Fraktal boyut ve lakunarite  hesaplamaları  ile parkların  dönemsel analizleri  ve değerlendirmeleri
Periodic analyzes and evaluation of the  parks with fractal dimension and lacunarity calculations
Yazar: NAZLI BAHAR URSAVAŞ
Danışman: PROF. DR. GÜLEN ÇAĞDAŞ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Bilişim Ana Bilim Dalı / Mimari Tasarımda Bilişim Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Mimarlık = Architecture
Dizin: Açık alanlar = Open spaces ; Fraktal boyut = Fractal dimension ; Parklar = Parks

Özet:
Fraktal örüntüler, sonsuz döngüye sahip, karmaşık, matematiksel denklemlerle oluşturulan ve birbirinin tekrarı olan kurgulardır. Doğada kendiliğinden var olan veya farklı bağlam ve örüntüler ile oluşan bu yapılar, günümüzde dijital olarak matematiksel yapılarla oluşturulmakta ve farklı alanlarda kullanılmaktadır. Fraktal örüntülerin varolduğu  alanlardan biri de yeşil alanlardır. Açık ya da yeşil alanlar günümüzde hızla büyüyen kentlerin estetik ve fonksiyonel eksiklerini tamamlamaktadır. Bu durumda kentsel mekan ögelerinden biri olan  yeşil alanların ve onların değerlendirilmesinde  aynı zamanda tasarımında kullanılan modeller önem kazanmıştır. 
Araştırmanın konusu olarak, bir yerleşim merkezinde kamu yararına düzenlenmiş ve bu şekliyle "park" olarak tanımlanan yeşil alanlar; karmaşık geometrik şekillerden oluşmaları, parçalı yapıları ve bazen de tekrar eden desenlere sahip olmaları nedeniyle fraktal özellikler taşımaktadır. Bu benzer özellikler dolayısıyla tezde, parkların fraktal geometri çerçevesinde ele alınması ve incelenmesi üzerine çalışılmıştır. Bu bağlamda kentsel sistemlerin bir parçası olan parkların fraktal boyut ve lakunarite hesaplamaları yönünden değerlendirmeleri ve analizlerine yer verilmiştir. 
Tez, öncelikli olarak bir literatür taraması içerirken bu literatür araştırmaları fraktallere ait olan kavram tanımlamaları ile başlamaktadır. Bu kavram açıklamalarını fraktal geometri ve ona ait başlıkların anlatımı takip etmektedir. Daha sonrasında fraktal boyut, lakunarite kavramlarına değinilmiş olup bu başlıklara ait hesaplama yöntemleri incelenmiştir.Bu çalışmalar kullanılacak olan hesaplamalı yöntem sonucunda ortaya çıkan verilerin değerlendirmesini desteklemek amacıyla ortaya konulmuştur. 
Tez çalışması kapsamında, fraktal geometrik analizlerde yer alan başlıca hesaplama yöntemlerinden biri olan "kutu sayma yöntemi" kullanılmış olup, bu yöntem sayesinde yeşil alanların objektif ve matematiksel verilere dayandırılarak karşılaştırılması için bir  yaklaşım önerilmiştir.  
Birbirlerinden farklı özelliklere sahip olması göz önünde bulundurularak seçilen çalışma alanları (bulundukları konum, kapasite, hacim, hitap ettikleri nüfusun yoğunluğu vs. parametreler göz önüne alınarak), bahsedilen kutu sayma yöntemi ile gözeneklilik(lakunarite) ve fraktal boyut hesabı yapılması uygun görülmektedir. Bu hesapların yapılabilmesi için ImageJ programına ait olan Fraclac eklentisi ile çalışılmıştır. Google Earth ve Global Human Settlement Layer'dan elde edilen uydu fotoğraflarının iki boyutlu aktarımı ile hesaplamalar yapılmıştır. Bu haritaların iki boyuta aktarılmasının temel sebebi de kullanılacak olan programa ait algoritmaların iki boyutlu imajlar ile daha doğru sonuç vermesinden kaynaklanmaktadır. 
Bu doğrultuda İstanbul ilinin farklı lokasyonlarında bulunan ve çeşitli parametrelere göre seçilmiş olan dört adet park kullanılmıştır. Seçilen bu parkların zaman içerisinde değişen yapıları gözlemlenerek ortaya çıkan farklılıkların, gelişim ya da dönüşümlerinin değerlendirilmesi amaçlanmaktadır. Yapılan incelemeler sonucunda parkların dönemsel olarak çeşitlilik gösteren yapılarının fraktal ve lakunarite hesaplama yöntemleri üzerinden analizleriyle gösterilmesi hedeflenmiştir. Yapılan analizlerin grafiksel dökümü ile de matematiksel karşılaştırmalar için veriler oluşturulmuştur.  
Çalışma sonucunda ortaya çıkan verilerin değerlendirilmesinde fraktal analizlerin üstlendiği rol üzerinde durulmuştur. Bu çözümlemelerde kullanılan yöntemlerin söz konusu olabilecek yeni araştırma alanlarına katkı sağlayabileceği düşünülmektedir.  Bu da bir kent ögesi olan yeşil alanların parçası olan parkların kullanıcılarından elde edilebilecek geri dönüşlerle yeni park tasarımları için veri oluşturabileceği öngörülmektedir.

Abstract:
Fractals are complex, repetitive pattens with endless loops, created with mathematical equations. These structures, which exist spontaneously in nature or formed with different contexts and patterns, are digitally created with mathematical structures and used in different fields. One of the areas where fractal patterns exist is green areas. Open or green spaces complete the aesthetic and functional deficiencies of rapidly growing cities today. In this case, green areas, which are one of the urban space elements, and the models used in their design at the same time gain importance.
As the subject of the research, green areas arranged for public benefit in a residential area and defined as "parks" in this way; They have fractal properties because they consist of complex geometric shapes, fragmented structures and sometimes repetitive patterns. Due to these similar features, it has been studied on the consideration and examination of parks within the framework of fractal geometry. In this context, evaluations and analyzes of parks, which are a part of urban systems, in terms of fractal dimension and lacunarity calculations are included. Additionally within the scope of the thesis, lacunarity has been used for measuring the porosity of the parks. 
While the thesis primarily includes a literature review, these literature studies begin with the concept definitions of fractals. Fractals are highly connected to the term of "chaos" so within the text, the first context about fractals is chaos and its definitions. When evaluating chaos and fractals together, one of the most striking elements is that fractals reveal the order within the chaos. 
After the mentioning about chaos, the study includes the types of the fractal which are natural fractals and artificial fractals. The reason why these types are examined in this part of the thesis is that the analyzes to be made within the scope of the thesis are examples of both natural fractals and artificial fractals of  parks those are parts of the green areas, which are a part of urban nature. While the natural formation of the green urban fabric over time can be considered as an intervention of nature, its shaping, growth, shrinkage and even disappearance with human intervention turns it into an artificial phenomenon. This situation necessitates mentioning both features of these areas in the context of the city. 
Furthermore, it is mentioned about what is fractal geometry and its features. Fractal geometry can be considered as the continuum of Euclidian geometry. The fields in which both are used are different. Fractal geometry does not replace the so-called classical geometry, Euclid, but enriches it and differentiates perspectives. By using fractal geometry calculation methods in computational areas, they can clearly present their structural units in each area.

Henceforwards, as the third chapter of the study it has been touched on fractal dimensions and lacunarity. In the context of the thesis, the calculations are being made of via using "box counting method", which is one of the main calculation methods in fractal geometric analysis and it was foreseen that the green areas would form a comparison example based on objective and mathematical data, thanks to this method. 
Considering that they have different characteristics from each other, it is considered appropriate to calculate the porosity (lacunarity) and fractal dimension with the mentioned box counting method, considering the selected study areas. In order to make these calculations, the Fraclac plugin belonging to the ImageJ program was used. Calculations were made with two-dimensional transfer of satellite photos obtained from Google Earth and Global Human Settlement Layer. The main reason for transferring these maps to two dimensions is that the algorithms of the program to be used give more accurate results with two-dimensional images. 
The case study of the thesis includes the selection of four parks located in different locations of Istanbul according to the parameters such as their location, capacity, volume, density of the population they address to. The selected parks are: Bebek Parkı, Göztepe 60. Yıl Parkı, Emirgan Parkı and Maçka Demokrasi Parkı. It is aimed to evaluate the differences, developments or transformations that arise by observing the changing structures of these selected parks over time. As a result of the calculations made, it is aimed to show the periodically varying structures of the parks with analyzes through fractal calculation methods. With the graphical analyzes, data were created for mathematical comparisons. 
For Bebek Parkı, when the periodic results of Bebek Park are compared with each other, an increase in fractal dimensions and a decrease in lacunarity values were observed on the map in 2010 compared to 2002. The situation this means; the pattern has become more complex and the porosity (lacunarity) has decreased. Based on this, when the maps of 2010 and 2021 are compared, a decrease in fractal dimension and an increase in lacunarity values are observed. When these three situations are compared at the same time, it is observed that there is a fluctuating change for both values. This shows that for the fractal dimension, it first goes up and then down in a certain year range, and for the porosity values, it first decreases and then goes up in the same ranges. 
For Göztepe 60. Yıl Parkı, when the periodic results are compared with each other, an increase in fractal dimensions and a decrease in lacunarity values were observed in the map in 2017 compared to 2009. However, when the maps of 2017 and 2021 are compared, an increase in lacunarity values is observed, with a very slight increase in fractal dimension. This indicates an increase in occupancy and vacancy rates despite the fact that the complexity of the parking structure remained almost the same during this period. When the three tables are compared at the same time, it is observed that the fractal dimension value increased and the lacunarity value decreased in the period from 2009 to 2021. Although the differences in the results did not change much between 2017 and 2021, the graphs still show linearity.
When the periodic results of Emirgan Park are compared with each other, an increase in fractal dimensions and a decrease in lacunarity values were observed on the map in 2010 compared to 2002. However, when the maps of 2017 and 2021 are compared, there is a significant increase in fractal dimension and a decrease in lacunarity values. This indicates a slight decrease in porosity, although the complexity of the park structure has increased during this period. When the four tables are compared at the same time, the fractal dimension value is constantly increasing in the period from 2002 to 2021, while a slight fluctuation is observed in the lacunarity values in 2010, with a big jump.
When the periodic results of Maçka Park are compared with each other, an increase in fractal dimensions and a decrease in lacunarity values were observed on the map in 2014 compared to 2002. However, when the maps of 2014 and 2021 are compared, a slight decrease in fractal dimension and an increase in lacunarity values are observed. This indicates that although the complexity of the park structure decreased a little during this period, the park had a more vacant and perforated structure and a more heterogeneous texture was formed. When all the tables created for Maçka Park are compared at the same time, the fractal dimension value follows a fluctuating path from 2002 to 2021, while the lacunarity values follow the same path.
After all the calculations, a graph containing fractal dimension and lacunarity values of the examined parks was created. Although the fractal dimension order in the created graph is similar to the order of the lacunarity values, it is not the same. Because fractal dimensions express pattern complexity, they do not affect lacunarity. In addition to these, considering the construction dates of the parks, it is seen that the selected parks belong to many different periods. One of the reasons taken into consideration while examining the selected parks is that they contain historical and periodical differences. In this way, it is aimed to examine whether the dates of existence or the processes of renewal and change have an effect on the calculation data obtained. Moreover the size of the parks are also investigated if they affect the fractal dimension and lacunarity values or not. 
As a result of the research, it is aimed to look at the use and design of green areas, which are an urban space element, from a different perspective, as a research subject in the future, based on the data obtained. The role of fractal analyzes in the evaluation of the data obtained as a result of the study was emphasized, and it was taken into account whether the methods used in these analyzes would contribute to new research stages. Thus, it has been one of the targeted results that it will be a work that creates an infrastructure to create a model that can address the city and public needs by combining the park design, which is one of the green space elements, which is an urban organization, and the data to be provided by the user in the future.