Presentation from Third InDOG Doctoral Conference in Olomouc, Czech Republic. 13. - 16. October 2014

1. FRACTAL DIMENSION
OF THE CZECH ROAD NETWORK
www.geoinformatics.upol.cz
Vít PÁSZTO
vit.paszto@gmail.com
Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc,
Czech Republic

2. PRESENTATION SCHEDULE
• Introduction
• Methods & Data
• Results (a lot of…)
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3. INTRODUCTION
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Source: ucl.ac.uk
John O‘Keefe
(Nobel Prize in Physiology or Medicine)

4. INTRODUCTION
• What are fractals?
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5. INTRODUCTION
• Do we live in a fractal world?
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6. INTRODUCTION
• „Clouds are not spheres, mountains are not cones
and lightning does not travel in a straight line“
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B. Mandelbrot
X

7. FRACTAL GEOMETRY
• Descriptive tool for the Chaos theory
• „Fractal“ firstly used by B. Mandelbrot in 1975 *
• Fractus = broken
• Accurate description of real objects
• For complexity measures
• Fractal dimension (FD):
– Non-integer dimension (1.25 D; 2.56 D, etc.)
– More complex object  higher fractal dimension
– Extreme cases – „classic“ Euclidean dimension
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8. WHAT I DID?
Road network
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Procedures
&
software

9. DATA & METHODS
• Data
– Road network of the Czech Republic (Data200 from COSMC)
– From highways to 3rd class roads
• Methods of FD estimation:
1) Box-counting method
• Boxes/cells covering the object
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10. DATA & METHODS
• Data
– Road network of the Czech Republic (Data200 from COSMC)
– From highways to 3rd class roads
• Methods of FD estimation:
1) Box-counting method
• Boxes/cells covering the object
www.geoinformatics.upol.cz

11. DATA & METHODS
2) General FD estimation
• Applied directly on vector data
• FD estimated for every single polyline
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d

12. PROCEDURES & SOFTWARE
A) „Within GIS“ procedure (ArcGIS for Desktop
and RStudio)
• Using box-counting method
B) Hawth‘s Tools for ArcGIS for Desktop
• Using general FD estimation
C) Fractalyse
• Using box-counting method
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13. A) „Within GIS“
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14. B) Hawth‘s Tools
• Hawthorne Beyer (University of Queensland, AU)
• Spatialecology.com
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15. C) Fractalyse
• Gilles Vuidel (Université de Franche-Comté)
• Fractalyse.org
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16. RESULTS – A)
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17. RESULTS – A)
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18. RESULTS – A)
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19. RESULTS – A)
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20. RESULTS – A)
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21. RESULTS – B)
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22. RESULTS – B)
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23. RESULTS – B)
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24. RESULTS – B)
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25. RESULTS – C)
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26. RESULTS – C)
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27. RESULTS – C)
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28. RESULTS
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29. RESULTS
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Hawth‘s tools FD histogram

30. RESULTS
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Average FD

31. FRACTAL DIMENSION
OF THE CZECH ROAD NETWORK
www.geoinformatics.upol.cz
Vít PÁSZTO
vit.paszto@gmail.com
Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc,
Czech Republic