paszto - fractal dimension of the czech road network
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www.geoinformatics.upol.cz
FRACTAL DIMENSIONOF THE CZECH ROAD NETWORK
Vít PÁSZTOvit.paszto@gmail.com
Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic
www.geoinformatics.upol.cz
PRESENTATION SCHEDULE
• Introduction• Methods & Data• Results (a lot of…)
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INTRODUCTION
John O‘Keefe(Nobel Prize in Physiology or Medicine)
Source: ucl.ac.uk
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INTRODUCTION
• What are fractals?
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INTRODUCTION
• Do we live in a fractal world?
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INTRODUCTION
• „Clouds are not spheres, mountains are not cones and lightning does not travel in a straight line“
B. Mandelbrot
X
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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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WHAT I DID?
Road network
Procedures&
software
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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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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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DATA & METHODS
2) General FD estimation• Applied directly on vector data• FD estimated for every single polyline
d
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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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A) „Within GIS“
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B) Hawth‘s Tools
• Hawthorne Beyer (University of Queensland, AU)• Spatialecology.com
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C) Fractalyse
• Gilles Vuidel (Université de Franche-Comté)• Fractalyse.org
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RESULTS – A)
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RESULTS – A)
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RESULTS – A)
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RESULTS – A)
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RESULTS – A)
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RESULTS – B)
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RESULTS – B)
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RESULTS – B)
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RESULTS – B)
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RESULTS – C)
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RESULTS – C)
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RESULTS – C)
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RESULTS
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RESULTS
Hawth‘s tools FD histogram
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RESULTSAverage FD
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FRACTAL DIMENSIONOF THE CZECH ROAD NETWORK
Vít PÁSZTOvit.paszto@gmail.com
Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic
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