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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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Procedural Architecture
Roreček, Pavel ; Tóth, Michal (referee) ; Milet, Tomáš (advisor)
This Bachelor's thesis describes implementation of library used for procedural generating of architecture. The thesis describes way of handling input files containing rules and symbols. Generated model is shown using visual application that uses OpenGL library and the model can be exported.
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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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Procedural Generation of City Topology
Zvěřina, Lukáš ; Navrátil, Jan (referee) ; Láník, Aleš (advisor)
This bachelor's thesis is about problematique of procedural modeling. It especially tatgets procedural generation of city topology, using fractal geometry, rewriting gramatics using L-systems, OpenGL library for displaying scene and detailed description of approaches in texturing, lighting and other graphics effects.
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Generating Procedural Terrains
Petlan, Michael ; Bartoň, Radek (referee) ; Přibyl, Jaroslav (advisor)
This thesis deals with algorithms of stochastic generating of height maps. The thesis describes the basic theoretical knowledge and extends it by usage of L-systems for generating a network of rivers. There has been implemented a library of the height map generating algorithms and a demo application within the thesis.
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Procedural Forest
Pfudl, Václav ; Kobrtek, Jozef (referee) ; Milet, Tomáš (advisor)
The main goal of this bachelor's thesis is to generate procedurally a forest (landscape with plants described in text template). Landscape is generated using Perlin noise and the interpret of L-systems was implemented for plants generation purposes. Both these techniques are described in more detail in theory section as well as the implementation section of this thesis. Furthermore, techniques such as phong lightning model, normal-mapping, shadow-mapping, realistic water, skybox and spriting for better realistic look of the scene, are also discussed in this thesis. Implemented application can also be used for the export of generated plant models in format .obj for further use by some extern application (for example Blender).
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L-Systems and Their Applications in Computer Graphics
Sojma, Zdeněk ; Čermák, Martin (referee) ; Koutný, Jiří (advisor)
This Bachelor's thesis describes deterministic context-free L-systems (D0L-systems), which function is parallel rewriting symbols in string for purpose of modeling plant-like structures, mainly plant leaves. Next it shows how to use such L-systems in computer graphics and explains usage of stochastic L-systems. They effect topology and geometry of plant by randomizing interpretation of the L-system and allow us to generate whole class of respectively different but still simile leaves. L-system interpreter is implemented in .NET framework with OpenGL library.
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Procedurally Generated City
Panáček, Petr ; Šolony, Marek (referee) ; Kajan, Rudolf (advisor)
This paper deals with problem of procedurally generated city. There are described steps of creation of city. These steps are: road generation, extraction of minimal cycles in graph, division of lots and generation of buildings. Road and buildings are generated by L-system. Our system generate a city from input images, such as height map, map of population density and map of water areas. Proposed approaches are used for implementation of application for generation of city.
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Multigrammars and Parsing Based on Them
Fiala, Jiří ; Lukáš, Roman (referee) ; Meduna, Alexandr (advisor)
This document deals with introduction focused on pragmatically oriented research at branch of theoretical computer science and with presentation of designed methods for chosen application topics. At this study the theoretical subject is represented by kind of generative system - multisequential grammar and application topics are chosen according to possibilities supported by multisequential grammars. In order to follow results published by Thompson (see [9]), Lindenmayer (see [26]), Mandelbrot (see [8]) and also studies published by Morneau (see [17]), which shows the relation between natural laws and human discipline - mathematics, we study the applications of multi-sequential grammars from two points of view: generative L-systems (which further includes applications of fractal geometry and biomathematics) and natural language processing (which further includes the design of proper abstract language). Some problems related to compiler construction are also mentioned.
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