Multifractal surfaces: Lucena and Stanley approaches
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30642 |
Resumo: | We review multifractal surfaces focusing on a comparison between Lucena and Stanley approaches. The multifractal model as presented by Stanley is basically a multinomial measure over a standard partition of a square. The Lucena approach is geometric oriented, the multifractality is not imposed over a regular lattice, but the lattice itself follows a partition where area tiles obey a multifractal distribution. The non-trivial tilling has a distribution of neighbors of lattice elements that shows a fat tail. Despite the strong differences in the two bidimensional models, both Liacir and Stanley multifractals can be reduced to the same object in one dimension. The message of this article is that there is no unique multifractal object in two dimensions and, as a consequence, we should caution about algorithms that estimate multifractal spectrum in two dimensions because it is not clear what kind of multifractality |
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Moreira, Darlan AraújoCorso, Gilberto2020-11-23T21:34:09Z2020-11-23T21:34:09Z2013-09CORSO, G.; MOREIRA, D. A.. Multifractal surfaces: Lucena and Stanley approaches. Fractals, [S.L.], v. 21, n. 0304, p. 1350020-1350020, set. 2013. Disponível em: https://www.worldscientific.com/doi/abs/10.1142/S0218348X13500205. Acesso em: 08 set. 2020. http://dx.doi.org/10.1142/s0218348x13500205.0218-348X1793-6543https://repositorio.ufrn.br/handle/123456789/3064210.1142/S0218348X13500205World Scientific PublishingAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessBidimensional MultifractalVoronoi TillingUniversality ClassFat TailIrregular LatticeBinomial DistributionMultifractal surfaces: Lucena and Stanley approachesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleWe review multifractal surfaces focusing on a comparison between Lucena and Stanley approaches. The multifractal model as presented by Stanley is basically a multinomial measure over a standard partition of a square. The Lucena approach is geometric oriented, the multifractality is not imposed over a regular lattice, but the lattice itself follows a partition where area tiles obey a multifractal distribution. The non-trivial tilling has a distribution of neighbors of lattice elements that shows a fat tail. Despite the strong differences in the two bidimensional models, both Liacir and Stanley multifractals can be reduced to the same object in one dimension. The message of this article is that there is no unique multifractal object in two dimensions and, as a consequence, we should caution about algorithms that estimate multifractal spectrum in two dimensions because it is not clear what kind of multifractalityengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALMultifractalSurfaces_Moreira_2013.pdfMultifractalSurfaces_Moreira_2013.pdfapplication/pdf612002https://repositorio.ufrn.br/bitstream/123456789/30642/1/MultifractalSurfaces_Moreira_2013.pdffa9fcbc257c1a2f35bdd24ecf812e166MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufrn.br/bitstream/123456789/30642/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30642/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTMultifractalSurfaces_MOREIRA_2013.pdf.txtMultifractalSurfaces_MOREIRA_2013.pdf.txtExtracted texttext/plain23374https://repositorio.ufrn.br/bitstream/123456789/30642/4/MultifractalSurfaces_MOREIRA_2013.pdf.txtaae010fb99560a1ee7aa1d7edce1ff39MD54THUMBNAILMultifractalSurfaces_MOREIRA_2013.pdf.jpgMultifractalSurfaces_MOREIRA_2013.pdf.jpgGenerated Thumbnailimage/jpeg1447https://repositorio.ufrn.br/bitstream/123456789/30642/5/MultifractalSurfaces_MOREIRA_2013.pdf.jpg64cc471ea94eb55eb1326151c2fdb541MD55123456789/306422021-11-10 16:39:55.548oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2021-11-10T19:39:55Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Multifractal surfaces: Lucena and Stanley approaches |
title |
Multifractal surfaces: Lucena and Stanley approaches |
spellingShingle |
Multifractal surfaces: Lucena and Stanley approaches Moreira, Darlan Araújo Bidimensional Multifractal Voronoi Tilling Universality Class Fat Tail Irregular Lattice Binomial Distribution |
title_short |
Multifractal surfaces: Lucena and Stanley approaches |
title_full |
Multifractal surfaces: Lucena and Stanley approaches |
title_fullStr |
Multifractal surfaces: Lucena and Stanley approaches |
title_full_unstemmed |
Multifractal surfaces: Lucena and Stanley approaches |
title_sort |
Multifractal surfaces: Lucena and Stanley approaches |
author |
Moreira, Darlan Araújo |
author_facet |
Moreira, Darlan Araújo Corso, Gilberto |
author_role |
author |
author2 |
Corso, Gilberto |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Moreira, Darlan Araújo Corso, Gilberto |
dc.subject.por.fl_str_mv |
Bidimensional Multifractal Voronoi Tilling Universality Class Fat Tail Irregular Lattice Binomial Distribution |
topic |
Bidimensional Multifractal Voronoi Tilling Universality Class Fat Tail Irregular Lattice Binomial Distribution |
description |
We review multifractal surfaces focusing on a comparison between Lucena and Stanley approaches. The multifractal model as presented by Stanley is basically a multinomial measure over a standard partition of a square. The Lucena approach is geometric oriented, the multifractality is not imposed over a regular lattice, but the lattice itself follows a partition where area tiles obey a multifractal distribution. The non-trivial tilling has a distribution of neighbors of lattice elements that shows a fat tail. Despite the strong differences in the two bidimensional models, both Liacir and Stanley multifractals can be reduced to the same object in one dimension. The message of this article is that there is no unique multifractal object in two dimensions and, as a consequence, we should caution about algorithms that estimate multifractal spectrum in two dimensions because it is not clear what kind of multifractality |
publishDate |
2013 |
dc.date.issued.fl_str_mv |
2013-09 |
dc.date.accessioned.fl_str_mv |
2020-11-23T21:34:09Z |
dc.date.available.fl_str_mv |
2020-11-23T21:34:09Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CORSO, G.; MOREIRA, D. A.. Multifractal surfaces: Lucena and Stanley approaches. Fractals, [S.L.], v. 21, n. 0304, p. 1350020-1350020, set. 2013. Disponível em: https://www.worldscientific.com/doi/abs/10.1142/S0218348X13500205. Acesso em: 08 set. 2020. http://dx.doi.org/10.1142/s0218348x13500205. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30642 |
dc.identifier.issn.none.fl_str_mv |
0218-348X 1793-6543 |
dc.identifier.doi.none.fl_str_mv |
10.1142/S0218348X13500205 |
identifier_str_mv |
CORSO, G.; MOREIRA, D. A.. Multifractal surfaces: Lucena and Stanley approaches. Fractals, [S.L.], v. 21, n. 0304, p. 1350020-1350020, set. 2013. Disponível em: https://www.worldscientific.com/doi/abs/10.1142/S0218348X13500205. Acesso em: 08 set. 2020. http://dx.doi.org/10.1142/s0218348x13500205. 0218-348X 1793-6543 10.1142/S0218348X13500205 |
url |
https://repositorio.ufrn.br/handle/123456789/30642 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
World Scientific Publishing |
publisher.none.fl_str_mv |
World Scientific Publishing |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRN instname:Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN |
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UFRN |
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