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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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Fractal of DNA sequence data
Nedvěd, Jiří ; Čech, Petr (referee) ; Valla, Martin (advisor)
This project is looking for fractal structury in DNA sequence data, which be maped in square ACGT. First, this project is introduced in problematics of fractals and targeted on making of Sierpinski gasket. Second, the project is introduced in DNA and DNA sequence. Next is sketched now known fractal’s structures in DNA sequence data or fractal’s structure closed DNA sequence. Then will changed metod chaos game of Sierpinski gasket to square ACGT, in where will drawen map of DNA sequences. Next, these pictures will processed by Box Counting Method and Power Spectrum Method.
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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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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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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
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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Fractal of DNA sequence data
Nedvěd, Jiří ; Čech, Petr (referee) ; Valla, Martin (advisor)
This project is looking for fractal structury in DNA sequence data, which be maped in square ACGT. First, this project is introduced in problematics of fractals and targeted on making of Sierpinski gasket. Second, the project is introduced in DNA and DNA sequence. Next is sketched now known fractal’s structures in DNA sequence data or fractal’s structure closed DNA sequence. Then will changed metod chaos game of Sierpinski gasket to square ACGT, in where will drawen map of DNA sequences. Next, these pictures will processed by Box Counting Method and Power Spectrum Method.
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