DOI: https://dx.doi.org/10.51148/jaas.2018.4

IRANIAN

GARDEN’S

ARCHITECTURAL

DESIGNING:

COLLOCATION OF VORONOI AND FRACTAL ALGORITHMS

IN THE CONTEXT OF NATURAL BACKGROUND



Somayyeh Omranifar¹, Shabnam Namdar², Nader ghaemi³, Yaser Narimanpour Maleki⁴

¹PhD student of Architecture, Architecture Department, Islamic Azad University, Tabriz Branch, Tabriz, Iran

²Assistant professor, Architecture Department, Islamic Azad University, Tabriz Branch, Tabriz, Iran

³Architecture Department, Islamic Azad University, Tabriz Branch, Tabriz, Iran

⁴Department of Architecture, Islamic Azad University, Mashad Branch, Mashad, Iran

ABSTRACT

In the present article, the collocation of the Fractal Geometries and Voronoi Algorithm

has been proved in line with the designing of garden’s digital architecture and it was

Research Article

made clear that the designing of the ancient four-segment gardens is considerably

PII: S238315531800004-7

matching with the contemporary architecture which has come about subject to the

effect of computers and software. The present study is a qualitative research of

descriptive-analytical type and it has been conducted with a glance at the history of

Iranian gardens’ designs and their delineated geometrical analyses concerning the

structural philosophy of Voronoi and Fractal algorithms. The primary goal of the

researcher is showcasing the timelessness in the designing of the Iranian garden so as

to prove that the prior designing has been in accordance with the novel patterns of the

contemporary architecture and it can get the paradise manifested like before in a

corner of the earthy ground in today's machining world. It can be stated as a part of the

obtained results that the idea of exhibiting water in the garden and the system of water

transmission to the most distant spots in the garden tries depicting the ancient

imaginations of the previous architects about Voronoi algorithm considering the use of

the shortest path which is a perpendicular line drawn towards a dot on a straight line.

Moreover, the use of four-segment garden’s basic module and its division in an

internally descending manner displays Fractal geometry in each of Voronoi levels of

the garden’s plots.

Received: 10 Sep. 2018

Revised: 05 Dec. 2018

Published: 15 Dec. 2018

 Corresponding author’s e-mail:

Somayeh.omranifar@gmail.com

KEYWORDS

Iranian garden, Geometry, Voronoi algorithm, Fractal, Water

INTRODUCTION

Iranians. The architectural context and garden-

building methods lost their performance and beauty

The thing that is currently seen in the Iranian cities

as buildings and urban spaces and elements has not

been able to crystalize the fruitful background of

Iranian architecture and garden-building and it is,

instead, depicting a sort of distinct identity lack and

self-alienation. Lack of paying attention to the social

and cultural values and hasty movement towards

modernity without the real perception of what is

being constructed and processed have led to visual,

cultural, social and identity unrest in the level of

Iranian cities and architecture [1].

Iranian garden has always endeavored since

long ago to stay in accord with a philosophical and

contextual-functional concept and it has been

embodied as one of the specifications of Iranian

architecture. Considerable differences were brought

about in the context of Iranian architecture and

garden-building with the beginning of the foreign

advisors’ trip to Iran from Safavid Era and the

blending of the Iranian architecture and decorations

with what has been offered as art and technique to

of their geometrical ground and their connection

rings were broken in such way that the

performance occasionally led to the discarding of

beauty and the paying of attention to the visual

beauties resulted sometimes in the creation of

insensible cases in the gardens’ grounds. Therefore,

the researchers have been coerced to subtly

contemplate about the functional and visual

designing of the Iranian gardens so as to identify the

meanings latent in them beyond the plan of Iranian

four-segment garden thereby to figure out the

missing rings of the function and beauty; it is by the

perception of the concepts existent behind the

functional and visual designing of the gardens that

solutions can be found for logical attachment to the

contemporary mankind’s psychological needs. In the

present study, the author proves the basics existent

in fractal geometry and digital Voronoi algorithms

within the former geometrical context of the Iranian

garden and shows that the nature’s flexible spirit has

been portrayed in the meaning-oriented designs by

Citation: Omranifar S, Namdar Sh, Ghaemi N,

2018 SCIENCELINE

Narimanpour Maleki

(2018). Iranian Garden’s

Journal of Art and Architecture Studies

Architectural Designing: Collocation of Voronoi and

Fractal Algorithms in the Context of Natural Background.

J. Art Arch. Stud., 7 (2): 28-33.

ISSN 2383-1553

JAAS

J. Art Arch. Stud. 7(2): 28-33, Dec. 15, 2018

DOI: https://dx.doi.org/10.51148/jaas.2018.4

J Art Arch Stud. 7(2): 28-33, 2018

the imaginative ancient architect in such a way that building of the garden falls in the intersection point

it has been able to absorb the psychological states [3 ].

and satisfy the needs of the today’s mankind in the

area of the contemporary naturalism.

System of Geometrical Structure:

The researcher seminally deals with the

The geometrical structure of the Iranian garden

theoretical foundations and the concepts usually is shaped in two substantial forms with one of the

encountered regarding the Iranian gardens; then, indices of its geometrical structure being the

the references of the Iranian gardens’ patters are relationship between the interior and exterior spaces

extracted. Next and after deeply studying the [4 ]: one is the creation of three stretches (in three

structural philosophy and theoretical foundations of axes) in parallel and along with the garden and the

Voronoi and fractal algorithms, the feasibility of other is the consideration of two primary

adjusting the current theoretical foundations and perpendicular axes and then dividing of the garden

their structural philosophy to the geometrical plan of into squares that per se have their own regular

the Iranian garden has been analyzed. All the geometrical divisions (Figure 1). In Iranian garden,

analyses have been discussed geometrically and, special attention was paid to the geometrical shapes

considering the functionalist and human-oriented and square that showcased a simple and clear-cut

grounds of the contemporary architecture and distance between the garden’s components enjoyed a

garden-building, the existing functional factor has particular importance [5].

been displayed as a connecting ring.

The main question of the present study is that

what is the primary functional factor that can, as a

connecting ring of the garden’s humanism and

naturalism concepts, make the geometrical design of

the garden approach the timeless concept?

How are such digital and naturalist geometries

like Voronoi and fractal algorithms matched on the

grounds of the Iranian garden? The author tries

answering the above-posited questions in five

chapters, namely the Iranian garden and formation

Figure 1. Geometrical structure of the garden [3].

process, Voronoi and fractal algorithms, Iranian

garden and collocation of water-transmission

function with Voronoi algorithm and Iranian garden

and fractal geometry in the geometry of the plots.

Voronoi Algorithm:

Voronoi algorithm is a geometrical algorithm.

This algorithm receives a series of points as its input.

These points can be selected randomly and/or be

certain points on a plane [6 ]. In this type of

algorithm, the input points lead to the production of

a series of regions on the plane and, problem-

specifically, give the closest answers with the highest

likelihood for the calculation of the region of a point

by considering all the line segments between the

given point and the other points. Then, the bisectors

of these line segments are drawn and the regional

bisectors are created around the given point [7]. In

this case, the algorithm juxtaposes the given regions

without overlapping. It has been recently proved

that many of the structures follow this algorithm in

nature (Figure 2), especially the micro-structures of

the nature wherein the Voronoi schemes are

abundantly found [6].

Iranian Garden and Formation Process:

The concept of “garden architecture” reflects a

“sense of place”; garden is defined as a space that

has the perfect and utmost reflection of the world in

it. This concept that fosters order and coordination

might be expressed more tangibly by means of

numbers, geometry, color and matter [2]. Based on

the studies that have been carried out on the

reference patterns of the Iranian garden, the

primitive sample of the archetypes has been applied

as the common contact surface between the patterns

of Iranian gardens and it has also been crystalized in

the Iranian carpets; it depicts a square-shaped area

of a relatively vast land which is surrounded inside

walls. The surface area of this land has been divided

by two axes (two water streams) perpendicular to

and intersecting one another with the main stream

eventually pouring into four ditches and with trees

finally surrounding the square. The most major

Omranifar et al., 2018

Figure 4 illustrates the unique and well-known

example of Voronoi algorithm has been displayed in

the cubic water building (the name that has been

given to the stadium of water sports in Pecan,

China). Besides having a lot of advantages in terms

of the architectural form and creation of modern and

innovative structures, this building is completely

environment-friendly and it is enumerated, in other

words, as a green and environment-compliant

structure. The primary idea of this complex’s

designing has been the formation of a cube that has

been brought to existence from the joining of water-

filled bubbles and it is completely transparent [8].

Figure 2. Voronoi algorithm in nature [8].

Fractal

There are also more complex forms of Voronoi

algorithms the regions of which are made by soft

curves in lieu of the broken lines. Furthermore, there

are also 3D images of this algorithm that receive the

initial points in a given space and gives the area

zoning by dividing of the spaces (Figure 3). In

architecture, various Voronoi algorithms have been

widely applied [8].

Fractal is a geometrical shape that is created

with the repetition of a simple logic in a recursive

manner. In a normal manner, the shape obtained

from the fractals can be divided into several parts

each of which resembling the overall shape. The

other interpretation existent about the fractals is

that they have indefinite components and/or they

possess similar structures making them look

identical in the various magnifications. The term

“fractal” was first used by Mandelbert in 1975. It is

derived from the Latin root “fractus” meaning

broken [9].

In the process of a fractal’s production, there are

at least two primary shapes: one basic and one

generative. In every stage of the repetition, the

generative shape is placed in the position of every

one of the basic shape’s fundamental segment or line

segment. From the theoretical perspectives, this

repetition can be continued endlessly. The algorithm

used for producing the fractal shapes is a basic

process the job of which is placing one shape

between two points. This process includes the size

change, rotation and displacement of the generative

shape for taking a position between the two

presumed points or two ends of a line segment.

Amongst the simplest types of the fractals are the

Sierpinski triangle (Figure 5) and fractal cube [6].

In the traditional Iranian architecture, as well,

the fractal pattern can be seen in Karbandi

Figure 3. The structure of Voronoi algorithm [8].

[geometrical

and

mathematical

planning],

Yazdibandi [roof covering] and ornamental corbel

vaults. In these patterns, the basic module is iterated

with a special order to create an integrated whole.

The fractal pattern has also been inserted in the

architectural form. This pattern is occasionally

symbolic and it is sometimes inserted in the wefts

and warps of the architectural function (Figure 6).

Figure 4. The structure of Voronoi algorithm

(http://arktourism.ir )

J Art Arch Stud. 7(2): 28-33, 2018

input points, an operator point and two result

points.

Figure 7. Functional formation of the basic four-

segment garden (source: the author)

Figure

(http://spnueng.blogfa.com )

Sierpinski

fractal

triangle

In order to accomplish the objective of water

display and water transmission to all the garden’s

spots, preparatory measures should be taken so that

the water can be transmitted to all the various spots

of the garden in respect to the land’s slope. In line

with this goal, some other points have been

considered as the input points of Voronoi algorithm

and, considering the water-transmission function

and water display, the shortest paths have been

offered according to the philosophy of Voronoi

algorithm in two states of the land slope.

Figure

Symbolic

fractal

architecture

(http://honartech.ir/product )

Iranian Garden and Collocation of Water-

Transmission

Algorithm:

Function

with

Voronoi

Figure 8. Formation of Voronoi algorithm in the

garden’s geometry (Source: the author)

Iranian garden is the geometrical embodiment

of paradise in the context of a scorching desert with

an extreme inclination towards water exhibition in

every corner being one of its primary specifications

[9]. That is because is considered as the symbol of

dynamicity and life in the desert. The most original

solution for showcasing it and taking a more

appropriate advantage thereof is its management in

the middle of the garden in such a way that the water

starts flowing from the longest edge of the garden

and proves presence in the entire garden while

performing its duty of satiation. Concentration on

the soil’s natural slope has been the easiest solution

in the previous gardens.

According to figure 7, points A and C are

considered as the input points of Voronoi algorithm.

Considering the use of square geometry for the easy

recognition of the distances in the garden, point B is

the place where the pond should be placed and its

stretching gives the points E and D. this way, the

preliminary pattern of the four-segment gardens is

formed by dividing the land into four areas with two

As it is seen in figure 8, the first case pertains to

gardens that have been positioned in respect to the

land’s natural slope in an ascending or descending

form. In this type of gardens, water starts flowing

from its source and is brought from a garden to

another [5]. Water enters through the point A and

reaches the point B from which it is distributed

along the operator ED axis in the lower half of the

garden. In order to transmit water to the upper

plots, the upper axis includes water inlet as the

secondary operator axis and water is subsequently

distributed in the upper plots.

The second case shows the method of water

transmission in the gardens that are usually irrigated

by wells’ water. In this type of gardens, the

intersection of the two primary axes is considered as

the water inflowing point and the land’s slope is

assumed to be towards the walls on the four sides of

the garden [5]. In this state, only one operator axis is

Omranifar et al., 2018

considered for the garden. The gardens in the the Iranian garden is adjusted to the contemporary

deserts usually make use of this method. The water digital architectural patterns drawn on Voronoi

line axis shows the water-transmission system.

Considering the Voronoi algorithm and

algorithm.

The stretch of the traditional market’s body

according to the goal of transmitting water to the within the city limits of Tabriz and the prominent

most distant spots in the garden, certain points are historical buildings like Dar Al-Fonun School, Darb

considered on the peripheral walls and vertical lines Baghmishe, Haramkhaneh Complex, municipality

are presumed from the water’s primary stream building and so forth as well as the valuable business

according

the

mathematical

principle edifices like the large market of artefacts and the

recommending the selection of the shortest large bazar of Tabriz’s leather have caused this

perpendicular route from the point onto the water region to be transformed into one of the tourism

stream following which the Iranian garden’s water- spots of the city. The adjacency of the unique

transmission network/system is formed within the tourism potentials to Tabriz County’s trade pole,

format of four-segment garden. It is by locating organized within the limits of Jomhouri Street, has

certain points on the wall that squares and caused the vehicles’ access to the aforesaid centers to

rectangles are geometrically formed in respect to the encounter considerable limitations and factors like

amount of water required to be transmitted to the excessive congestion of the region, lack of cargo-

plots.

transportation infrastructures and blending of the

Considering the Voronoi algorithm, the thing industrial and tourism uses and heavy traffic on

that is effective in the shape obtained from the Shahid Madani Street and adjacent streets have

algorithm is the number of the points to which water caused the creation of problems in terms of urban

should be transmitted in respect to water power and tourism in the foresaid region.

land’s shape. If a garden is square in shape with

large dimensions and the soil slope is not so much

Iranian Garden and Fractal in the Plots’

steep and/or if water is withdrawn from wells for Geometry:

satiating the garden, smaller Voronoi areas will be

The most original factor in the formation of

attained. However, if the surface area is considered fractal geometry is the basic module and the

similar to the previous example with a rectangular scattering path and method of this module in the

geometry, the resulting shape will be different and general format. Considering the functional system of

follows the land’s slope following which the number the square-shaped geometry of the garden, the upper

of the plots will be reduced.

section is defined as the basic module in the garden

and the entirety of the garden’s surface area is

covered through the arrangement of this module

based on Voronoi algorithm and the primary

geometry of the plots is formed in a descending

(downsizing) trend in the module-dividing state.

Figure 10 illustrates the plots’ fractal process in

Iranian gardens.

Figure 9. Voronoi algorithm based on the basic

four-segment pattern (Source: the author)

Figure 9 exhibit the Voronoi algorithm in Figure 10. Formation of the fractal pattern (source:

collocation with the water-transmission function in the author)

the garden and proves that the original pattern of

J Art Arch Stud. 7(2): 28-33, 2018

According to the pictorial information and their implemented in the adjacency of the water inlet with

analysis, it was made clear that the four-segment an internal-descending multiplication in the whole

garden’s geometry that has been applied as the four-segment garden on the ground surface.

primary geometry in the architectural designing of

the Iranian gardens follows and is matched with the

patterns produced in Voronoi and fractal algorithms.

Competing interests

The authors declare that there is no competing

In addition, the water-transmission function and the interest.

idea of water display is the ring connecting the

garden’s geometry to Voronoi and fractal algorithms.

The former architect and garden-builder followed

the nature to create a beautiful paradise in the heart

of a scorching desert and getting the imaginary

nature manifested in the grounds of the available

land. It is worth mentioning that the naturalism

ground in Voronoi and fractal algorithms as well as

the geometrical designing of the gardens have

created the aforesaid harmony and match.

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CONCLUSION

In the present study and through more subtle study

of the geometrical and functional systems of the

gardens, the geometrical adjustability of the garden’s

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