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.