<div class="csl-bib-body">
<div class="csl-entry">Großkopf, P. (2020). <i>Intersecting the twin dragon with rational lines</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.67762</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2020.67762
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/1350
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description
Decomposed Zeichen konvertiert!
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dc.description.abstract
The Twin Dragon is a certain well known compact, connected subset of the plane. It appears in the radix representation of complex numbers in base -1+i and its boundary is a fractal with Hausdorff dimension 1.5236... . It is expected that intersecting a (Borel) fractal in the plane with a straight line reduces its Hausdorff dimension by 1, which holds for a family of lines of positive Lebesgue measure. Although this theorem applies to the Twin Dragon, all intersections for which the Hausdorff measure is known lie in the exceptional null set. Following techniques of Akiyama and Scheicher using Büchi automata it is possible to analyze further rational lines. To understand the given problem an introduction into fractal geometry is given including Hausdorff dimension, box-counting dimension, self-similarity, canonical number systems, self-similar tiles and Büchi automata.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Fraktale
de
dc.subject
Automaten
de
dc.subject
Hausdorff Dimension
de
dc.subject
Fractals
en
dc.subject
Automaten
en
dc.subject
Hausdorff dimension
en
dc.title
Intersecting the twin dragon with rational lines
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dc.title.alternative
Schnitte des Twin Drachen mit rationalen Geraden
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2020.67762
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Paul Großkopf
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC15618952
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dc.description.numberOfPages
83
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-135868
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.languageiso639-1
en
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item.openairetype
master thesis
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item.grantfulltext
open
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.openaccessfulltext
Open Access
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crisitem.author.dept
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
