# Geospatial Assessment of the Territorial Road Network by Fractal Method
## 3 The Main Research  
### Research Methodology  
The research methodology provided for the development of a model for the geospatial assessment of a territory's transport development is based on the fractals theory, in accordance with Equations (7) and (8).  
In this study, the box-counting method was used to calculate the fractal dimension [9; 27]. The essence of the method is as follows. The original dataset was split into a square box of size \(\varepsilon\) as a fixed grid (Figure 1). Next, the minimum number of square boxes N (\(\varepsilon\)) that cover the original object was calculated. Calculations of N(\(\varepsilon\)) were performed for various sizes of \(\varepsilon\). For a small \(\varepsilon\) value, the square box number should behave like \(\sim\)\(\varepsilon^{-\text{D}}\), and in this case, \(\text{logN}(\varepsilon)=\text{D}\cdot\text{log}1/\varepsilon\). According to the data obtained, we constructed a dependence of the following form:  
\[lnN(\varepsilon)=f(ln(1/\varepsilon)) \tag{9}\]  
Then, we calculated its slope d, defined as  
\[D=-\underset{\varepsilon\to 0}{lim}\frac{lnN(\varepsilon)}{ln(\varepsilon)} \tag{10}\]  
To find the slope of Equation (8) in logarithmic scale, we had to build the general linear regression, expressed in the following form:  
\[lnN(\varepsilon)=\alpha+\beta ln(1/\varepsilon)+\Delta \tag{11}\]  
where \(\Delta\) represents the error of a linear approximation.  
The transport development of the territory was calculated as the ratio of the studied road dimension to the area dimension (i.e., a dimension equal to 2), based on Equation (8).  
To implement the model, was created a Python script that calculated the fractal dimension for a polyline shapefile with a road network in the ArcMap program of the ArcGIS platform. In accordance  
Figure 2: An example of maximum transport provision of territories.  
with the proposed model, the study area was covered with a network of hexagons of a given size. Then, using the box-counting method, the road network fractal dimension and the territory transport development within each hexagon were calculated, as in Equation (8).  
The script execution result was a polygonal shapefile, the attribute table of which had a numerical field added with the territory transport development's calculated value for each polygonal object (hexagon).  
As they were required for the script to work, base maps of the administrative area (boundary) and the road network were imported from the OpenStreetMap dataset in.shp format [28].  
Modeling was performed for the following countries: Ukraine, Germany, and Bolivia. To compare their transport development level values, the same hexagon size was chosen, equal to 1000 km\({}^{2}\), so that most settlements had a single transport development and did not introduce additional errors into the study on the selected scale of countries. In the attributive tables of polyline layers of the road networks of countries, using an SQL query, only major trunk roads of international and regional importance were selected. These polyline features are tagged with highway = (motorway; trunk; primary; secondary).  
Testing of the script was also carried out for a large-scale map, representing the territory of the city of Odessa (Ukraine). All road types were considered, including streets and roads within residential areas. The hexagon area was chosen as 0.25 km\({}^{2}\). The results obtained made it possible to compare the network fractal dimension indicators within the same settlement.