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Dissertations / Theses on the topic 'Box counting fractal dimension'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Brandão, Daniela Teresa Quaresma Santos. "Dimensões fractais e dimensão de correlação." Master's thesis, Universidade de Évora, 2008. http://hdl.handle.net/10174/17740.

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O objetivo deste trabalho é o estudo da dimensão fractal, nomeadamente a dimensão de Hausdorff, dimensão de capacidade e dimensão de correlação, relacionando-as e efetuando o cálculo em alguns exemplos. Sempre que se considera indispensável, são apresentadas noções introdutórias para uma melhor compreensão dos conceitos analisados. O Capítulo 2 é dedicado ao estudo da dimensão de Hausdorff, introduzindo, previamente, uma noção de medida, de Hausdorff. No Capítulo 3 analisamos a dimensão de capacidade, suas propriedades e inconvenientes, relacionando, no final, esta dimensão com a dimensão de H

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2

Simonini, Marina. "Fractal sets and their applications in medicine." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8763/.

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La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici

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3

HUANG, KUAN-YU. "Fractal or Scaling Analysis of Natural Cities Extracted from Open Geographic Data Sources." Thesis, Högskolan i Gävle, Avdelningen för Industriell utveckling, IT och Samhällsbyggnad, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-19386.

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A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are ma

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4

Berlinkov, Artemi. "Dimensions in Random Constructions." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3160/.

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We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.

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5

Le, Huy. "Numerické metody měření fraktálních dimenzí a fraktálních měr." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417160.

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Tato diplomová práce se zabývá teorií fraktálů a popisuje patričné potíže při zavedení pojmu fraktál. Dále se v práci navrhuje několik metod, které se použijí na aproximaci fraktálních dimenzí různých množin zobrazených na zařízeních s konečným rozlišením. Tyto metody se otestují na takových množinách, jejichž dimenze známe, a na závěr se výsledky porovnávají.

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6

ZANINI, ALESSANDRO. "Analisi dei dati da emissione acustica per la valutazione del danneggiamento strutturale." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/686.

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Viene studiata una nuova metodologia di diagnostica, basata sull’analisi di dati derivanti dall’Emissione Acustica (EA), per lo studio della nucleazione e della propagazione di difetti durante prove di laboratorio su provino sotto carico e serbatoi in pressione. L’applicazione dell’analisi frattale al segnale di EA risulta particolarmente efficace e permette di identificare la distribuzione spaziale delle sorgenti stesse, esplicitandone la correlazione tra gli eventi. E’ così possibile ottenere molte informazioni associate al danneggiamento dei differenti casi studiati. L’intensità della solle

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7

Dathe, Annette. "Digitale Bildanalyse zur Messung fraktaler Eigenschaften der Bodenstruktur." Doctoral thesis, [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=965898083.

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8

Leifsson, Patrik. "Fractal sets and dimensions." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7320.

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<p>Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.</p><p>In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and com

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9

Fraser, Jonathan M. "Dimension theory and fractal constructions based on self-affine carpets." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3869.

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The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively well-understood world of self-similar sets and the far from understood world of general self-affine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, an

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10

Wang, Nancy. "Fractal Sets: Dynamical, Dimensional and Topological Properties." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-233147.

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Fractals is a relatively new mathematical topic which received thorough treatment only starting with 1960's. Fractals can be observed everywhere in nature and in day-to-day life. To give a few examples, common fractals are the spiral cactus, the romanesco broccoli, human brain and the outline of the Swedish map. Fractal dimension is a dimension which need not take integer values. In fractal geometry, a fractal dimension is a ratio providing an index of the complexity of fractal pattern with regard to how the local geometry changes with the scale at which it is measured. In recent years, fracta

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11

Sant'anna, Douglas Azevedo. "Derivadas fracionárias, funções contínuas não diferenciáveis e dimensões." reponame:Repositório Institucional da UFABC, 2009.

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12

Nedvěd, Jiří. "Zpracování genomických signálů fraktály." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2012. http://www.nusl.cz/ntk/nusl-219634.

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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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13

Fuhrmann, G., M. Gröger, and T. Jäger. "Non-smooth saddle-node bifurcations II: Dimensions of strange attractors." Cambridge University Press, 2018. https://tud.qucosa.de/id/qucosa%3A70708.

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We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.

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14

Grierson, Greg Michael Jr. "Analysis of Amur honeysuckle Stem Density as a Function of Spatial Clustering, Horizontal Distance from Streams, Trails, and Elevation in Riparian Forests, Greene County, Ohio." Wright State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=wright1621942350540022.

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15

Archer, Kassie. "Box-counting dimension and beyond /." 2009. http://hdl.handle.net/10288/1259.

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16

Liao, Yu-Jie, and 廖昱杰. "Vessel Box Counting Dimension of Chicken Chorioallantoic Image." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/89613802283699986031.

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碩士<br>國立中興大學<br>資訊管理學系所<br>104<br>Cancer has been the leading first of - first ten causes of death in humans in the past ten years. Many researchers have invested in the cancer experiments in order to find the cure for cancer. Because cancer cells have to rely on oxygen and nutrients in biological vessel to survive, researchers usually need small animals for experimental sample (for example: rabbits, mouses, etc ….), put cancer cells into the small animals’ bodies to make them infected, inject the experimental drug and observe the changes in blood vessels to determine whether the experimental

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17

Wang, Shih-Chieh, and 王世杰. "An Iris Recognition System Based on Fractal Analysis Using Entropy-Box-Counting Method." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/25837290551313309088.

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碩士<br>中興大學<br>資訊科學系所<br>95<br>In this thesis, we propose a new method of fractal analysis using entropy-box-counting (EBC) for automatic iris recognition. First, the annular iris image is normalized into a rectangular iris image and divided into forty-eight blocks. We calculate the fractal dimension values for these image blocks and then concatenate all these features together as the iris feature vector. The similarity of two irises can be measured by the spatial distance. We use the Minimum Distance Classifier (MDC) to determine whether two irises belong to the same class. Experimental result

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18

Wen-Chau, Wu, and 吳文超. "Limitations of box counting fractal analysis on digital images using automated computer analysis: Examples on biomedical applications." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/00484063358868564845.

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博士<br>國立臺灣大學<br>電機工程學研究所<br>91<br>Morphometric analysis is important in the assistance of differential diagnoses in histopathology. However, for morphologically complicated biological structures, description of texture using conventional Euclidean geometry has been difficult because the estimation of shape parameters such as area or perimeter may vary significantly with the magnification at which the specimen examinations are performed. Examples include colorectal polyps, epithelial lesions in the oral cavity, breast cancer on mammograms, or tumor vasculature. The search for an objective me

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19

Lavoie, François. "Écoulements granulaires par avalanches : indices de fluidité, fractales et multifractales." Thèse, 2004. http://hdl.handle.net/1866/15619.

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20

Vaughan, Josephine. "Measuring Fallingwater: a computational fractal analysis of Wright’s Kaufman House in the context of his theories and domestic architecture." Thesis, 2017. http://hdl.handle.net/1959.13/1353331.

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Research Doctorate - Doctor of Philosophy (PhD)<br>Sited above a waterfall on Bear Run stream, in a wooded gulley in Mill Run, Pennsylvania, the Kaufman house, or Fallingwater as it is commonly known, is one of the most famous buildings in the world. This house, which Frank Lloyd Wright commenced designing in 1934, has been the subject of enduring scholarly analysis and speculation for many reasons, two of which are the subject of this dissertation. The first is associated with the positioning of the design in Wright’s larger body of work. Across 70 years of his architectural practice, most of

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21

Śpiewak, Adam. "Geometric properties of measures in finite-dimensional dynamical systems." Doctoral thesis, 2020. https://depotuw.ceon.pl/handle/item/3779.

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Poniższa rozprawa składa się z dwóch części. Obie z nich badają geometryczne własności miar występujących w skończenie wymiarowych układach dynamicznych, głównie z punktu widzenia teorii wymiaru. Część pierwsza dotyczy probabilistycznych aspektów twierdzenia Takensa o zanurzaniu, zajmującego się zagadnieniem rekonstrukcji układu dynamicznego z ciągu pomiarów wykonanych za pomocą jednowymiarowej obserwabli. Klasyczne wyniki z tej dziedziny orzekają, że dla typowej obserwabli, dowolny stan początkowy układu jest jednoznacznie wyznaczony przez ciąg pomiarów, o ile ich ilość przekracza dwukrotnie

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