|
| |
|
|
Hausdorff dimension of the lightning
Kočendová, Alžběta ; Druckmüller, Miloslav (referee) ; Hoderová, Jana (advisor)
In this thesis, the theory related to the Hausdorff dimension is described. The Hausdorff dimension is used to describe the fragmentation of a fractal. Fractals include many natural objects and phenomena. One such phenomenon is lightning, which is the focus of this work. This work involves the development of a MATLAB program to detect lightning in an image and then calculate the Hausdorff dimension of this lightning.
|
|
|
Hausdorff dimension of certain sets
Vaněček, Ondřej ; Zelený, Miroslav (advisor) ; Spurný, Jiří (referee)
In the thesis we pursue the term Hausdorff measure and dimension. Hausdorff measure is a non-negative quantity, which in a certain way distinguishes among sizes of sets. Using it we define the term Hausdorff dimension, which is useful at studying fractals. These are distinct from other sets by the value of their dimen- sion. By an example of Cantor set we demonstrate the existence of sets, whose dimension in not an integer. Afterwards, we construct a complex theory on the basis of the defined terms, according to which we reach a simple formula allowing us to estimate Hausdorff dimension using an easier method. In conclusion we pay attention to another fractal, Koch curve.
|
|
|
Impossible sets
Silber, Zdeněk ; Pražák, Dalibor (advisor) ; Zelený, Miroslav (referee)
In this work we de fine Hausdorff measure and dimension, describe the geometrical construction of a Besikovitch set and adapt this approach to construct a Kakeya set. We also describe another construction of a Besicovitch set using the properties of projections of irregular sets. Finally we present other examples of "impossible sets". Powered by TCPDF (www.tcpdf.org)
|
|
| |
guest ::
