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This chapter aims to analyze the fractal geometry of the façade plane of 3 (three) historical public buildings in Afyonkarahisar city center by box counting method. Within the scope of the study, 3 (three) historical public buildings belonging to the First National Architecture period were selected. The examples in this study were selected from the entrance façades of historical public buildings in the city of Afyonkarahisar. According to the historical public building façades defined, the dimensions of the façades remained in their original state, the façade reliefs of 3 (three) sample buildings were taken and their two-dimensional front views were drawn in vector, and the fractal fiction between each other was analyzed using the “box counting method”. Fractal analysis was performed by box counting method in the context of occupancy-vacancy ratios formed by building elements such as windows, doors, jambs, floor erasures, buttresses, eaves that make up the façade structure. As a result of the study, how the façade features of the First National Architecture period corresponded to the façade constructions of the selected public buildings were interpreted based on numerical data obtained from fractal analysis.
Department of Interior Architecture and Environmental Design, Afyon Kocatepe University, Afyonkarahisar, Turkey
Şerife Ebru Okuyucu*
Department of Interior Architecture and Environmental Design, Afyon Kocatepe University, Afyonkarahisar, Turkey
*Address all correspondence to: ebruokuyucu@hotmail.com
1. Introduction
The First National Architecture movement covers a period between 1908 and 1930 that emerged as an anti-Westernization movement in Turkey. On the basis of the First National Architecture movement, there is the idea of giving Turkish identity to buildings by adapting Turkish Seljuk and Turkish Ottoman architectural forms to the new functions of contemporary architecture. In this context, an eclectic architectural approach called “national style” was seen in the buildings built during this period. In this period, especially the façade designs of public buildings were given great importance in the context of image and Ottoman architectural elements (dome, arch, portico, crown door, etc.) manifested themselves in the form of the use of ornamental motifs and applied in new layouts on the façades. In this context, in this study, the mathematical expressions of the façade designs of public buildings produced in the First National Architecture period were calculated by fractal analysis method.
There are very few quantitative methods that can measure the thousands of architectural lines (such as windows, doors, pilasters, buttresses, jambs, floor moldings, eaves lines) on the façade of a historical building of a certain period. One of the methods used for this purpose is fractal analysis. The method of fractal analysis is used to calculate two-dimensional linear constructions. Fractal geometry is a geometric form formed by the combination of complex, repetitive and continuous fictions [1].
Within the scope of the study, three public buildings with different functions were selected from the First National Architecture period in Afyonkarahisar: “Zafer Museum”, “Rıza Çerçel Cultural Center” and “Police Station Building”. The construction dates of these three public buildings are close to each other and it is seen that the façade designs are compatible with the features of the First National Architectural Period. The architectural style and eclectic approach in the façade designs of public buildings of this period are expressed in complex lines on the façade. In order to analyze the façade structure of these structures, a mathematical expression was used and façade readings were made by evaluating the occupancy-gap ratios with numerical data based on fractal geometry. While the façade readings of the public buildings were made, the occupancy- vacancy ratios were evaluated in the context of the frames formed by the building elements such as windows, doors, jambs, floor moldings, eaves and buttresses on the façade. In order to perform fractal analysis on the façades of public buildings, first of all, façade survey drawings of public buildings were prepared. In the study, the structures were analyzed using façade drawings. The analysis was performed using the “box counting method” within the mathematical concept of “fractal geometry”. The calculated fractal dimension value was obtained for each structure. Box counting method is a technique used to calculate and read the complexity of architectural façades and plans. This method takes into account the richness of detail and reconstruction of various textures with two-dimensional complex structures that cannot be calculated by other methods.
In this context, fractal analyses made on the façades of three different public structures belonging to the First National Architectural Period, “Zafer Museum”, “Rıza Çerçel Cultural Center” and “Police Station Building”, were converted into numerical data by box counting method. In line with the numerical data obtained, a comparison was made between the façade structures of the public buildings of the “Zafer Museum”, “Rıza Çerçel Cultural Center” and “Police Station Building” and the façade features of the First National Architectural Period. After all, it was seen that the numerical expressions corresponding to the mobility and complexity in the façade constructions of these structures coincided with the data obtained from the fractal analysis using the box counting method.
2. Features of the first national architectural period
After the declaration of the Second Constitutional Monarchy in 1908, architecture emerged as one of the key domains that significantly shaped the conditions and structure of the period, alongside the political, social, economic and cultural initiatives of the Union and Progress Party. In this period, it is seen that many thinkers, such as Ziya Gökalp pioneered the way of awakening national consciousness, reviving it and adopting concepts such as returning to the essence. In particular, the ideas developed by Gökalp in the fields of economy, politics, philosophy, law, religion and language became widespread over time and this situation allowed to create an environment suitable for developments in the field of architecture [2].
The First National Architecture period, which emerged as a result of the Turkism Movement influencing architecture as well as in every field and which existed between 1908 and 1930, was a process in which there was a reaction against Westernization in architecture and foreign architects [3]. Architects such as Kemalettin Bey, Vedat Tek, Muzaffer Bey, Arif Hikmet Koyunoğlu, Alexander Valaury, Guilio Mongeri, who pioneered this movement, examined the elements of past architecture and created the works of the First National Architectural Period, which was the Neoclassical style of the period [2, 4, 5, 6]. A national architectural movement was tried to be established by placing building elements representing the classical period Ottoman and Seljuk architecture on the Neorenaissance building masses of Western origin [2]. For this reason, it is possible to see the influences of the Bat culture at the root of the National Architecture that began to develop in the twentieth century and became stronger after 1908. In the buildings of the First National Architectural Period, the influences of foreign architects and Western artists can be seen very clearly. It is possible to list the general characteristics of the works of this period as follows:
There is a symmetrical and axial understanding of mass arrangement and plan schemes that are based on the examples.
The façades are symmetrical and majestic. The use of Ottoman and Seljuk motifs in the buildings built in this period, especially on the exteriors, supported the formation of national consciousness [4].
The schemes used are parallel to European Neoclassicism [7] in terms of the dimensions and proportions of the spaces, the façade arrangements and the composition rules. Apart from religiously functional structures, all types of buildings, especially their facades, are divided into three sections with continuous stone belts, in accordance with the rules of Neorenaissance architecture. Each section is organized in its own right as a whole. On each floor, different window forms are applied. The structures are given a certain rhythmic appearance in vertical order.
The national body has tried to be used in non-structural elements and decoration with elements selected from the classical Ottoman religious architecture in the fifteenth and sixteenth centuries. However, in the surface arrangement methods, the understanding of form of Western architecture is also dominant [8]. In this arrangement, which formed the basis of nineteenth-century European architecture, is stated that instead of the Classical Greek and Roman styles in Europe, building elements such as flattened or pointed arches, column capitals with beads or mukarnas, moldings decorated with geometric reliefs, tile panels, wide eaves with ornamented lower surfaces and false domes were used [5].
Another decisive feature of buildings built in the First National Architectural style is the tower, which began with Art Nouveau long before the use of the tower in Turkey. Art Nouveau [9] is a style that is not included in the classical tradition of Europe and is fed by many sources, so it came to Turkey in forms originating from North Africa, East and Far Abroad. The First National Architects, who had to adapt the knowledge and values they acquired from Europe or through their education to the conditions of Turkey, also manifested the emergence of Turkish Neoclassicism by incorporating these styles [10].
The Seljuk and Ottoman architectural elements used by Turkish architects during the First National Architectural Period were not always in harmony with the functions of the buildings they designed. With these works, the architects tried to respond to the functional needs of the society as well as the integrative symbolic needs that emphasize the identity of the nation. In this understanding of architecture, they combined architectural and ornamental elements taken from Seljuk and Ottoman architecture with the design principles and construction techniques of Europe. In accordance with Turkish identity, the concept of “nationality” replaces religion [11].
According to Ünsal [12], the selective style adopted during the First National Architecture period, which encompassed national feeling and thought, served as a fitting attire for the new buildings that defined the city. This style was particularly prominent in the construction of banks, post offices, educational buildings, hotels, other public structures. Ünsal [12] stated that the plan was not taken into consideration in this period, that the façades were prioritized and if the façade was good, the survey of the plan was carried out.
Despite the “Turkish” architectural features sought in the buildings of the First National Architectural Period, a nationalist approach was not exhibited in terms of materials and mostly materials brought from the West were used. However, although the materials were imported from the West, it was emphasized by the architects that the ways of using these materials should be compatible with the architectural understanding of the period. During this period, the main idea was to combine decorative elements taken from classical Ottoman architecture, especially Ottoman domes in the form of half domes, wide roof consoles with supporting elbows, pointed arches and new construction techniques such as reinforced concrete with tile decoration. A kind of Turkish eclecticism has been created by the domes used, oval arched windows, hedgehog eaves, tile panels, ornate front façades, rhythmic window layouts on the façades, compartment-like interior designs consisting of spaces placed on both sides of a corridor, hipped roof application, separation of façades with moldings, animation with plasters. Considering the financial conditions and urban scale of the period, most, if not all, of them were large buildings and were built on multiple floors. A structure similar to European Neoclassicism is observed in terms of the plans and schemes used, the measurements and proportions in masses and spaces, the composition rules and multi-storey construction techniques [13].
It is possible to see the first examples of architectural structures of the First National Architectural Movement starting from 1900 until the first years of the establishment of the Republic. During the effort to create a new nation, construction initially focused on public buildings (such as banks, hospitals, palaces, schools), then built apartment buildings and business khans [14].
To date, architecture has been analyzed by many different methods. In studies focusing on the relationship between architecture and the user, it is seen that methods such as survey, simulation techniques, interviews, physical traces, behavior observation are used. Today, these methods, which are not based on numerical data and are intuitive, have been replaced by methods that reveal more systematic and numerical data. One of these methods is the Fractal Theory.
Fractal theory is the analysis method of this study. It was first introduced in 1975 by the mathematician B. Mandelbrot for the description of forms that repeat each other at different scales. B. Mandelbrot published an article in the journal “Science” entitled “How long is the length of the British coastline”, stating that there is an inversely proportional relationship in which the length of the coastline varies depending on the length of the measurement used to measure the coastline, and that the length of the coastline lengthens as the length of the instrument decreases [1, 15]. Derived from the Latin word “fractus”, which means broken, fragmented, and the English word “fraction”, which means part, division, fractal fictions describe a universe consisting of indented protruding, broken, bent, interlocking shapes that cannot be round or straight lines [16, 17]. It is stated that even when zooming in on fractals, which are very complex and have unlimited detail, the detail of the whole shape can be seen, and similar shapes will emerge regardless of how close or distant the shape is. When defined as a fractal function, “x, f(x), f(f(x)), …”, that is, it can be repeated forever [18].
Although it was first named in 1975, it was founded in the twentieth century. At the beginning of the century, many mathematicians used forms that showed fractal properties. These forms, which are also the source of Mandelbrot’s work, have been called monsters because of their irregular, complex structure. The Cantor Set, introduced by George Cantor and forming the basis of set theory in mathematics, underpinned many fractal fictions and has been called classical fractals (Figure 1) [19].
Figure 1.
Cantor set [19].
It is stated that a structure must meet certain conditions to be called fractal and the conditions are;
having a perfect structure,
being too indented to be explained by Euclidean geometry,
self-similarity,
having a fractional size,
occurrence as a result of a simple rule of repetition [20].
Fractals, which exhibit self-similarity and are found in various forms, can be classified in multiple ways based on different criteria. According to Mandelbrot, fractals are classified into man-made artificial fractals and natural fractals [18].
Natural fractals exist in nature in their own form and can be found in a maximum of 3 or 4 cycles. Fractals in nature lose detail in their structure during any cycle. At the core of natural fractals, they have the property of their own resemblance, and these formations can be found in the structure, in the scale of the tissue. Clouds, stars, plants, mountains, boundary lines, nerves in the human body, age rings that appear when the trunk of a tree is cut down can be cited as examples of natural fractals (Figure 2) [21, 22].
Figure 2.
Examples of natural fractals [24, 25, 26, 27].
Artificial fractals are produced by humans, which can be found in an infinite number of cycles. These fractals created in the mathematical environment are also called generative algorithms, which are formed within the framework of certain geometric rules. All the dividing parts of the artificial fractals have the same detail and are exactly similar to the whole fractal. An infinite number of self-repeating geometric shapes form ideal fractal patterns, and they appear only in mathematical theories or digital graphs. The Koch curve, the Sierpinski triangle, the Minkowski curve, the Barnsley fern are cited as examples [23]. When the Koch curve example is examined, it is seen that the first cycle is completed by dividing the structure with a line, dividing the line into three equal parts and transforming the middle part into an equilateral triangle and applying the same rule to each line. This process is repeated to produce a snowflake like shape (Figure 3) [23].
Figure 3.
Koch curve [27].
In fractal geometry, the value obtained as a result of measuring the complexity of a fractal is defined as the fractal dimension, and the high fractal dimension value indicates that the complexity of the surface is high. In the context of fractal analysis, when the obtained fractal value falls closer to 1, it is generally considered an indicator of simplicity and less complexity. On the other hand, when the value approaches 2, it suggests increased complexity [21]. Different methods have been developed for calculating the fractal dimension, which was introduced in the 1970s. Self-similarity dimension, measure dimension and box counting dimension are some of these methods [21]. In self-similarity dimension calculations, it is stated that a curve similar to itself should consist of repeating parts, and that the self-similarity method is not suitable for calculation because of the small number of repetitive structures in two-dimensional complex constructions. The measure dimension method cannot be used in two-dimensional fictions where curved forms are not present. It has been suggested that for fractals where the aforementioned methods are not applicable, the box counting dimension method can be used to determine the fractal value [1, 28].
3.1 Box counting method
The box counting method is the most preferred mathematical method for calculating the fractal dimension. In this method, the calculation of the fractal size is based on the logic of calculating the number of boxes that contain data in a two-dimensional drawing. This is done by dividing the drawing into a grid system and determining the number of boxes that contain relevant information. In this method, as the details increase, the fractal dimension also increases, and the details such as window records, doors, floor moldings, façade decorations on the façades cause the fractal dimension to be high [29].
In the box counting method,
The surface for which the fractal size is to be calculated is covered with a grid system (Figure 4).
Grids within the grid system that contain data at any point are considered full and their number is determined.
To account for the observer’s distance from the structure and the changing scale, the grid sizes in the grid system created for calculating the fractal size are adjusted. As the observer approaches the surface, the dimensions of the grids are halved, resulting in a new grid system. This process is repeated constantly, forming a cycle of grid adjustments.
During each cycle, the number of boxes containing data is calculated and noted.
D=logx−logylogz−logq The fractal value is calculated with the help of the formula (x: the number of boxes with data in it calculated in the next cycle, y: the number of boxes with data in the previous cycle, z: the number of boxes with data in the direction x in the next cycle, q: the number of boxes in the x direction in the previous cycle).
The fractal value is calculated using this formula for each cycle, repeating the process until the fractal value converges [1, 21, 29]. If the difference between the result decreases as the cycles continue, the process is terminated and the final value obtained is considered the fractal dimension.
Figure 4.
Box counting method grid system [29].
The fractal value obtained by this method is always between 1 and 2, and it is stated that as you approach 1, the fiction is simple, plain and based on Euclidean geometry, and as you approach 2, the fiction is complex and irregular (Figure 5) [21, 30].
Figure 5.
Box counting method grid system grid size change [29].
Within the scope of this study, in line with the purpose of the study, the Fractal theory, which provides the analysis of architecture with numerical data, was used for the analysis of the façades of the public buildings of the First National Architectural Period in Afyonkarahisar. In this direction, the box counting method, which is the most commonly used method for calculating the fractal dimension value of the façades, was preferred.
3.2 First National Architectural Period Public Buildings in Afyonkarahisar
Within the scope of the study, three public buildings belonging to the First National Architectural Period in Afyonkarahisar were selected. Fractal analysis of the façades of the Zafer Museum (1919–1920), the Rıza Çerçel Cultural Center (1930) and the Police Station Building (early 1900s) was performed using the box counting method. The architectural features of public buildings are as follows:
3.3 Zafer museum
The building possesses the characteristic of being the first municipally-designed structure. While limited information is available regarding the architect of the building constructed in 1919–1920, it is stated that an Armenian architect was responsible for its construction [31, 32]. The building was registered as a cultural property to be protected by the High Council of Monuments on 11.07.1980 [33].
The building, located in the city square in the center of the city, was built as a two-storey masonry [34]. The main entrance is provided by the pointed arched structure facing the city square, and there are also entrances on the back and side façades of the building. On the side façade, there is a door accessed by a staircase at the corner of the first floor, and on the rear façade, there is an entrance obtained by transforming the window opening to the hall into a door. The presence of horizontal moldings on both sides of the main door, as well as between floors, is evident on all façades of the building [35]. The main and intermediate walls of the building are made of stone, the ceiling tiles and roof are made of wood. On the exterior of the building, the perimeter and corners of the entrance door located in the front are covered with andesite stone, the arched windows of the building, the windowsills and perimeter of the arched windows and the keystone on the top are covered with finely carved stone. The entrance eaves of the building are high and decorative ornamented woods are nailed to the eaves. The roof of the building is covered with Turkish style tiles (Table 1) [33].
Table 1.
Zafer museum Façade analysis.
The building hosted the Afyonkarahisar Congress in 1920, was used as the Greek headquarters until 25 August 1922, and as the command center of the Turkish army after the enemy occupation of Afyonkarahisar on 27 August 1922. The main decisions of the Dumlupınar War were made in this building. The building has a historical significance in this respect. Between 1922 and 1940 the building was used as municipality building, between 1963 and 1985 it is used as police department and 26 August 1995 it started to be used as the Zafer Museum [33].
3.4 Rıza Çerçel cultural center
The building, which was designed as the Turkish Hearth building, started in 1930, to be used as the branch of the Community Centers in Afyon on 19 February 1932. The projects of the building were prepared by Architect Arif Hikmet Koyunoğlu, the project designer of the Ankara Türk Ocakları service building [36].
The building, located on Ordu Boulevard in the center of the city, is a two-storey masonry building. The entrance of the building, where the main entrance is on the façade facing Ordu Boulevard, is provided by a nine-step staircase with a marble railing. The entrance hall is reached when you enter through the two-winged wooden entrance door. Located on the front, the room has a balcony, the front of which is covered with glass and iron joinery.
The roof of the building is hipped roof and covered with Marseille tiles. The wide eaves of the building are decorated with laths by creating geometric patterns [34].
It is stated that Atatürk visited this building during his visit to Afyon on 2 March 1931 and wanted the building to be converted into a Community Center, where upon the building used as a Turkish Hearth was converted into a Community Center [36, 37]. The building was transferred to the Ministry of Finance upon the closure of the Community Centers and was used as the Revenue Office until 1992 [34]. With the establishment of Afyon Kocatepe University, it started to be used as the Rectorate building, and today it has been used as a cultural center affiliated to Afyon Kocatepe University (Table 2) [38].
During the early1900s, the Police Station Building was built with the purpose of ensuring security in Yaylabağı and the surrounding villages. It served this role effectively for many years. The building, which is open on four sides, was used as a police station, Greek headquarters and school in the historical process and was emptied and abandoned in the 1970s.
The two-storey building, which is masonry with a hipped roof, is made of cut stone and the windows are plastered on the brick. The building has a stone window and a flattened arch. On the ground floor of the building, there are two rooms and a staircase hall, one of which provides access to the structure, and on the first floor, there are two rooms and a staircase hall.
In the examinations carried out in 2005, it was determined that there were collapses between the roofs and floors of the abandoned structure, the window and door joinery were broken, and the plaster was poured. Upon the application of Yaylabağı Municipality, the building was restored and re-functioned as a reading hall and library (Table 3) [37].
Table 3.
Yaylabağı Karakolu Cephe Analizi.
4.1 Fractal analysis of the Façades of the first national architectural period public buildings in Afyonkarahisar
Within the scope of the study, firstly, building façade survey drawings were prepared for the analysis of the façades of three public buildings belonging to the First National Architectural Period in Afyonkarahisar with the box counting method, and a 3×5 grid system was added on the façade drawing of each structure. In order to calculate the fractal value in the first cycle, the number of filled boxes was determined and the fractal value was calculated according to the formula. In the next cycles, the grid system was changed to 6×10, 12×20, 24×40, 48×80, respectively, and the number of filled-empty boxes for the façades is shown in the tables (Tables 4–6).
Table 4.
Zafer museum box count metrics.
Table 5.
Rıza Çerçel cultural Center box count metrics.
Table 6.
Police Station building box counting measurements.
In line with the data in Tables 4–6, with the help of the formula, calculations D=logx−logylogz−logq were made for each building façade and the fractal dimension values resulting from the calculations were shown in Table 7.
Zafer Museum
Rıza Çerçel Cultural Center
Police Station Building
1. Conversion
1.58
1.93
1.38
2. Conversion
1.90
1.71
1.70
3. Conversion
1.86
1.73
1.53
4. Conversion
1.93
1.72
1.16
Table 7.
Fractal dimension values of building façades.
As a result of the calculations, it was seen that the fractal dimension values of the three selected structures varied between 1 and 2. According to the values obtained as a result of 4 conversions; the building with the highest fractal dimension value is the Zafer Museum with a value of 1.93, while the building with the lowest fractal dimension value is the Police Station Building with a value of 1.16.
The objective of this chapter is to analyze the façade layout of three public buildings belonging to the First National Architectural Period in Afyonkarahisar by fractal method. In this direction, first of all, the architectural features of the First National Architectural Period were revealed in the study and the façade layouts of the three selected historical buildings were analyzed in the context of these features. Then, in order to obtain numerical data for the systematic analysis of the façade layouts, fractal size calculations of the façades were made by box counting method.
It has been seen that the structure with the highest fractal size is the Zafer Museum. During the analysis, it was determined that the entrance façade of the Zafer Museum exhibited distinct characteristics associated with the First National Architectural Period. These features included the presence of horizontal and vertical staggers, the use of pointed arches to emphasize window gaps, the inclusion of floor moldings that allowed the reading of floor traces from the façade, an elevated entrance accessible via stairs, a façade divided into three parts, and the utilization of variety of materials. These characteristics contributed to the overall composition and reading of the façade. In this structure, the proximity of the fractal size value to 2 has been interpreted as an indication of the intricate complexity of the façade layout and the presence of numerous intricate details.
The building with an average fractal size is the Rıza Çerçel Cultural Center. This situation belongs to the First National Architectural Period on the façade of the Rıza Çerçel Cultural Center. It was determined that features such as the presence of horizontal and vertical cascades, the use of eaves with wide and sub-surface decorations, an entrance reached by a raised staircase, the façade consisting of three parts and the use of uniform materials were related to the reading from the façade. In this structure, the interpretation of the fractal size value ranging between 1.5 and 2 suggests that the façade layout is relatively simple in its overall composition. However, it also indicates the utilization of intricate details within the design.
It was seen that the structure with the lowest fractal size was the Police Station Building. It was determined that this situation was related to the fact that the features of the First National Architectural Period in the Police Station Building such as the appearance of floor traces only with floor moldings, an entrance reached by a raised staircase, the balcony above the entrance, the flattened arched window spaces and the use of uniform materials were read from the façade. In the façade layout of this historical building, the features of the First National Architectural Period are less visible than the other buildings selected within the scope of the study. It was seen that this situation was also reflected in the numerical data obtained and the fractal dimension value of the façade of the building was lower than the other structures within the scope of the study. The interpretation of the fractal dimension value being close to 1 in this structure suggests that the façade has a simpler and more streamlined design compared to other structures. The value approaching 1 indicates a reduced level of complexity and intricacy in the façade layout.
As a result, it is seen that the features of the First National Architectural Period in the façade fictions of the buildings selected within the scope of the study cause mobility and complexity in the building facades and this is reflected in the numerical expressions of the façade fictions. It is concluded that the façade characteristics of the structures selected within the scope of the study coincide with the numerical data obtained in the study.
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