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Fractal Dimension Analysis And Fractal Properties of Financial Markets
Jedličková, Marie
Financial markets are a subject of many studies and research purposes. The ability to correctly observe and describe the dynamics of financial markets would mean the possibility to predict its future behaviour. Many approaches and methods have been used to achieve this objective. In recent history it has come to light that many natural phenomena could be described using fractal geometry. Alongside with the fractals can be often found the application of fuzzy logic and also the theory of chaos. These three concepts are recently very powerful in describing complex system and getting closer to understanding them. This paper deals with the basic concepts of fractal analysis and also fuzzy logic and the possibility to use those to observe financial markets and analyze their behaviour. The purpose of this is to present the reader with introduction to the problematics and propose starting concepts to begin the research into the matter.
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LEGO Mindstorms: Didactic utilization in mathematics with a focus on fractals
Čadek, Jan ; Jančařík, Antonín (advisor) ; Pilous, Derek (referee)
TITLE: LEGO Mindstorms: Didactic utilization in mathematics with a focus on fractals ABSTRACT: The objective of this thesis is to determine whether the teaching of fractal geometry supported by computer and robotic LEGO Mindstorms NXT has its place in the education of primary and secondary schools pupils in the Czech Republic. The theoretical part focuses on key topics and personalities closely connected to fractal geometry problematics. It provides a brief historical overview of the fractal geometry development, its potential use in teaching mathematics (with reference to Turkish curriculum documents), and a description of LEGO Mindstorms NXT which can well serve as a manual for teachers and pupils. The practical part contains instructions for building a robotic turtle as well as a proposal of teaching block aimed to support pupils' algorithmic and geometric thinking including key competencies. Quantitative comparison of the results taken from Turkish studies and evaluation of the project by the author and pupils are a part of the experiment as well. KEYWORDS: LEGO Mindstorms NXT, fractal, programming, Logo, learning by doing, turtle, Papert, L-system, microworlds
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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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Fractal pattern patch antenna
Prouza, Jakub ; Pítra, Kamil (referee) ; Raida, Zbyněk (advisor)
This bachelor thesis deals with the application of fractal layouts in the design of microstrip antennas. Attention is turned to assessing their impact on properties of a conventional patch antenna. The first part of thesis is focused on theoretical knowledge of fractal geometry and planar antennas. In the next part of this thesis, first antenna is describer together with ways of its design. In the final section, next fractal antenna design is given. Proposed antenna is made, the results obtained are compared and benefits of the fractal design are evaluated.
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Transcendental aspects of architectural design as factors of sustainability
Volnohradský, Radan ; Peřinková, Martina (referee) ; Loutocká, Vlasta (referee) ; Uřídilová, Marcela (referee) ; Urbášková, Hana (advisor)
This thesis deals with complex processes, relationships and phenomena which go beyond the assumed and accepted materialistic perception of the world in general and the process of architectural design specifically. It clarifies and actually redefine the sustainability from a point of higher universal principles forming our environment. At the beginning this thesis presents an extensive knowledge base of existing holistic design systems including Feng-shui, sacred geometry, geomancy or numerology. The purpose is to build and establish a solid foundation for understanding and further research as well as objectively interpreting lesser known topics as a whole. On the basis of intersecting information through the above mentioned topics we specify the hypothesis which proposes the pre-existence of one unifying design matrix of harmonic structures in architecture. The structure of its verification takes us from an analysis of the science of human perception to systems of self-similar contextual references of animated and inanimated forms. These systems of emergent form and flow are basically known as fractals, and could be expressed in both mathematical and geometrical languages. The thesis research then consists of analysing chosen examples of urban and architectural scale in sense of fractality, symbolism and geometrical matrices. We include and integrate the research of associated and relevant phenomena in pedagogical practice, and a case study of the application of fractals in development of a chosen town. From the results of this thesis we abstract five non-dogmatic guidelines or tenets for architectural design; which are supported by experimental verification on some of the author´s buildings. These tenets stand as pillars of implosive architecture. This kind of architecture in context of transcendental overlaps means a possibility of how to bring our anthropogenic environment closer to the natural and harmonic code of the Universe.
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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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Hypertextury v JaGrLib
Bártová, Kristina ; Pelikán, Josef (advisor) ; Pavlík, Ivo (referee)
The object of this work is to implement and test ray marching algorithm in graphical library JaGrLib. Through the use of this algorithm, we will be able to render hypertextures - objects with very complex surface or with not well defined boundary surface. In this project we will make use of already implemented ray tracing algorithm, which we will extend to the march method. Ray marching will be tested on soft objects and the functions used to create hypertextures will be defined by noise and fractal functions.
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Visual Educational System of Fractals
Friedrich, Tomáš ; Škarvada, Jaroslav (referee) ; Gajda, Zbyšek (advisor)
The target of this work is to explain basics of fractals generation and theory. The introdaction to the fractal geometry is mentioned first. Certain types od fractals are explained and demostrated by examples next.For easier understanding of all mentioned types of fractals a grafical aplication was designed where it is possible to experience fractals characteristics and behaviour. The aplication is available on the internet.
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Space Filling Curves
Staňo, Marek ; Švub, Miroslav (referee) ; Šiler, Ondřej (advisor)
The objective of my work is introduce space filling curves, and try to generalize them to multidimensional spaces. Below are in the work informations about recursive and non-recursive solving of these curves, and usage curves in practice. The main objective is to create program which can draw these curves. Based on theory and practical knowledge I design program, which can compute the coordinates of the curve, and another program which uses these coordinates to draw the curve. To make this I will use programming language C and graphics library Gd.
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