When and Where is a City Fractal?

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. The paper presents an analysis of the development of the Tel Aviv metropolis using the concept of fractal. The fractal density of the whole urban ensemble and of its parts was estimated as a function of the time, from 1935 on. The central part and the northern tier is fractal at all times. Its fractal dimension increase with time. However, the whole ensemble can be said to be fractal only after 1985. There is a general tendency toward fractality in the sense that the fractal dimensions of the different parts converge toward the same value. Terms of use: Documents in EconStor may

Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy

“…Using the datasets, we can calculate state entropy, information entropy, and Renyi entropy ( Table 2). The relationships between [46], whose fractal discriminant criterion is standard error σ < 0.04, the fractal structure of Beijing's urban form is significant because the errors of fractal dimension values are less than 0.1 (Table 3). Note: The base of the logarithm is 2, thus the unit of information quantity is bit.…”

“…The standard errors of all the fractal dimension values are less than 0.04. According to Benguigui et al [46], whose fractal discriminant criterion is standard error σ < 0.04, the laws based on dilation symmetry [9]. This method can better reflect the cascade structure of a fractal city, and thus better estimate its fractal dimension.…”

“…Two types of box counting can be applied to fractal dimension estimation of cities [31,42]: one is to fix the largest box [46], and the other is to unfix the largest box [44]. In the former way, the size and shape of the first level box do no change for different years; in the latter way, the size and shape of the largest box change with urban growth in different years.…”

“…The standard errors of all the fractal dimension values are less than 0.04. According to Benguigui et al [46], whose fractal discriminant criterion is standard error σ < 0.04, the …”

On the Spaces and Dimensions of Geographical Systems

“…The notation of arrow "→" means "approach to". Both D f (R) and D p (R) can be estimated with the radius-number scaling relation, or box-counting method or grid method in real space (Batty and Longley, 1994;Benguigui et al, 2000;Feng and Chen, 2010a;Frankhauser, 1998). Similarly we get…”