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Processing of fractal genomic signals
Nedvěd, Jiří ; Provazník, Ivo (referee) ; Valla, Martin (advisor)
This diploma project is showen possibilities in classification of genomic sequences with CGR and FCGR methods in pictures. From this picture is computed classificator with BCM. Next here is written about the programme and its opportunities for classification. In the end is compared many of sequences computed in different options of programme.
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The Manual
Klusová, Katarína ; Houser, Milan (referee) ; Rathouský, Luděk (advisor)
A mixture of symbols, authorities and theories that man need´s to absorb nowdays, is source for many confusing manuals, how to deal with our life, make decisions, or which political party to vote. Exactly the same time, these symbols of authority and theories are an essential part of our culture and education, and that they are looking for inspiration, information and explanations. Sometimes I dream that my source of information is nothing more than nature and its observations. In a utopian world without information provided by them I watched the world at my own pace, subsequently walking from one information to another.In the real world from different disciplines, which explore the universe in great detail, vast quantities of information flows, which the ordinary man in his level is not capable scientificly understand. For instance, when I read about Hawking's paradox, I can imagine how it's probably meant, but I don´t understand the calculations, and resources .. Well anyway, I add this information to my concept of understanding space and black holes. I perceive universe through intuition and its fragments-specific expression of the universe- I perceive through reason. The first series is a picture of my view of the universe by means of symbols - codes that people agreed use- to communicate the inexpressible. Universe is still on the eyes, and whenever I start to deal with its sub-parts, I can recognize its wholeness . Other pictures are formulation and development of selected key topics of the universe (according to my personal priorities).At this point, my work is mainly based on switching between a total and detail. What happens to the "collection" image, and affects other images detail. The last image of the series is once again the image of the wholeness . The spiral development to the second floor above the first image. Projecting the universe through me will be images transformation. Picture, even it is symbolic and symbolizing, is forming to kind of logo. Moreover, It occurs the same logo as a symbol of the universe mirroring by my being. Universe in the universe. Microcosm in the macrocosm. My individuality in the universe. Fractal.
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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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Analysis of chaotic behavior in double pendulum
Brázda, Tomáš ; Lošák, Petr (referee) ; Sosna, Petr (advisor)
This thesis deals with the presentation of basic knowledge regarding chaos theory. There are mentioned several basic methods of dimension calculation as well as the overall use of this theory in various scientific disciplines. The main part is devoted to the complete analysis of a double pendulum. To initiate into the issue, this situation was outlined on a simple mathematical basis pendulum. There is derived a numeral system of two differential equations of second order to work with the double pendulum. Thanks to computer program Matlab there was created a fractal that represents chaotic behavior of the double pendulum. Knowledge acquired from dimension calculation was used here to classify the fractal and to work out its dimension. In addition there was analyzed impact of parameters of behavior in system. This overall chaotic behavior has been verified by the largest Lyapunov exponent and the 0–1 test, which identified areas, where this system behaves chaotically and where it is stable.
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Fractal Analysis of Track Geometry
Nejezchlebová, Jitka ; Holcner, Petr (referee) ; Svoboda, Richard (advisor)
The master’s thesis deals with the fractal analysis of track geometry. The theoretical part is primarily focused on introducing the basics of fractal geometry. There is also concisely described the current methodology for evaluating track geometry. In the practical part is verified the accuracy of the methods for determining the fractal dimension of the curve. For different curves with the same standard deviation is calculated the fractal dimension to demonstrate the possible advantages of using this analysis. Further is researched the use of the fractal dimension for the analysis of track geometry data. All mathematical procedures are done using the MATLAB system.
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Procedurally Generated Landscape in Fragment Shader
Leitner, Denis ; Milet, Tomáš (referee) ; Chlubna, Tomáš (advisor)
This thesis deals with rendering of procedurally generated landscape without the use of input geometry or textures. It describes techniques for generation and realistic rendering of natural outdoor scenes. These techniques include terrain generation and realistic atmosphere and cloud rendering. Thesis also describes the use of raymarching for terrain and shadow rendering and realistic lighting for terrain which includes ambient and indirect light approximation.
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L-systems online
Fišer, Marek ; Pelikán, Josef (advisor) ; Mráz, František (referee)
An L-system in its simplest form is a variant of a context-free grammar. Originally, L-systems were developed and are still mainly used for modeling plant growth, though with L-systems it is possible to create general fractals, models of towns or even music. However, anyone interested in L-systems and wanting to experiment with them may have difficulty finding an appropriate application. The goal of this work was to create an online system, suitable for a wide range of users, for working and experimenting with L-systems. The resulting solution consists of two parts. The first part is a universal, easily-expandable library for processing L-sys- tems. Expandability is achieved thanks to its modularity. All input is processed through interconnected components that are specialized in particular activities. The specialization of the components also contributes to the clarity and reliability of the whole processing system. The library is independent and multiplatform and can thus be readily used in other applications. The second part consists of a modern web interface designed to be under- standable for beginners and yet also capable of providing advanced features for more advanced users. Part of the site is a gallery of L-systems to which each user can contribute and which thus helps to create a user-community. The...
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A guide to fractal geometry
Hajmová, Kateřina ; Pokorný, Dušan (advisor) ; Boček, Leo (referee)
This text is intended for the general public. The aim of this work is acquaint readers with foundations of the fractal geometry. The thesis explains important terminology, such as the coastline paradox or the fractal dimension. A great emphasis is placed on explaining the concept of the box-counting dimension. The thesis includes the construction methods of the L-systems, IFS, TEA and random fractals. In addition, it shows the use of fractal geometry in practice. The text is completed with illuminating figures drawn in most cases in Geogebra software and Wolfram Mathematica.
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