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Dissertations / Theses on the topic 'Tiling (mathematics)'

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Published: 4 June 2021

Last updated: 24 February 2023

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1

Gupta, David (David Gregg) 1969. "Some tiling moves explored." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50012.

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2

Pachter, Lior 1973. "Domino tiling, gene recognition and mice." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85308.

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3

Persons, Michael Joseph. "Methods for creating corner colored Wang tiles." Pullman, Wash. : Washington State University, 2010. http://www.dissertations.wsu.edu/Thesis/Spring2010/m_persons_041210.pdf.

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Thesis (M.S. in computer science)--Washington State University, May 2010.<br>Title from PDF title page (viewed on May 18, 2010). "School of Engineering and Computer Science." Includes bibliographical references (p. 104-106).

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4

Hillman, Chris. "Sturmian dynamical systems /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5806.

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5

Son, Younghwan. "Some results on joint ergodicity, sets of recurrence and substitution and tiling systems." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1369046202.

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6

Yu, Xiaojiang Gabardo Jean-Pierre. "Wavelet sets, integral self-affine tiles and nonuniform multiresolution analyses." *McMaster only, 2005.

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7

Nielsen, Mark J. "Tilings of topological vector spaces /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5763.

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8

Savinien, Jean P. X. "Cohomology and K-theory of aperiodic tilings." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24732.

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Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008.<br>Committee Chair: Prof. Jean Bellissard; Committee Member: Prof. Claude Schochet; Committee Member: Prof. Michael Loss; Committee Member: Prof. Stavros Garoufalidis; Committee Member: Prof. Thang Le.

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9

Praggastis, Brenda L. "Markov partitions for hyperbolic toral automorphisms /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5773.

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10

Laperriere, Christiane. "Positive cocycles for minimal Zd-actions on a cantor set resulting from cut and project schemes: The octogonal tiling." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28269.

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We study the cut and projection method, which is a way to construct tilings. This construction leads to a minimal Zd -action on the Cantor set. In this thesis, we will focus our attention on two examples that we will describe in full details. the Fibonacci tiling on R and the octogonal tiling on R2 . For the octogonal tiling, we find small strictly positive cocycles for the minimal action on specific cones of Z2 .

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11

Karpenko, Daria. "Self-assembly of Self-similar Structures by Active Tiles." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4095.

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The natural capacity of DNA for molecular self-assembly has already been exploited to create DNA based tiles which can self-assemble into nano-scale arrays and carry out nano-scale computation. Thus far, however, all such self-assembly has been passive, in the sense that the binding capacities of a tile are never altered throughout the assembly. The idea of active tiles, tiles that can send signals to each other and activate latent binding sites, has been proposed but never incorporated into a formal model. Here, I present an extension of the existent abstract tile assembly model by defining a

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12

Lightcap, Andrew. "Minimum Degree Conditions for Tilings in Graphs and Hypergraphs." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/111.

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We consider tiling problems for graphs and hypergraphs. For two graphs and , an -tiling of is a subgraph of consisting of only vertex disjoint copies of . By using the absorbing method, we give a short proof that in a balanced tripartite graph , if every vertex is adjacent to of the vertices in each of the other vertex partitions, then has a -tiling. Previously, Magyar and Martin [11] proved the same result (without ) by using the Regularity Lemma. In a 3-uniform hypergraph , let denote the minimum number of edges that contain for all pairs of vertices. We show that if , there exists

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13

Dietert, Grant. "An integer linear programming formulation for tiling large rectangles using 4 x 6 and 5 x 7 tiles /." Online version of thesis, 2010. http://hdl.handle.net/1850/12275.

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14

Colle, Cleber Fernando 1985. "Propriedades dinâmicas e ergódicas de shifts multidimensionais." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307026.

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Orientador: Eduardo Garibaldi<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-19T00:20:51Z (GMT). No. of bitstreams: 1 Colle_CleberFernando_M.pdf: 1068657 bytes, checksum: 78c9700800b05194ffcf66838581b081 (MD5) Previous issue date: 2011<br>Resumo: Focaremos sobre aspectos dinâmicos e ergódicos de shifts multidimensionais, atentando especialmente para suas relações com estados fundamentais e quase-cristais em reticulados. Por exemplo, em mecânica estatística, dado um potencial in

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15

Leskow, Lucila Helena Allan 1972. "Tesselações hiperbólicas aplicadas a codificação de geodésicas e códigos de fonte." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261081.

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Orientador: Reginaldo Palazzo Junior<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação<br>Made available in DSpace on 2018-08-18T16:51:18Z (GMT). No. of bitstreams: 1 Leskow_LucilaHelenaAllan_D.pdf: 2583405 bytes, checksum: 3161d9deabaa60a8965a9e3d20ff36aa (MD5) Previous issue date: 2011<br>Resumo: Neste trabalho apresentamos como contribuição um novo conjunto de tesselações do plano hiperbólico construídas a partir de uma tesselação bem conhecida, a tesselação de Farey. Nestas tesselações a região de Dirichlet é formada por polígonos h

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16

Bérard, Caroline. "Modèles à variables latentes pour des données issues de tiling arrays. Applications aux expériences de ChIP-chip et de transcriptome." Phd thesis, AgroParisTech, 2011. http://tel.archives-ouvertes.fr/tel-00656841.

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Les puces tiling arrays sont des puces à haute densité permettant l'exploration des génomes à grande échelle. Elles sont impliquées dans l'étude de l'expression des gènes et de la détection de nouveaux transcrits grâce aux expériences de transcriptome, ainsi que dans l'étude des mécanismes de régulation de l'expression des gènes grâce aux expériences de ChIP-chip. Dans l'objectif d'analyser des données de ChIP-chip et de transcriptome, nous proposons une modélisation fondée sur les modèles à variables latentes, en particulier les modèles de Markov cachés, qui sont des méthodes usuelles de clas

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17

Michel, Jean-Luc. "Polysimplices in euclidean spaces and the enumeration of domino tilings of rectangles." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209922.

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Nous étudions, dans la première partie de notre thèse, les polysimplexes d’un espace euclidien de dimension quelconque, c’est-à-dire les objets consistant en une juxtaposition de simplexes réguliers (de tétraèdres si la dimension est 3) accolés le long de leurs faces. Nous étudions principalement le groupe des symétries de ces polysimplexes. Nous présentons une façon de représenter un polysimplexe à l’aide d’un diagramme. Ceci fournit une classification complète des polysimplexes à similitude près. De plus, le groupe des symétries se déduit du groupe des automorphismes du diagramme. Il découle

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18

Bush, Albert. "Two Problems on Bipartite Graphs." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/72.

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Erdos proved the well-known result that every graph has a spanning, bipartite subgraph such that every vertex has degree at least half of its original degree. Bollobas and Scott conjectured that one can get a slightly weaker result if we require the subgraph to be not only spanning and bipartite, but also balanced. We prove this conjecture for graphs of maximum degree 3. The majority of the paper however, will focus on graph tiling. Graph tiling (or sometimes referred to as graph packing) is where, given a graph H, we find a spanning subgraph of some larger graph G that consists entirely of

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19

Stucky, Eric. "An Exposition of Kasteleyn's Solution of the Dimer Model." Scholarship @ Claremont, 2015. http://scholarship.claremont.edu/hmc_theses/89.

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In 1961, P. W. Kasteleyn provided a baffling-looking solution to an apparently simple tiling problem: how many ways are there to tile a rectangular region with dominos? We examine his proof, simplifying and clarifying it into this nearly self-contained work.

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20

Karpenko, Daria. "Active Tile Self-assembly and Simulations of Computational Systems." Scholar Commons, 2015. https://scholarcommons.usf.edu/etd/5519.

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Algorithmic self-assembly has been an active area of research at the intersection of computer science, chemistry, and mathematics for almost two decades now, motivated by the natural self-assembly mechanism found in DNA and driven by the desire for precise control of nanoscale material manufacture and for the development of nanocomputing and nanorobotics. At the theoretical core of this research is the Abstract Tile Assembly Model (aTAM), the original abstract model of DNA tile self-assembly. Recent advancements in DNA nanotechnology have been made in developing strand displacement mechanisms

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21

Alves, Alessandro Ferreira. "Análise dos emparelhamentos de arestas de polígonos hiperbólicos para a construção de constelações de sinais geometricamente uniformes." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261080.

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Orientador: Reginaldo Palazzo Junior<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação<br>Made available in DSpace on 2018-08-19T09:31:01Z (GMT). No. of bitstreams: 1 Alves_AlessandroFerreira_D.pdf: 1080224 bytes, checksum: 0748952c3176e9548151bec7e6d9c71d (MD5) Previous issue date: 2011<br>Resumo: Para projetarmos um sistema de comunicação digital em espaços hiperbólicos é necessário estabelecer um procedimento sistemático de construção de reticulados como elemento base para a construção de constelações de sinais. De outra forma, em co

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22

Bennett, Robert. "Fibonomial Tilings and Other Up-Down Tilings." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/84.

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The Fibonomial coefficients are a generalization of the binomial coefficients with a rather nice combinatorial interpretation. While the ordinary binomial coefficients count lattice paths in a grid, the Fibonomial coefficients count the number of ways to draw a lattice path in a grid and then Fibonacci-tile the regions above and below the path in a particular way. We may forgo a literal tiling interpretation and, instead of the Fibonacci numbers, use an arbitrary function to count the number of ways to "tile" the regions of the grid delineated by the lattice path. When the function is a combin

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23

Spreafico, Elen Viviani Pereira 1986. "Novas identidades envolvendo os números de Fibonacci, Lucas e Jacobsthal via ladrilhamentos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307509.

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Orientador: José Plínio de Oliveira Santos<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T02:14:38Z (GMT). No. of bitstreams: 1 Spreafico_ElenVivianiPereira_D.pdf: 1192138 bytes, checksum: 2b12cd351b94a0f2f7ec24fc172305c9 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho, colaboramos com provas combinatórias que utilizam a contagem e a q-contagem de elementos em conjuntos de ladrilhamentos com restrições. Na primeira parte do trabalho utilizamos os ladrilhamentos para demo

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24

Nieser, Matthias [Verfasser]. "Parameterization and tiling of polyhedral surfaces / Matthias Nieser." Berlin : Freie Universität Berlin, 2012. http://d-nb.info/1027308481/34.

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25

Lenngren, Nils. "k-uniform tilings by regular polygons." Thesis, Uppsala universitet, Algebra, geometri och logik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159395.

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26

Korn, Michael Robert 1978. "Geometric and algebraic properties of polyomino tilings." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16628.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.<br>Includes bibliographical references (p. 165-167).<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>In this thesis we study tilings of regions on the square grid by polyominoes. A polyomino is any connected shape formed from a union of grid cells, and a tiling of a region is a collection of polyominoes lying in the region such that each square is covered exactly once. In particular, we focus on two main the

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27

Knizel, Alisa. "Random tilings : gap probabilities, local and global asymptotics." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112900.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 119-125).<br>In the thesis we explore and develop two different approaches to the study of random tiling models. First, we consider tilings of a hexagon by rombi, viewed as 3D random stepped surfaces with a measure proportional to q-volume. Such model is closely related to q-Hahn orthogonal polynomial ensembles, and we use this connection to obtain results about the local behavior of this model. In terms of the q-Hahn ort

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28

Linnell, Joshua Randall. "Multilattice Tilings and Coverings." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8911.

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Let L be a discrete subgroup of \mathbb{R}^n under addition. Let D be a finite set of points including the origin. These two sets will define a multilattice of \mathbb{R}^n. We explore how to generate a periodic covering of the space \mathbb{R}^n based on L and $D$. Additionally, we explore the problem of covering when we restrict ourselves to covering \mathbb{R}^n using only dilations of the right regular simplex in our covering. We show that using a set D= {0,d} to define our multilattice the minimum covering density is 5-\sqrt{13}. Furthermore, we show that when we allow for an arbitrary nu

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29

Bugarin, Enrico Paolo [Verfasser]. "On quotient cohomology of substitution tiling spaces / Enrico Paolo Bugarin." Bielefeld : Universitätsbibliothek Bielefeld, 2014. http://d-nb.info/1053467478/34.

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30

Moustafa, Haïja. "Gap-labeling des pavages de type pinwheel." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2009. http://tel.archives-ouvertes.fr/tel-00509886.

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Dans cette thèse, nous montrons que le groupe de K-théorie $K_0$ de la $C^*$-algèbre associée aux pavages de type pinwheel est isomorphe à la somme de $\ZZ \oplus \ZZ^6$ et d'un groupe cohomologique $H$.\\ Cette $C^*$-algèbre est de plus munie d'une trace qui induit une application linéaire sur ce groupe de $K$-théorie.\\ Nous calculons explicitement l'image, sous cette application, du sommant $\ZZ \oplus \ZZ^6$, montrant que l'image de $\ZZ$ est nulle et que l'image de $\ZZ^6$ est contenue dans le module de fréquences des patchs du pavage de type pinwheel.\\ Nous montrons également que l'on p

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31

Mohammed, Soud. "Tilting and Relative Theories in Subcategories." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1825.

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<p>We show that, over an artin algebra, the tilting functor preserves (co)tilting modules in the subcategories associated to the functor. We also give a sufficient condition for the category of modules of finite projective dimension over an artin algebra to be contravariantly finite in the category of all finitely generated modules over the artin algebra. This is a sufficient condition for the finitistic dimension of the artin algebra to be finite [3].</p><p>We also develop relative theory and in certain subcategories of the module category over an artin algebra in the sense of [10,11]. We use

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32

Ricke, Charlotte [Verfasser]. "On tau-Tilting Theory and Perpendicular Categories / Charlotte Ricke." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1122193823/34.

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33

Manimala, Binoy James. "Mathematical modelling for the evaluation of a tiltwing aircraft." Thesis, Glasgow Caledonian University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287856.

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34

Ahmed, Bako. "Limit Shapes for qVolume Tilings of a Large Hexagon." Thesis, KTH, Matematik (Avd.), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-280758.

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Lozenges are polygons constructed by gluing two equilateral triangles along an edge. We can fit lozenge pieces together to form larger polygons and given an appropriate polygon we can tile it with lozenges. Lozenge tilings of the semi-regular hexagon with sides A,B,C can be viewed as the 2D picture of a stack of cubes in a A x B x C box. In this project we investigate the typical shape of a tiling as the sides A,B,C of the box grow uniformly to infinity and we consider two cases: The uniform case where all tilings occur with equal probability and the q^Volume case where the probability of a ti

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35

Razafindrazaka, Faniry H. [Verfasser]. "Quad Layout Generation and Symmetric Tilings of Closed Surfaces / Faniry H. Razafindrazaka." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1084634538/34.

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36

Nordenstam, Eric. "Interlaced particles in tilings and random matrices." Doctoral thesis, Stockholm : Matematik, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9834.

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37

Marks, Frederik [Verfasser], and Steffen [Akademischer Betreuer] König. "Interactions between universal localisations, ring epimorphisms and tilting modules / Frederik Marks. Betreuer: Steffen König." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2015. http://d-nb.info/1068810939/34.

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38

Jakobi, Tobias [Verfasser], Michael [Akademischer Betreuer] Baake, and Friedrich [Akademischer Betreuer] Götze. "Radial projection statistics: a different angle on tilings / Tobias Jakobi ; Michael Baake, Friedrich Götze." Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1137624329/34.

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Kolbe, Benedikt Maximilian [Verfasser], Myfanwy [Akademischer Betreuer] Evans, John [Akademischer Betreuer] Sullivan, Myfanwy [Gutachter] Evans, John [Gutachter] Sullivan, and Jean-Marc [Gutachter] Schlenker. "Structures in three-dimensional Euclidean space from hyperbolic tilings / Benedikt Maximilian Kolbe ; Gutachter: Myfanwy Evans, John Sullivan, Jean-Marc Schlenker ; Myfanwy Evans, John Sullivan." Berlin : Technische Universität Berlin, 2020. http://d-nb.info/1217326049/34.

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Whitaker, erica j. "Congruence and Noncongruence Subgroups of Γ(2) via Graphs on Surfaces". The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1321205804.

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Hlushchanka, Mikhail [Verfasser], Dierk [Akademischer Betreuer] [Gutachter] Schleicher, Keivan [Gutachter] Mallahi-Karai, Mario [Gutachter] Bonk, Volodymyr [Gutachter] Nekrashevych, Kevin M. [Gutachter] Pilgrim, Dylan [Gutachter] Thurston, and Daniel [Gutachter] Meyer. "Invariant graphs, tilings, and iterated monodromy groups / Mikhail Hlushchanka ; Gutachter: Dierk Schleicher, Keivan Mallahi-Karai, Mario Bonk, Volodymyr Nekrashevych, Kevin M. Pilgrim, Dylan Thurston, Daniel Meyer ; Betreuer: Dierk Schleicher." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2017. http://d-nb.info/1141379759/34.

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42

Thapper, Johan. "Combinatorial Considerations on Two Models from Statistical Mechanics." Licentiate thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10141.

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43

Julien, Antoine. "Complexité des pavages apériodiques : calculs et interprétations." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00466323.

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La théorie des pavages apériodiques a connu des développements rapides depuis les années 1980, avec la découvertes d'alliages métalliques cristallisant dans une structure quasi-périodique.Dans cette thèse, on étudie particulièrement deux méthodes de construction de pavages : par coupe et projection, et par substitution. Deux angles d'approche sont développés : l'étude de la fonction de complexité, et l'étude métrique de l'espace de pavages.Dans une première partie, on calcule l'asymptotique de la fonction de complexité pour des pavages coupe et projection, généralisant ainsi des résultats conn

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44

Front, Mathias. "Émergence et évolution des objets mathématiques en Situation Didactique de Recherche de Problème : le cas des pavages archimédiens du plan." Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10250/document.

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Étudier l'émergence de savoirs lors de situations didactiques non finalisées par un savoir préfabriqué et pré-pensé nécessite un bouleversement des points de vue, aussi bien épistémologique que didactique. C'est pourquoi, pour l'étude de situations didactiques pour lesquelles le problème est l'essence, nous développons une nouvelle approche historique et repensons des outils pour les analyses didactiques. Nous proposons alors, pour un problème particulier, l'exploration des pavages archimédiens du plan, une enquête historique centrée sur l'activité du savant cherchant et sur l'influence de la

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45

Zhang, Tianfang. "Machine learning multicriteria optimization in radiation therapy treatment planning." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-257509.

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In radiation therapy treatment planning, recent works have used machine learning based on historically delivered plans to automate the process of producing clinically acceptable plans. Compared to traditional approaches such as repeated weighted-sum optimization or multicriteria optimization (MCO), automated planning methods have, in general, the benefits of low computational times and minimal user interaction, but on the other hand lack the flexibility associated with general-purpose frameworks such as MCO. Machine learning approaches can be especially sensitive to deviations in their dose pr

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46

Benali, Abdelkader. "Comportement dynamique des butées hydrodynamiques." Poitiers, 1988. http://www.theses.fr/1988POIT2011.

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47

Funke, Frank. "Steuerung der Beinmotorik von Grillen durch ein Paar gravizeptiver Interneurone." Doctoral thesis, [S.l.] : [s.n.], 2004. http://webdoc.sub.gwdg.de/diss/2004/funke/funke.pdf.

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48

"Tiling of the integers." 2008. http://library.cuhk.edu.hk/record=b5893703.

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Leung, Fung Bun.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.<br>Includes bibliographical references (leaves 36).<br>Abstracts in English and Chinese.<br>Abstract --- p.i<br>Acknowledgement --- p.iii<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Tiling of Integers --- p.3<br>Chapter 2.1 --- General Assumptions --- p.3<br>Chapter 2.2 --- Periodicity of Tiling --- p.4<br>Chapter 2.3 --- Cyclotomic Polynomials --- p.5<br>Chapter 2.4 --- Equivalence --- p.10<br>Chapter 3 --- Theorems of Integer Tiles --- p.12<br>Chapter 3.1 --- Main Theorems --- p.12<br>Chapter 3.

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"Self-affine tilings, digit sets classification, and related problems." 2004. http://library.cuhk.edu.hk/record=b5892153.

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Abstract:

Cheung Wai-Man.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (leaves 62-64).<br>Abstracts in English and Chinese.<br>Abstract --- p.ii<br>Acknowledgement --- p.iv<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Fundamental Results of Self-Affine Tiles --- p.11<br>Chapter 2.1 --- Construction of self-affine tiles --- p.11<br>Chapter 2.2 --- The requirements of self-affine tiles --- p.14<br>Chapter 2.3 --- Tiling sets of self-affine tiles --- p.22<br>Chapter 3 --- Digit sets of Self-Affine Tiles --- p.42<br>Chapter 3.1 --- Inte

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Starling, Charles Benjimen. "Computation of the Ruelle-Sullivan map for substitution tilings." 2005. http://hdl.handle.net/1828/778.

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