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Fractals and Their Applications in Computer Graphics
Tesař, Martin ; Čermák, Martin (referee) ; Koutný, Jiří (advisor)
First part of this bachelors thesis consists of fractal theory, Hausdorff dimension and their applications in computer graphics. In second part is choosen idea for application. It is interactive creation of flame fractals. In this section, there is defined mathematical system of iterated functions, that is the heart of flame fractals. After mathematical examination follows analysis of original algorithm for creation of flame fractals. Thesis continues with methods for image improvement and suggests new enhancements.
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Fractals in Computer Graphics
Šelepa, Jan ; Venera, Jiří (referee) ; Sumec, Stanislav (advisor)
The goal of this work is to give introduction and specification of fractals. The first chapter presents the basics of fractal geometry. The second chapter maps the history of fractals and points out the most important people of fractal science. The third chapter presents fractal classification based on several criteria and gives basic examples. The fourth chapter is a summary of widely used applications for fractal creation. The last chapter describes the application that was made to demonstrate given algorithms and fractals mentioned in this thesis.
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Clouds and Hills Generation Using Fractal Geometry
Tůma, Petr ; Zuzaňák, Jiří (referee) ; Venera, Jiří (advisor)
This work is concerned with generation of landscape objects using fractal geometry. In this work is explained what the fractal is and terms associated with them. The other parts describe basic theoretical ideas and implementation of these algorithms. The Capital theme is generation of models clouds and hills in values of input parameters, their presentation and date media saved there. The project includes my algorithm extension for hills generation of course. At the conclusion of this work are summarized tendencies of next development and my results.
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Fractals in Computer Graphics
Heiník, Jan ; Španěl, Michal (referee) ; Herout, Adam (advisor)
This Master's thesis deals with history of Fractal geometry and describes the fractal science development. In the begining there are essential Fractal science terms explained. Then description of fractal types and typical or most known examples of them are mentioned. Fractal knowledge application besides computer graphics area is discussed. Thesis informs about fractal geometry practical usage. Few present software packages or more programs which can be used for making fractal pictures are described in this work. Some of theirs capabilities are described. Thesis' practical part consists of slides, demonstrational program and poster. Electronical slides represents brief scheme usable for fractal geometry realm lectures. Program generates selected fractal types. Thesis results are projected on poster.
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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.
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Fractals in Computer Graphics
Šelepa, Jan ; Venera, Jiří (referee) ; Sumec, Stanislav (advisor)
The goal of this work is to give introduction and specification of fractals. The first chapter presents the basics of fractal geometry. The second chapter maps the history of fractals and points out the most important people of fractal science. The third chapter presents fractal classification based on several criteria and gives basic examples. The fourth chapter is a summary of widely used applications for fractal creation. The last chapter describes the application that was made to demonstrate given algorithms and fractals mentioned in this thesis.
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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.
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