Fractality and Lacunarity of Turkish Cities

Abstract

For the first time in this article, fractal dimensions and lacunarity coefficients of all the cities in Turkey are calculated using an open-source software ImageJ and a plugin FracLac. According to these values, 81 Turkish cities are grouped into 10 clusters. While the distribution of the lacunarity coefficients pass the goodness of fit test for the normal distribution; the distribution of fractal dimensions did not pass this test, since it is a two-moded distribution. From the results obtained, we understand that there is a weak, negative, significant (5% significance level) correlation between fractal dimension and lacunarity; a weak, positive significant (1% significance level) relationship between fractal dimension and population; and also there is a moderate, positive significant (1% significance level) relation between fractal dimension and gross domestic product per capita by provinces. No significant relationship was found between lacunarity and population. Although it has been stated that, “in the mean, the larger cities are alike”, when we examine the similarities of Turkish cities in multivariate context using fractal dimensions and lacunarity coefficients, small cities were found to be more alike.

Keywords

• City Morphology
• Fractal Geometry
• Lacunarity
• Complexity

Türk Kentlerinin Fraktalite ve Lakunaritesi

Abstract

Bu makalede ilk defa, Türkiye'deki tüm şehirlerin fraktal boyutları ve lakunarite katsayıları açık kaynaklı bir yazılım olan ImageJ ve FracLac eklentisi kullanılarak hesaplanmıştır. Bu iki değere göre, 81 Türk kentinin 10 kümede gruplandığı görülmüştür. Normal dağılımından dolayı lakunarite katsayılarının dağılımı ki-kare uyum iyiliği testini geçerken; iki modlu bir dağılımda olduğu için fraktal boyutların dağılımı bu testi geçememiştir. Elde edilen sonuçlardan, fraktal boyut ile lakunarite arasında zayıf, negatif, anlamlı (% 5 anlamlılık düzeyinde) bir korelasyon olduğu anlaşılmıştır; fraktal boyut ile nüfus arasında zayıf, pozitif anlamlı (% 1 anlamlılık düzeyinde) bir ilişki; ayrıca fraktal boyut ile il bazında kişi başına gayri safi yurtiçi hasıla arasında orta düzeyde, pozitif anlamlı (% 1 anlamlılık düzeyinde) bir ilişki bulunmuştur. Lakunarite ve nüfus arasında anlamlı bir ilişki bulunamamıştır. “Genellikle büyük şehirlerin birbirine benzediği” belirtilmiş olsa da; fraktal boyutlar ve lakunarite katsayıları kullanılarak çok değişkenli bağlamda Türkiye şehirlerinin benzerliklerini incelediğimizde küçük şehirlerin daha benzer olduğu görülmüştür.

Keywords

• Kent Morfolojisi
• Fractal Geometry
• Lakunarite
• Karmaşıklık

References

1. Batty, M. (1994). Fractal Cities A Geometry of Form and Function, New York Academic Press.
2. Bettencourt, A.M. L., Lobo, J., Strumsky, D., & West, B. G. (2010). Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities. PLOS ONE, 5(11). Retrieved from https://doi.org/10.1371/journal.pone.0013541
3. Borys, P. (2009). On The Relation Between Lacunarity and Fractal Dimension, Acta Physica Polonica B, 40 (5): 1485-1490. Retrieved from https://www.semanticscholar.org/paper/On-the-Relation-Between-Lacunarity-and-Fractal-Borys/257db60cbba998f97843f57506c38e37d248e630?p2df
4. Bovill, C. (1996) Fractal Geometry in Architecture and Design. Birkhauser Boston.
5. Chen, Y., & Wang, J. (2013). Multifractal Characterization of urban form and growth: the case of Beijing. Environment and Planning B: Planning and Design, 40(5), 884-904. Retrieved from https://doi.org/10.1068/b36155
6. Caglioni, M., & Giovanni, R. (2006). Contribution to the Fractal Analysis of Cities: A Study of the Metropolitan Area of Milan. Cybergeo. Retrieved from https://doi.org/10.4000/cybergeo.3634
7. Düşündere, T. A. (2019) 1992-2018 Dönemi için Gece Işıklarıyla İl Bazında GSYH Tahmini: 2018'de 81 İlin Büyüme Performansı. Türkiye Ekonomi Politikaları Araştırma Vakfı. Retrieved [15 May 2020] from https://www.tepav.org.tr/upload/files/1553236580-5.Gece_Isiklariyla_Il_Bazinda_GSYH_Tahmini_1992_2018.pdf
8. Ediz, Ö., & Çağdaş, G. (2005). Mimari tasarımda fraktal kurguya dayalı üretken bir yaklaşım. itüdergisi/a mimarlık, planlama, tasarım, 4(1): 71-83. Retrieved from http://itudergi.itu.edu.tr/index.php/itudergisi_a/article/view/943

9. Ediz, Ö., & Ostwald, J. M. (2012). The Süleymaniye Mosque: A Computational Fractal Analysis of Visual Complexity and Layering in Sinan’s Masterwork. Architectural Research Quarterly (ARQ), 16(2), 171-182. Retrieved from https://doi.org/10.1017/S1359135512000474
10. Erdoğan, G. (2015). Kent Makroformlarının Mekanı Kullanma Verimliliklerinin Fraktal Boyut İle İncelenmesi. Dokuz Eylül Üniversitesi, İzmir.
11. Forsythe, A., Nadal, M., Sheehy, N., Cela-Conde, J. C., & Sawey, M. (2011). Predicting beauty: Fractal dimension and visual complexity in art. British Journal of Psychology, 102(1): 49-70. Retrieved from https://doi.org/10.1348/000712610X498958
12. Gözübüyük, G. (2007). Farklı Mimari Dillerde Fraktallere Dayalı Form Üretimi. İTÜ, İstanbul.
13. İlhan, C., & Özgür, E. (2019). Kent Dokusu Morfolojik Değişiminin Fraktal Geometri Aracılığıyla Hesaplanması: Bursa Örneği. Mimarlık ve Yaşam, 4(1): 117-140. Retrieved from https://doi.org/10.26835/my.546927
14. Vaughan, J., & Ostwald, J. M. (2009) Nature and architecture: revisiting the fractal connection in Amasya and Sea Ranch. 43rd Annual Conference of the Architectural Science Association, ANZAScA 2009, University of Tasmania
15. Karperien, A. (1999-2003). FracLac for ImageJ. https://imagej.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm
16. Karperien, A., Jelinek, H. F., & Milošević, N. (2011). Reviewing Lacunarity Analysis and Classification of Microglia in Neuroscience. Proceedings of the 8th European Conference on Mathematical and Theoretical Biology European Society for Mathematical and Theoretical Biology (ESMTB) 2011 MS#88. Retrieved from https://doi.org/10.13140/2.1.3576.6082
17. Kaya, H. S., & Bölen, F. (2017). Urban DNA: Morphogenetic Analysis of Urban Pattern. ICONARP International Journal of Architecture Planning, 5(1), 10-41. Retrieved from https://doi.org/10.15320/ICONARP.2017.15
18. Kaya, H. S., & Dökmeci, V. (2017). Development of urban hierarchies at the country and regional levels in Turkey. A/Z ITU Journal of Faculty of Architecture, 14(2), 131-149.
19. Lagarias, A., & Prastacos, P. (2017). Estimation of Fractal Dimensions of Mediterranean Cities Using Data For Different Built-Up Densities. 'Cities and regions in a changing Europe: challenges and prospects', Panteion University, Athens, Greece, 5-7 July 2017.
20. Lagarias, A., & Prastacos, P. (2018). Comparing the urban form of South European cities using fractal dimensions. Environment and Planning B: Urban Analytics and City Science. Retrieved from https://doi.org/10.1177/2399808318820911
21. Larkham, J. P., & Adams, D. (2019). Persistence, Inertia, Adaptation And Life Cycle: Applying Urban Morphological Ideas To Conceptualize Sustainable City-Centre Change. ICONARP, 7 (Special issue): 73-94. Retrieved from https://doi.org/10.15320/ICONARP.2019.78
22. Lynch, K. (1960). The Image of the City, New York: M.I.T. Press.
23. McAdams, M. A. (2007). Fractal Analysis and the Urban Morphology of A City in A Developing Country: A Case Study of Istanbul. Marmara Coğrafya Dergisi, 15: 149-172. Retrieved from http://dspace.marmara.edu.tr/handle/11424/2515
24. Meredith, S. (2018). Two-thirds of global population will live in cities by 2050, UN says. Cnbc archive. Retrieved from https://www.cnbc.com/2018/05/17/two-thirds-of-global-population-will-live-in-cities-by-2050-un-says.html
25. Ostwald, J. M., & Vaughan, J. (2016) The Fractal Dimension of Architecture (eBook). Springer International Publishing, Switzerland.
26. Prastacos, P., Lagarias A., & Chrysoulakis N. (2017). Using the Urban Atlas dataset for estimating spatial metrics; methodology and application in urban areas in Greece. CyberGeo. Retrieved from https://doi.org/10.4000/cybergeo.28051
27. Rauch, E. (2019). Introduction to Lacunarity. Eric Rauch online archive. Retrieved [20 December, 2019] from http://groups.csail.mit.edu/mac/users/rauch/lacunarity/lacunarity.html
28. Reiss, A. M., Lemmerer B., Hanslmeier A., & Ahammer H. (2016). Tug-of-war lacunarity-A novel approach for estimating lacunarity. Chaos: An Interdisciplinary Journal of Nonlinear Science. Retrieved from https://doi.org/10.1063/1.4966539
29. Salat, S. (2012). The Fractal Pattern of Cities. Óbuda University e-Bulletin, 3(1): 263-273.
30. Shen, G. (2002). Fractal dimension and fractal growth of urbanized areas. International Journal of Geographical Information Science, 16(5): 419-437. Retrieved from https://doi.org/10.1080/13658810210137013
31. Shreevastava, A., Suresh P., Rao C., & McGrath, G. S. (2019). Emergent Self-Similarity and Scaling Properties of Fractal Intra-Urban Heat Islets for Diverse Global Cities. Physical Review E. Retrieved from https://doi.org/10.1103/PhysRevE.100.032142
32. Terzi, F., & Kaya, H. S. (2011). Dynamic spatial analysis of urban sprawl through fractal geometry: The case of Istanbul. Environment and Planning B Planning and Design, 38(1),175-190. Retrieved from https://doi.org/10.1068/b35096
33. Triantakonstantis, P. D. (2012). Urban Growth Prediction Modelling Using Fractals and Theory of Chaos. Open Journal of Civil Engineering, 2(2): 81-86. Retrieved from https://doi.org/10.4236/ojce.2012.22013
34. TUİK. (2018). Yıllara göre il nüfusları, 2000-2018. Retrieved from [15 December 2019] http://www.tuik.gov.tr/Start.do
35. Url-1 Retrieved from [10 December 2019] http://metrocosm.com/history-of-cities/
36. Url-2 Retrieved from [25 April 2020] https://pudding.cool/2018/10/city_3d/
37. Url-3 Retrieved from [1 April 2020] Google Maps https://www.google.com/maps/d/edit?mid=1ChqsKJA_yzrrZ52SKp_WXjA0GqJR3Xsv&ll=40.132092310883536%2C26.421455753221707&z=13