LE, H. Numerické metody měření fraktálních dimenzí a fraktálních měr [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2020.
This thesis deals with possibilities of so called fractal dimension and fractal measure estimation. After its discovery, fractal geometry had many chances of advancement. In present, however, it is somewhat stagnant because research in this area is often based on incorrect mathematical background. This work draws attention to some of these errors, it introduces correct definition of terms fractal, fractal dimension, Hausdorff and grid dimension and measure. In accordance with the specified goal, the work describes the box counting method and the power function method which was puiblished only in 2014 and tests their accuracy on sets with a known fractal dimension. Author has done a lot of theoretical and experimental work. Work assignment was very difficult for author because fractal geometry is not taught at this school and the presented work is the result of self-study. Despite of this fact, the work goal was met in full. Student worked completely on her own, only a few consultations was realised. Submitted work has a high level in my opinion.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | B | ||
| Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry | A | ||
| Využitelnost výsledků v praxi nebo teorii | A | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | A | ||
| Práce s literaturou včetně citací | A | ||
| Samostatnost studenta při zpracování tématu | A |
I consider this master thesis to be a very well written and useful monograph dealing with fractal geometry and numerical methods of fractal dimension estimation. It contains both intuitive and rigorous approach to fractal geometry which makes the study of the text easy and straightforward. Some time ago fractal geometry was a very popular and trendy mathematical tool in many branches of natural sciences. Especially fractal dimension was used as a "measure" of chaotic behaviour. Unfortunately the mathematical approach was often incorrect and led to unreliable results which weakened the confidence in this theory. The main goal of this master thesis was to build a correct mathematical theory of fractals and a correct method of fractal dimension estimation. These goals were fully fulfilled. Numerical experiments on fractals with known fractal dimension are a usable guideline for choosing a suitable fractal dimension estimation method. I evaluate this master thesis as excellent.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | C | ||
| Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry | A | ||
| Využitelnost výsledků v praxi nebo teorii | B | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | A | ||
| Práce s literaturou včetně citací | A |
eVSKP id 125350