The bachelor thesis focuses on a fractal and calculation of its dimensions. Three non-integer dimensions were selected after consulting the supervisor of this thesis - counting dimension, correlation dimension and lacunarity.
The theoretical part deals with the description of fractal, fractal dimensions and the method of calculating the dimensions. The review part contains the use of these dimensions in practical problems of geography.
The practical part calculates the fractal dimension of the socio-economic data (roads and houses). A total of 18 towns in the Czech Republic with the population between 50,000 and 170,000 inhabitants were selected. Data was provided by the German Geofabrik server that provides data only in shp. format. Algorithms take into account only the matrix so data had to be converted to a raster format in ArcGIS 10.1 program before the calculations.
Some of the algorithms of selected fractal dimensions were created and some modified from the MathWorks website. All the algorithms are written in Matlab code. The thesis comprises of 108 calculations. The final task was to determine whether there is any correlation between the dimensions. The Calculation of correlation conducted in the RStudio program. Other statistical calculations were carried out in Microsoft Office 2007.
The calculations are written in a set of charts and graphs. All results and scripts are available on the website of the Department of Geoinformatics in Olomouc in the appendix on DVD
Keywords: lacunarity,correlation dimension, box counting