Voronoi Pattern got certain attributes to bring sustainability, I think...!

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Architect Vijesh Kumar V graduated B.Arch with Gold Medal & Outstanding Student
Award from National Institute of Technology, Tiruchirappalli, in 2010. Completed
M.Tech Infrastructure Design & Management from Indian Institute of Technology,
Kharagpur, in 2012. Currently working as Assistant Professor in SAN Academy of
Architecture, ACC Pirivu, Navakkarai (P.O.), Mavuthampathy Village, Walayar,
Coimabatore, Tamilnadu – 641105.
A STUDY OF VORONOI TESSELLATION IN THE CONTEXT OF
SUSTAINABILITY IN ARCHITECTURE AND PLANNING
Vijesh Kumar V
Assistant Professor, SAN Academy of Architecture, Walayar, Tamilnadu
(E-mail: architectvijeshkumarv@gmail.com, mob: 09487005023)
Mailing Address: SAN Academy of Architecture, ACC Pirivu,
Navakkarai (P.O.), Mavuthampathy Village, Walayar, Coimabatore,
Tamilnadu - 641105
Abstract
Everything in this visible world are woven by the invisible threads of forces of
geometry. This very belief raises the curiousity in Arhitects and Planners as a parametric
enquiry of form finding, governed by nature’s laws that connects both visible and invisible.
The discovery of sacred geometry and golden section gave way for a different thought
approach towards architecture and planning. These methods gave an extra precision on
mimicking the geometries of nature to attain sustainability and eco-effective solutions; called
bionic architecture, in the latest trend is called parametric architecture – everything as
parameters which will affect on the evolution of form, not as one but deriving many
possibilities. One of the observable geometric pattern in nature is Voronoi Pattern. It
explains certain geometries observed in the nature; in visible things which includes leaves,
wings of dragonfly, carapace of a turtle, honey comb, skin, it goes on; and in invisible things
which includes personal space, service area, economic areas of similarity, it goes on. These
observations increases the curiousity to use it as a tool to attain sustainability in architecture
and planning. This paper will make an attempt to study and discuss about possibilities of
Voronoi Patterns as an natural geometry to attain sustainability in architecture and
planning.
Keywords: Algorithm; Architecture and Planning; Optmization; Parametric
architecture; Voronoi Pattern

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1. INTRODUCTION
Architects and Planners works
together to meet the needs of the people.
Architecture and Planning is said to be
sustainable when it performs its functions
over the dynamics of environment and of
users and their activities, providing
psycho-physical-physiological comfort.
The character of sustainability increases as
the effectiveness increases in the use and
movement of materials and energy.
Architects and Planners always seek ways
to optimize the activity nodes and
circulation paths between those; which
will lead to reduction in time and energy
management. In the age of bionic
architecture and planning scholars seeks
the ways to optimize energy use through
representing the concepts from biological
order called as bionic architecture. These
observable solution forms recreated by
mimicking various guiding parameters to
evolve multiple solution forms in
evolution called parametric architecture.
1.1. Understanding Sustainability
Sustainability is an impact
network. Today people are alert with
resource depletion and energy usage, in the

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way they are conscious of their survival,
individually and socially. So, when the
society becomes sustainable the individual
will, and vice versa. (See Fig: 1)
1.2. Role of Technology in Sustainability
Technology has a greater impact on
Sustainability with respect to its use in
controlling performance of environment
through optimizing various factors with
respect to the dynamics of contextual
environment, through artificial intelligence
providing optimal conditions for human
well being in its widest sense while using
minimum non–renewable resources.
Parametric form finding will be the future.
2. VORONOI PATTERN
It is an algorithm, which is used to
divide a multi-dimensional space into sub-
spaces with respect to the central nodes by
defining bisect vectors as center of sub-
spaces. It is used for representing natural
phenomena through multidimensional
geometrical modelling. This algorithm has
been used for structural and spatial
derivations.
Dated use of Voronoi diagram is on
1644 to Rene Descartes. In 1850 Lejeune
Dirichlet used in his studies of quadratic
forms used 2D and 3D charts of Voronoi.
British doctor John Snow in 1854 used it
for representing the distribution of
deceased people. Georgy Voronyi, in
1908 he conducted research on the n-
dimensional shapes and he defined them. It
is also known as Voronoi tessellation,
Voronoi decomposition or Dirichlet
tessellation.
It has the geometric potential to derive
a variety of complex geometries. It is an
organizational phenomenon that
sometimes named as ‘nature’s rule’. It
happens in a variety of scales with
different materials and forms. It is
suggested as an attractive and non-
repetitive design tool. This pattern can be
created with several algorithms as;
Incremental Algorithm, Divide and
Conquer Algorithm, Chain Algorithm,
Fortune’s Algorithm, sweep Algorithm
and 3D Projection Algorithm.
It is used for searching for the nearest
neighborhood, determining the position
function (nodes), finding the largest empty
circle (cells) and path planning (edges).
Infinite solutions are possible in a given
space by this method (See Fig: 4; Pattern:
5 – 20 & Fig: 5; Pattern: 4 - 9). This
algorithm used as an application in
biology, geophysics, anthropology,
computer graphics, architectural design
and urban planning.

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3. Applications in Architecture
The task of architecture is to create
intelligent spaces as per architectural
requirements with the complex of society
and nature. Voronoi patterns can be
modelled by the use of parameters to
build spatial relationships. It is a rarely
limited geometry, includes unexpected
results too. Architects such as Toyo Ito,
Fuller or Frei Otto were inspired by
formation principles, geometries, spatial
effect and constructions in nature
(Friedrich, 2008).
3.1. Kaohsiung National Centre for
the Performing Arts in Taiwan by Zaha
Hadid & Patrik Schumacher
Spatial organization and public
progression through site are derived from
Voronoi pattern, as a strategy to analyze
the relationship between the environment
and site data (trees, monuments and
borders). A strong sense of organic
coherence is generated using this method.
The local treasured trees, historic buildings
and site boundaries are closely packed
with resulting voronoi pattern. The
resultant design was able to respect the
crrent situation of the site and to cultivate
a strong affiliation between all the spaces.
3.2.Tulum Museum in Mexico by
Andrew Kudless
As an extremely important
archeological site, the primary concern at
Tulum is the minimization of human
impact on the landscape and historical
artifacts. This is achieved through the
relocation of the museum site to align with
the existing flow of movement. This
location avoids clearing large areas of
forest as well as places the museum
between the existing entrance and exit to
the ruins. The solution was to choreograph
a spatial rhythm, to utilize the empty
spaces between the spatial nodes using
voronoi pattern.
The structure relates directly to the
stone aggregate walls of the Tulum site by
use of 3D voronoi tile system: the structure
could be considered as the materialization
of the voids between the individual stones.

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Thus, the museum structure refers to the
existing tectonic yet renders it lightweight
and airy. It is the invisible made visible.
3.3.NetLab by G_nome, London, 2006
This is 16 months research on
Parametric Architecture using algorithms
to generate a variety of solutions on forms
in real contexts, redefining the architect’s
role by integrating design, analysis and
production-manufacturing as a whole
formal process. Using algorithms to
express different social systems, scale and
needs of the users using Voronoi Pattern.
This research gives access to an iterative
process of feedback, adjustment and
optimization of the design. It connects
different working-patterns as a non-linear
network based on the Voronoi algorithm.
This research would not be a
replacement to the designer nor an
automation of the design process, but
rather it represents an open framework
where the designer can develop a more
integral relationship between the various
conflicting and overlapping issues of an
architectural project.
3.4. National Aquatics Center (Water
Cube) at Beijing
It was built alongside Beijing National
Stadium in the Olympic Green for the
swimming competitions of the 2008 Summer
Olympics. Despite its nickname ‘Water Cube’,
the building is not an actual cube, but a cuboid
(a rectangular box) of 178 metres (584 ft)
square and 31 metres (102 ft) high.
The Water Cube was specially
designed and built by a consortium made up of
PTW Architects (an Australian architecture
firm), Arup international engineering group,
CSCEC (China State Construction
Engineering Corporation), and CCDI (China
Construction Design International) of
Shanghai. The concept came up with team
effort; the Chinese partners felt a square was
more symbolic to Chinese culture and its
relationship to the Bird's Nest stadium, while
the Sydney-based partners came up with the
idea of covering the 'cube' with bubbles,
symbolising water. Contextually the cube
symbolises earth whilst the circle (represented
by the stadium) represents heaven.
The outer wall is based on the
Weaire–Phelan structure, a structure devised
from the natural pattern of bubbles in soap
lather. The complex Weaire–Phelan pattern
was developed by slicing through bubbles in
soap foam, resulting in more irregular, organic
patterns than foam bubble structures proposed
earlier by the scientist Kelvin. It is a 3D
voroical pattern.

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3.5. Activity programming with
personal space
Territorial Behaviour of Animals
and Vegetations are observed as Voronoi
Pattern. If all the subjects settle at the same
time, then the distribution of Voronoi
centers can be that for a centroidal
Voronoi tessellation.
In an experiment illustrated by G.
W. Barlow in his book ‘Hexagonal
Territories, Animal Behavior’, the
territories created by male Tilapia
mossambica fishes inside a polarizing
filter through digging a sand pit formed a
pattern of polygons were similar to
voronoi pattern.
This spatial dominance competition
not only visible in animals and plants,but
also in humans. Scott Sona Snibbe created
computer generative voronoi patterns on
the floor with the movement of people,
with his well-known full-body interactive
work ‘Boundary Functions (1998)’,
premiering at Ars Electronica 1998. The
pattern created are very dynamic.
4. In Planning
The task of planning is to locate the
services and infrastructure requirements of
a region. For example, to check the
convenience of mailbox placement

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throughout a population, taking
assumptions:
 A person will use the mailbox nearest
to their home.
 The cost to a person of using a mailbox
is a function of the distance from the
person to the mailbox.
 The cost to the general population is
measured by the distance to the nearest
mailbox averaged over the population.
 The optimal placement of mailboxes is
one that minimizes cost, or the distance
to the population in general.
The central nodes obtained will tell the
location of mail boxes in the region.
The very idea can be used in many
different aspects of urban and regional
planning on the placement of resource,
utility and service infrastructures.
5. Conclusion
Architecture and Planning are
increasingly becoming a simulation to
implement complex relationship between
environment. There are many reasons and
benefits for its use as: deriving structural
properties; organization of space based on
the neighborhood and closeness proximity;
Many natural forms can be described with
the help of these diagrams like soap
bubbles, foam, bone cells, goes on;
Creating a systematic design process for
urban design using parametric system;
Balancing of forces and tensions in the
structural design; Variety of design options
in the design of a balanced hierarchical
system. With further development, it may
be used as a mean to explain tangible
natural phenomena and non-tangible social
phenomena.
6. Acknowledgements
I extend my gratitude to my student who
helped me with the works namely: Pugal
Varma.
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