies in the way they are transformed
and come into being. Especially doing the experiments with different kind of
scales and without a plan.

With quick development of technology,
architects of the 21st century can overcome the boundaries that the
analog experiments had, and transform any abstract form into a building. Digital
experiments are done at universities and architectural firms. Zaha Hadid is has
invested a lot of time in digital form finding and contributed on creating
ground breaking architecture.

This paper will introduce the history of
form finding from the pioneers to architects of today. It will examine the
Analog experiments done by Antonio Gaudi and Frei Otto will be used as case
studies. An overview of the digital experiments done in AA school of
architecture and Zaha Hadid projects will illustrate the difference between
analog and digital form finding. Will Perform experiments in bundling systems
in Maya.



It was until 20th century a
mathematician D’Arcy Wentworth Thompson extended the ideas to make a modern
understanding that there are inclusive laws that emerge from principal math and
that reflect the growth and form in biological systems. Thompson worked on the relationship between common forms
and numerical models and appeared likenesses between
such things as jellyfish forms and drops of fluid. His book,
on growth and form got to
be a vital way discoverer in the study of
nature and the instrumental in the later rise of the field of

The image shows the shapes made by drops
on water (left) and the tentacles of a jellyfish(Right).






By understanding
Thompson’s relationship between natural schemes, form &
structures and absolute definable rules, the appreciation of natural
schemes has gotten to be a developing field of interest.
Soap film studies have given us bits of
knowledge into minimal structures, bee hives have given us
an understanding in honeycomb structures which
are currently utilized in lightweight panel systems, and an
understanding of photosynthesis has helped in creating photovoltaics has ended
up as a major sustainable energy source. While observing a flock
of birds or a school of fish it teaches us the development of dynamic
structures. In urban planning, we
have indeed seen the study of non-planned settlements where
social, cultural and external limitations permit settlements
to create incrementally because of actions and reactions.


Bundling in nature

Philip Ball a science writer
expressed that pattern and form in nature are not only
generated through organic coding, but too there are simple
physical laws behind them. Hence, we can repeat complex forms in
nature by repeating these rules. From all these thoughts, we can
say that there are a few natural forces in the world and they
are acting on natural and inorganic things and decide their
appearances. Since external forces cause similarities and differences we can
repeat their impact on forms by repeating these physical forces.

Pattern or form is often mixed up with
just repeating array of identical components. However, pattern or form can incorporate clusters that
are not fundamentally identical, and repeat in a manner
than is not fundamentally standard or with well-defined
symmetry. form in nature encapsulates this concept. Through
its energetic characteristic, it can assimilate changing
conditions, change its visual appearance, all while remaining
topologically the same.

We find that bundling patterns repeat again and again in different
situations but still they show some similarities with one another.
Like tree roots bear a resemblance to lightning, a neuron in a cell body to
London underground map.









Form finding in architecture

Traditionally in
the architectural design process, there is a fundamental belief that
the design process is a rational linear one and that
the designer is some way acting as the inventor.
The traditional method brings up individual taste and reproduction of
historical styles while the form finding one, is based on a process and
interactions between components.

As a design process, form finding has
existed way long before the digital revolution. At the beginning of the
twentieth century, architects like Frei Otto and even before him Antonio Gaudi
started implementing design methods that today we see them we can say that are
based on computational approach.

Over the past century architects have been
using various form finding strategies that are still being made used of today.

Form finding by geometry used by
Frank Lloyd wright and Le Corbusier in his book Modular he related the golden
ratio as beauty. Corbusier also went on to apply the geometry rules and
proportions in to same of his project like Notre dame du haut.

Form finding driven by nature this
approach architects design approach focused on use of typological elements.
Aldo Rossi was well known to use pure shapes of the site like the teatro del
Mondo in Venice.







Form finding driven nature, the
architect observes a progression in nature to discover ways to organize the
project. This study allows the architect to come with an ideal form. Through
this process the architects translate living organism process into architecture
itself rather than just a concept or inspiration. This has been used by
Santiago Calatrava’s city of arts and sciences in Valencia.

architecture is just phenomenal and inventive and exciting. It’s very skeletal,
like you’re looking at the vertebrae of a dinosaur or prehistoric fish,”
said Chernov. Movie producer.

Performance driven form finding method is completely different from other form finding method. In this
approach architects focus on minimal path or form, obtaining from material
properties and structural performance. Through this approach the building
relation to its context is minimal. New structural techniques and digital
fabrication drives structural optimization systems for complex curved surfaces.

Minimal form made advancement in light
construction, to constructing thin concrete shells structure as we can see in
Stockholm at Wyss Garden Centre, to constructing tents and membranes.
Performance driven method unites both aesthetics and function. Architects like Buckminster
fuller in America, Felix candela in Mexico and Pier Luigi in Italy used form
finding driven by performance approach. Fuller’s usage of tensegrity
structures, Candela’s Los Manantiales Mexico which has four intersecting
hyperbolic paraboloids, with a thin concrete shell and Luigi ‘s Palazetto dello
sport in Rome 1960 he used thin concrete shell dome. Designers of today have
embraced this method at applied it in their project.















In the next chapter will focus more on
Antonio Gaudi and Frei Otto who used analog experiments to come up with form
finding solutions. And, will discuss on digital research done by universities
and experiments done by Zaha Hadid.

Antoni Gaudi

The pioneer of form finding is Antoni
Gaudi, and the first to use analog experiments in designing his projects. He
was mostly inspired by nature especially the environment around him, like
Mallorca caves, prades mountain behind Reus and Montserrat mountain which
comprises of different peaks in Catalonia He studied organic forms in nature
and tried to express in architectural language. At first Gaudi was influenced
by Neo-gothic movement in the end of 19th century. Later he joined modernisme
and described gothic style as imperfect. As he said:

Gothic art is imperfect, only half resolved; it is a style created
by the compasses, a formulaic industrial repetition. Its stability depends on
constant propping up by the buttresses: it is a defective body held up on
crutches. (…) The proof that Gothic works are of deficient plasticity is that
they produce their greatest emotional effect when they are mutilated, covered
in ivy and lit by the moon. -Antoni gaudi

Gaudi preferred to work with
three-dimensional models rather than drawing detail plans for his projects. He
experimented the 3D models by adding weights on them to find the best form and
the correct construction method. He hanged strings where the columns will be
placed in the project. Then he hanged the weights onto the strings.  By adding weights on a model that was placed
in upside-down manner curves were formed in vaults and arches. By doing this
Gaudi was looking for the structure of for arches and vaults. He will then take
pictures of the model and painted over the photographs. The ‘hanging chain’
model took him ten years to build but through this process we would really
analyze the organic form.








He designed his master works following
this approach like the Colonia Guell and Sagrada Familia. His projects bear a
resemblance to branching systems because of the arches are divided into
branches and they come together. Inspired from nature as the branching systems
of the arches symbolize trees. This led Gaudi to the use of ruled surfaces like
hyperboloid vaults in Sagrada Familia. His even said that; Paraboloids, hyperboloids and helicoids, constantly varying the
incidence of the light, are rich in matrices themselves, which make
ornamentation and even modelling unnecessary. -Antonio Gaudi

























Frei Otto

If Antoni Gaudi is the father of form
finding, then Frei Otto is the master of the process of form finding. His
concern to achieve more with less material and energy made him take on
experiments and research on lightweight structures. As a result, he gave
attention to form finding and based it on researching self-formation and
developing natural constructing methods that are less damaging to the planet.
The research group involved different kind of people from architects, engineers
to biologist and each one of them had a task. One of the architect’s task was
to find a link between nature and building while the engineers had to research
the self-formation mechanism and the biologist had to work the natural quality
of the structure and quality of those living in nature.

Frei Otto was really into the study of
natural forms. As he used to refer to himself as natural scientist than an
engineer. In 1964 he established the institute of lightweight structures at the
university of Stuttgart, where he established the process of form finding
through many experimentations with physical models. Which was based on
mathematical patterns found in nature.

A vast number of experiments were
conducted at the institute of lightweight structures as basic research
programme by teams which were supervised by Frei Otto himself. He came up with
methods in which form generates themselves to analyze the process by which form
originates from nature. Some of his investigations includes soap film
experiments to come up with minimal surfaces, optimized pathways by using
thread as branched systems, pneumatic membrane using rubber skin, suspended
constructions experimenting with chains and floating magnets to experiment
surface occupation in urban development.

Soap film experiment producing minimal surface

A soap film are membranes made up of
liquids. They always bond to the smallest surface. Thus, taking up the minimal
surface which is mathematically defined. Otto used this experiment and came up
with a different way of building tents.








Pneumatic construction experiments

Plastic stiffened rubber films are used in
this kind of experiments. When inflated it hardens. This construction system
comprises of a membrane which is supported by air pressure. In lightweight
structures pneumatic construction which is also known as air hall is the most
extreme because it supported by air pressure compared to tents which are
supported by poles. That’s why it was never considered as a serious building
material. But after Frei Otto’s intensive research they started producing
pneumatically tensioned membrane constructions. Like the exhibition pavilion in
Rotterdam which was reinforced with rope. Otto with other colleagues in 1971
proposed an air hall at the city of Antarctica. Frei Otto also did studied
airship as part of ‘airfish’ project and came up with different form and









Suspended constructions experiments

In this experiments Frei Otto was
suspending chains in a model. The suspended chains if its dense it gives the
form of a suspended roof that are stabilized by their own weight. The suspended
chain forms a hyperboloid line which is perfect form for a free-standing arch. Frei
Otto applied this kind of form finding when he designed a temporary
accommodation for medical school in elm. He also did a competition design of a
suspended roof in Stuttgart stadium.








Experiment to simulate surface occupation

Frei Otto experimented attraction
occupation by using soap bubbles floating on water. The bubbles come together
and form one pack. On urban scale he simulated both attraction and repellent
simulation by using magnetized pins floating on water.



Experimenting on optimized path and branch systems

The shortest way to connect two points is
with a straight line but for different points a direct path will be longer. So,
Frei Otto carried out experiments to investigate minimal pathways connect
different points. One of the experiments was to study the minimal path of
traffic routes. He was dipping threads in water and with the surface tension
the threads were bundling. After bundling the threads, the results showed that
the area and overall length needed to construct the traffic routes is
significantly smaller than the direct path.














Frei Otto went further to experiment on optimizing
frame construction. He was looking to for a way to use less material and have
long free span. He tried different kinds of branching system that produce
minimal paths by hanging threads loosely between two points then he will moist
the threads with water to bundle them. Like the braced fan construction reduced
buckling because the compression members were reduced.









Other architects started using this king
of construction as we can see in Barajas airport when Richard rogers used the y
shaped columns to have minimal visual impact effect through the façade. Also,
Stuttgart airport Gerkan and partners used branched structure.












Digital Form finding

At the beginning of the 21st century
there was rapid advancement of computers in the field of architecture and
engineering. With the help from Computer Aided Design (CAD) designers can transform
an abstract geometry into a building and allows to visualize geometries and
study the behavior of the most complex form.  In different fields, from product design,
automotive to architectural design CAD has changed the design process and how
work flows.

3D modelling has significantly affected
various industries but mostly importantly it affected film industry and
automotive industry. Because of the opposite objective of the two industries,
two different methods of 3D modelling were developed. Polygon modelling it’s
easy to operate often used with animation and film industry and nurbs modelling
which allows for accuracy and precision used in automotive industry.

One of the first engineers to use digital
form finding was Arup engineers. They employed this technic when working for
Sydney opera house in the late 1950s. Sydney opera house is a complex project
and was achieved by utilizing computers by modelling the complex roof geometry
and analyze the structure.

It was until the 90s when computers were
started to be used in the architectural industry. In the first place CAD was used
for 2D drawing as a replacement for hand drawing. It was the way forward in
architecture because drawings were produced faster but it did not change design
process. Some designers rejected computer modelling arguing that it kills
creativity. But other accepted computer modelling and became as design tool and
it was until this time that changes happened in the field of architecture.

It was a slow process in architectural
industry to adopt CAD software, but now digital modelling is widely used by
architects. 3D form finding can be seen in projects of architects like Frank
Gehry, grimshaw architects, Zaha Hadid just to mention a few. A lot of
experiments in digital form finding have been at Architectural Association
Design Research Lab (AADRL).



Zaha Hadid

Is one of the prominent architects that
contributed a lot on digital form finding. Her works are known to be fluid and
free form. When talking about her work.

“My architecture takes the fluid dynamism of the sketching hand as
a literal option for an architecture that is driven by new developments in
digital design and enhanced manufacturing capabilities” -Zaha Hadid

Kartal pendik master plan is a winning
competition project that Zaha Hadid architects used minimal pathways and
bundling system a design tool. It is a redevelopment of an industrial area at
the east of Istanbul turkey. The site lies where important nodes of different
infrastructure come together like highways connecting Europe side and Asia, railways
connecting to the city, ferry stations and bus stations. Having this nodes on
site Zaha Hadid tried to link the infrastructure to the urban context. She
joined all major roads with the intersecting points with a straight line
creating a network. She then started to bundle them together to find the
minimal path required to connect the major points.












She then placed a regular grid on top of
the site which it can adopt to the surrounding. The grid was stretched through
the site to form programmatic areas. Using lattice in maya software, other areas
were pulled up to form towers others formed the street and certain places
completely fade away to form open spaces and green areas. The grid also extends
to the sea and creates marinas and shops which has a very strong relation to
the rest of the master plan.









Zaha Hadid also applied different
constraints like attraction and repulsion to simulate the movement of people
and generate different spaces while the constraints act as the attractors. By
studying the simulation, it created open spaces on the master plan, created building
close together and created a network which connected the whole master plan.
With digital experimentation Zaha created a smooth transition from one part of
the masterplan to another. From high rise end to completely flat area.














Architectural Association Design Research Lab (AADRL)

Architectural schools are conducting a lot
of research on form finding to come up with minimal material used and
structurally. How we build our project has changed due to advancement in 3D
modelling and fabrication. There is debate that is architectural research and
the digital society are at per? Or is architectural
research far ahead compared to the built environment?

Well experiments done in universities
really pushes boundaries on how we are used to build or come up with forms in
architecture. The advantage of digital over analog experiments is that it
allows to experiment on a very large model, can come up with infinite
alterations within a short time and it is easy to analyze structural













Architectural Association school of
architecture have invested a lot of effort and time in digital research. They
have graduate design program that focuses on advanced architecture.
Architectural Association Design Research Lab was founded in 1997 by Patrick
Schumacher. Today it is regarded as one of the best in digital architecture and
architectural research. Will discuss a few researches based projects done at
the AADRL in digital form finding.



Experiment 1

This project was conducted by three
students at the AA and they were investigating solutions to temporary housing.
Their goal was to come up with a lightweight structure and sustainable. They
controlled the design by using computers and started experimenting. Started
with a basic shape and by adding constraints they were bundling the line to
achieve minimal surface and enhance on the performance. The group generated
different iterations to find the best form.











Fabrication was key to in this research as
the machine controlled digitally rotates around to give the minimal material
required. Due to different programmes of the project the material circulated









Experiment 2

This research was based on investigating fibrous
material on how it can produce construction method that has both aesthetic and
performance. The project was in a fish market in Japan where the students were
to improve the circulation. They studied by making simulation of movement by
adding constraints and analyzing the structural capabilities of tensile fibers.










A controlled woven system
was achieved by densifying the tensile fibers and connecting them digitally
with some boundaries. By adding constraints on the woven system like gradient
and applying external forces the tensile fibers settled and formed a spatial vocabulary.













·       Shape
Finding or Form Finding? By Nicholas S. GOLDSMITH, FAIA LEED AP

·       Self-Organizational
Architecture: Design Through Form-Finding Methods thesis by Allison Jean Isaacs

·       Thompson,
D’Arcy. 1961. On Growth and Form. Cambridge university Press: Cambridge.

·       Otto,
Frei and Bodo Rasch. 1995. Finding Form: Towards an Architecture of the
Minimal. Deutscher Werkbund Bayern.

·       Flores,
Carlos (2002). Les lliçons de Gaudí (in Catalan). Translated by Glòria Bohigas.

·       Gaudi:
His Life, His Theories, His Work by César Martinell translated by Judith Rohrer

·       Computational
form-finding of fabric formworks: an overview and discussion

·       Generative
Design: Form-Finding Techniques in Architecture by Asterios Agkathidis

·       Suzumori,
S., 2006. ‘Formwork as Design Tool’, Master thesis, Massachusetts Institute of



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