[H-GG01] Dialogues on natural resources and environment between earth and social sciences

[HGG01-P01] A New indicator for Quantifying Hierarchal Structure of Settlements: 3D Fractal Dimension

*Sai Durga Malleswar Thota¹, Yuzuru Isoda¹ (1.Human Geography, Graduate school of Science, Tohoku University)

Keywords:Fractals, settlement patterns, fractal dimension, gridded populaiton data, nested hierarchal structure, rural planning

Settlement patterns are a result of the spatial distribution of human agglomeration. These patterns are expected to provide crucial insights into underdevelopment in rural regions or integration of that region into the national economy. Settlement patterns are complex spatial objects which cannot be quantified using conventional mathematical models. The application of fractals helps us overcome spatial problems like scale, irregularity, and complexity. In this study, we use fractals to quantify the hierarchy of settlement patterns using fractal dimension. We proposed a 3D box-counting method to estimate the fractal dimension of the gridded population dataset without any preprocessing. The key objective of this study was to achieve accurate quantification to represent the pattern of settlement hierarchies of any region using the proposed fractal dimension (FD), regardless of urban or rural. We hypothesized the settlement hierarchies as an imaginary self-similar structure and estimated the 3D fractal dimension of the gridded population dataset. We applied the differential box-counting method to estimate FD, and scaling is done using least linear squares. We estimated FD for two study areas, the USA and India. The entire dataset of each country was split into grid cells of 100 km×100 km to estimate local FD. Random cases were picked from the USA and India to explain the significance of the FD value. Our results agree with the hypothesis and show that FD varies systematically with the visual impression of population clusters visible on the map. We were able to distinguish the settlements with organized hierarchy from other types of settlements using the estimated FD even though they have a similar population count. Other findings include the relation between population count and FD, which is not perfectly linear. However, upon the classification of research units into four quantiles, the change in FD value has explained the clustering behavior of the population.