# Geospatial Assessment of the Territorial Road Network by Fractal Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Statement of the Problem

#### 2.1. Classical Indicators of the Transport Provision of Territories

^{2}, H is the total population in thousands of people, N is the number of settlements, and t is the total weight of the cargo sent to the territory.

#### 2.2. Calculation of the Transport Provision of Territories Based on the Fractals Theory

_{0}such that $\underset{\mathsf{\epsilon}\to \infty}{\mathrm{lim}}{m}_{p}=\infty $ for all p < p

_{0}and $\underset{\mathsf{\epsilon}\to \infty}{\mathrm{lim}}{m}_{p}=0$ for all p > p

_{0}. This value p

_{0}= D

_{H}is the value of the Hausdorff–Besicovitch dimension.

^{−2}= (1/10)

^{−2}= 100. The Hausdorff measure is m

_{p}(Q) = N(ε)ε

^{p}= ε

^{p−2}. Let us say ε → 0. Then, m

_{p}(Q) → ∞ for all p < 2, and m

_{p}(Q) → 0 for all p > 2. Thus, D

_{H}(Q) = DimQ = 2.

## 3. The Main Research

#### 3.1. Research Methodology

^{−D}, and in this case, logN(ε) = D⋅log1/ε. According to the data obtained, we constructed a dependence of the following form:

^{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).

^{2}. The results obtained made it possible to compare the network fractal dimension indicators within the same settlement.

#### 3.2. Results

## 4. Discussion

^{2}. The resulting vector map, consisting of 710 polygon features, was classified by the TP field, which contained the calculated values of the transport provision indicator in accordance with Equation (11).

^{2}. The simulation results are presented in Table 2. In 61% of Bolivia’s territory, the indicator of transport provision is less than 0.5, including 47% of the territory that lacks a road network (i.e., the indicator is zero). This is due to the presence of large areas of Amazonian rainforests in this part of the country. The Bolivia territory is also crossed by the Andean mountains, which contributes to the scarcity of transportation lines. In the remaining 39% of the territory, various values of transport provision are observed, with a predominance of values in the range from 0.5 to 0.79. As for Germany, about 79% of its territory has a transport provision index above 0.625, including 34% above 0.75.

^{2}. The data source is the OpenStreetMap map service. All road types were considered, including streets and roads within residential areas. The hexagon area was 0.25 km

^{2}.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 11.**Modeling results for the territory of the city of Odessa, showing (

**a**) the transport network and (

**b**) the transport development level.

**Table 1.**The change of N(ε) versus different values of ε for the example in Figure 5.

Steps | Step 0 | Step 1 | Step 2 | Step 3 | Step 4 |
---|---|---|---|---|---|

N(ε) | 1 | 4 | 11 | 28 | 65 |

ε | 1 | 0.5 | 0.25 | 0.125 | 0.0625 |

Specifications | Ukraine | Germany | Bolivia |
---|---|---|---|

Area of the country (km^{2}) | 603,628 | 357,386 | 1,099,000 |

Length of paved roads (km) | 78,660 | 45,395 | 31,216 |

Population (thousand people) | 49,980 | 83,020 | 11,350 |

Hexagon area (km^{2}) | 1000 | 1000 | 1000 |

Number of hexagons | 710 | 429 | 1190 |

Script execution time (s) | 2694 | 1652 | 2435 |

TP < 0.5 (very low) (%) | 11 | 11 | 60 |

TP = (0.5 ÷ 0.625) (low) (%) | 14 | 10 | 23 |

TP = (0.625 ÷ 0.8) (average) (%) | 63 | 67 | 17 |

TP = (0.8 ÷ 0.875) (high) (%) | 12 | 10 | – |

TP = (0.875 ÷ 1) (very high) (%) | – | 2 | – |

Density of roads (km/km^{2}) | 0.130 | 0.127 | 0.028 |

Coefficients of Engel (K_{E}) | 14.3 | 8.3 | 8.8 |

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**MDPI and ACS Style**

Karpinski, M.; Kuznichenko, S.; Kazakova, N.; Fraze-Frazenko, O.; Jancarczyk, D. Geospatial Assessment of the Territorial Road Network by Fractal Method. *Future Internet* **2020**, *12*, 201.
https://doi.org/10.3390/fi12110201

**AMA Style**

Karpinski M, Kuznichenko S, Kazakova N, Fraze-Frazenko O, Jancarczyk D. Geospatial Assessment of the Territorial Road Network by Fractal Method. *Future Internet*. 2020; 12(11):201.
https://doi.org/10.3390/fi12110201

**Chicago/Turabian Style**

Karpinski, Mikolaj, Svitlana Kuznichenko, Nadiia Kazakova, Oleksii Fraze-Frazenko, and Daniel Jancarczyk. 2020. "Geospatial Assessment of the Territorial Road Network by Fractal Method" *Future Internet* 12, no. 11: 201.
https://doi.org/10.3390/fi12110201