Fractal analysis of urban growth in complex systems

A complex network consists of number of elements which may interact with each other to form a complex system. The fractal feature is one of the most important characteristics in complex networks. This study examines the fractal analysis of Madaba City Centre as a complex system through the period to 1953-2022. In order to reveal the fractal characteristics of the study area box-counting (Db) and information (Di) dimensions were calculated using Benoit for five satellite images for years 1953, 1981, 1992, 2000, and 2022. Results showed that Madaba road networks have fractal characteristics for the study period, and the calculated fractal dimensions are between 1 and 2. Db values for years 1953, 1981, 1992, 2000, and 2022 are 1.38, 1.51, 1.55, 1.58, and 1.65, while Di values are 1.37, 1.52, 1.57, 1.60, and 1.67 respectively. The difference between Db and Di values for the same year was small, indicating the similarity between the two methods. Increasing the complexity of the system components and dynamic activities are other indicators of its growth, and there is a significant positive relationship between the fractal dimension value and the complexity level of the city in terms of population growth and area expansion; which increase the importance of fractal theory in studying the growth of the complex system like cities.