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

Öz

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.

Anahtar Kelimeler

• Kent Morfolojisi
• Fractal Geometry
• Lakunarite
• Karmaşıklık

Kaynakça

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