Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações do Mackenzie |
Texto Completo: | https://dspace.mackenzie.br/handle/10899/28608 |
Resumo: | Number conserving cellular automata can represent or model equally conservative realworld dynamics. In the literature, this property has been extensively addressed for the one-imensional case and for the two-dimensional von Neumann neighbourhood. The present work aimed at a computational exploration in the space of two-dimensional rules with Moore neighbourhood of unit radius. As such, the main related concepts were revisited, such as number conservation in the elementary space and in the two-dimensional case with von Neumann neighbourhood; the general conditions for number conservation in hyper-rectangular neighbourhoods; the composition of conservative rules; and the decomposition algorithm of division and disturbance rules. From this, it was possible to derive a regular expression for the identity and displacement rules; propose a method to list the traffic rules of the space at issue; and introduce a heuristic to obtain rules in the desired space, based on the composition of one-dimensional conservative rules. Additionally, when applying the split-and-perturb decomposition algorithm, the conservative rules in Moore neighbourhood obtained were revealed to be the same as those in von Neumann’s 4-dimensional neighbourhood. The conservative rules obtained were analysed from a phenomenological point of view, which led to their grouping into classes, and revealed a rich variety of patterns of temporal evolution. |
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2021-12-18T21:44:23Z2021-12-18T21:44:23Z2020-12-08ROCHA, Felipe Gonçalves da. Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore. 2020. 82 f. Dissertação ( Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo, 2020.https://dspace.mackenzie.br/handle/10899/28608Number conserving cellular automata can represent or model equally conservative realworld dynamics. In the literature, this property has been extensively addressed for the one-imensional case and for the two-dimensional von Neumann neighbourhood. The present work aimed at a computational exploration in the space of two-dimensional rules with Moore neighbourhood of unit radius. As such, the main related concepts were revisited, such as number conservation in the elementary space and in the two-dimensional case with von Neumann neighbourhood; the general conditions for number conservation in hyper-rectangular neighbourhoods; the composition of conservative rules; and the decomposition algorithm of division and disturbance rules. From this, it was possible to derive a regular expression for the identity and displacement rules; propose a method to list the traffic rules of the space at issue; and introduce a heuristic to obtain rules in the desired space, based on the composition of one-dimensional conservative rules. Additionally, when applying the split-and-perturb decomposition algorithm, the conservative rules in Moore neighbourhood obtained were revealed to be the same as those in von Neumann’s 4-dimensional neighbourhood. The conservative rules obtained were analysed from a phenomenological point of view, which led to their grouping into classes, and revealed a rich variety of patterns of temporal evolution.Autômatos celulares conservativos (number conserving) podem representar ou modelar dinâmicas igualmente conservativas do mundo real. Na literatura, essa propriedade foi amplamente abordada para casos unidimensionais e bidimensionais em vizinhança de von Neumann. O presente trabalho visou realizar uma exploração computacional no espaço de regras bidimensionais com vizinhança de Moore de raio unitário. Para tanto, foram revisitados os principais conceitos sobre o tema, tais como a conservabilidade no espaço elementar e no espaço bidimensional de von Neumann; as condições gerais para conservabilidade em vizinhanças hiper-retangulares; a composição de regras conservativas; e o algoritmo de decomposição de regras por divisão e perturbação. A partir disso foi possível derivar uma expressão regular para as regras identidade e as que apresentam deslocamentos; propor um método para listar as regras do tráfego do espaço em questão; e introduzir uma heurística para obter regras do espaço desejado, a partir da composição de regras conservativas unidimensionais. Adicionalmente, ao se aplicar o algoritmo de decomposição de regras por divisão e perturbação, as regras conservativas em vizinhança de Moore obtidas revelaram-se ser as próprias regras em vizinhança de von Neumann de 4 dimensões. As regras conservativas obtidas foram analisadas do ponto de vista fenomenológico, o que levou ao agrupamento delas em classes, e revelou uma rica variedade de padrões de evoluções temporais.Coordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfporUniversidade Presbiteriana MackenzieEngenharia ElétricaUPMBrasilEscola de Engenharia Mackenzie (EE)autômatos celulares bidimensionaisconservabilidade vizinhança de Moorevizinhança de Mooreequivalência dinâmicacomposição de regrasdecomposição de regras por divisão e perturbaçãoCNPQ::ENGENHARIASExplorando o espaço de autômatos celulares conservativos binários com vizinhança de Mooreinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOliveira, Pedro Paulo Balbi dehttp://lattes.cnpq.br/9556738277476279Ruivo, Eurico Luiz Prosperohttp://lattes.cnpq.br/5918644808671007Mendonça, José Ricardo Gonçalves dehttp://lattes.cnpq.br/8792749813872106http://lattes.cnpq.br/2322148521706681Rocha, Felipe Gonçalves datwo-dimensional cellular automatanumber conservationmoore neighbourhooddynamical equivalencerule compositionsplit-and-perturb decompositioninfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações do Mackenzieinstname:Universidade Presbiteriana Mackenzie (MACKENZIE)instacron:MACKENZIELICENSElicense.txttext/plain2108https://dspace.mackenzie.br/bitstream/10899/28608/1/license.txt1ca4f25d161e955cf4b7a4aa65b8e96eMD51ORIGINALFELIPE GONÇALVES DA ROCHA - protegida.pdfFelipe Gonçalves da Rochaapplication/pdf2632511https://dspace.mackenzie.br/bitstream/10899/28608/2/FELIPE%20GON%c3%87ALVES%20DA%20ROCHA%20-%20protegida.pdf85da7b5da43a1fe12ec12acf3f98868bMD52TEXTFELIPE GONÇALVES DA ROCHA - protegida.pdf.txtFELIPE GONÇALVES DA ROCHA - protegida.pdf.txtExtracted texttext/plain146190https://dspace.mackenzie.br/bitstream/10899/28608/3/FELIPE%20GON%c3%87ALVES%20DA%20ROCHA%20-%20protegida.pdf.txtbfe975d6deadf7ceb51e00c95ae6cc74MD53THUMBNAILFELIPE GONÇALVES DA ROCHA - protegida.pdf.jpgFELIPE GONÇALVES DA ROCHA - protegida.pdf.jpgGenerated Thumbnailimage/jpeg1215https://dspace.mackenzie.br/bitstream/10899/28608/4/FELIPE%20GON%c3%87ALVES%20DA%20ROCHA%20-%20protegida.pdf.jpg3fedd24ce74dd9213979dd677bbab9c2MD5410899/286082021-12-19 03:02:36.698TElDRU7Dh0EgREUgRElTVFJJQlVJw4fDg08gTsODTy1FWENMVVNJVkEKCkNvbSBhIGFwcmVzZW50YcOnw6NvIGRlc3RhIGxpY2Vuw6dhLCB2b2PDqiAobyBhdXRvciAoZXMpIG91IG8gdGl0dWxhciBkb3MgZGlyZWl0b3MgZGUgYXV0b3IpIGNvbmNlZGUgw6AgVW5pdmVyc2lkYWRlIFByZXNiaXRlcmlhbmEgTWFja2VuemllIG8gZGlyZWl0byBuw6NvLWV4Y2x1c2l2byBkZSByZXByb2R1emlyLCAgdHJhZHV6aXIgKGNvbmZvcm1lIGRlZmluaWRvIGFiYWl4byksIGUvb3UgZGlzdHJpYnVpciBhIHN1YSB0ZXNlIG91IGRpc3NlcnRhw6fDo28gKGluY2x1aW5kbyBvIHJlc3VtbykgcG9yIHRvZG8gbyBtdW5kbyBubyBmb3JtYXRvIGltcHJlc3NvIGUgZWxldHLDtG5pY28gZSBlbSBxdWFscXVlciBtZWlvLCBpbmNsdWluZG8gb3MgZm9ybWF0b3Mgw6F1ZGlvIG91IHbDrWRlby4KClZvY8OqIGNvbmNvcmRhIHF1ZSBhIFVuaXZlcnNpZGFkZSBQcmVzYml0ZXJpYW5hIE1hY2tlbnppZSBwb2RlLCBzZW0gYWx0ZXJhciBvIGNvbnRlw7pkbywgdHJhbnNwb3IgYSBzdWEgdGVzZSBvdSBkaXNzZXJ0YcOnw6NvIHBhcmEgcXVhbHF1ZXIgbWVpbyBvdSBmb3JtYXRvIHBhcmEgZmlucyBkZSBwcmVzZXJ2YcOnw6NvLgoKVm9jw6ogdGFtYsOpbSBjb25jb3JkYSBxdWUgYSBVbml2ZXJzaWRhZGUgUHJlc2JpdGVyaWFuYSBNYWNrZW56aWUgcG9kZSBtYW50ZXIgbWFpcyBkZSB1bWEgY8OzcGlhIGEgc3VhIHRlc2Ugb3UgZGlzc2VydGHDp8OjbyBwYXJhIGZpbnMgZGUgc2VndXJhbsOnYSwgYmFjay11cCBlIHByZXNlcnZhw6fDo28uCgpWb2PDqiBkZWNsYXJhIHF1ZSBhIHN1YSB0ZXNlIG91IGRpc3NlcnRhw6fDo28gw6kgb3JpZ2luYWwgZSBxdWUgdm9jw6ogdGVtIG8gcG9kZXIgZGUgY29uY2VkZXIgb3MgZGlyZWl0b3MgY29udGlkb3MgbmVzdGEgbGljZW7Dp2EuIFZvY8OqIHRhbWLDqW0gZGVjbGFyYSBxdWUgbyBkZXDDs3NpdG8gZGEgc3VhIHRlc2Ugb3UgZGlzc2VydGHDp8OjbyBuw6NvLCBxdWUgc2VqYSBkZSBzZXUgY29uaGVjaW1lbnRvLCBpbmZyaW5nZSBkaXJlaXRvcyBhdXRvcmFpcyBkZSBuaW5ndcOpbS4KCkNhc28gYSBzdWEgdGVzZSBvdSBkaXNzZXJ0YcOnw6NvIGNvbnRlbmhhIG1hdGVyaWFsIHF1ZSB2b2PDqiBuw6NvIHBvc3N1aSBhIHRpdHVsYXJpZGFkZSBkb3MgZGlyZWl0b3MgYXV0b3JhaXMsIHZvY8OqIGRlY2xhcmEgcXVlIG9idGV2ZSBhIHBlcm1pc3PDo28gaXJyZXN0cml0YSBkbyBkZXRlbnRvciBkb3MgZGlyZWl0b3MgYXV0b3JhaXMgcGFyYSBjb25jZWRlciDDoCBVbml2ZXJzaWRhZGUgUHJlc2JpdGVyaWFuYSBNYWNrZW56aWUgb3MgZGlyZWl0b3MgYXByZXNlbnRhZG9zIG5lc3RhIGxpY2Vuw6dhLCBlIHF1ZSBlc3NlIG1hdGVyaWFsIGRlIHByb3ByaWVkYWRlIGRlIHRlcmNlaXJvcyBlc3TDoSBjbGFyYW1lbnRlIGlkZW50aWZpY2FkbyBlIHJlY29uaGVjaWRvIG5vIHRleHRvIG91IG5vIGNvbnRlw7pkbyBkYSB0ZXNlIG91IGRpc3NlcnRhw6fDo28gb3JhIGRlcG9zaXRhZGEuCgpDQVNPIEEgVEVTRSBPVSBESVNTRVJUQcOHw4NPIE9SQSBERVBPU0lUQURBIFRFTkhBIFNJRE8gUkVTVUxUQURPIERFIFVNIFBBVFJPQ8ONTklPIE9VIEFQT0lPIERFIFVNQSBBR8OKTkNJQSBERSBGT01FTlRPIE9VIE9VVFJPIE9SR0FOSVNNTyBRVUUgTsODTyBTRUpBIEEgVU5JVkVSU0lEQURFIFBSRVNCSVRFUklBTkEgTUFDS0VOWklFLCBWT0PDiiBERUNMQVJBIFFVRSBSRVNQRUlUT1UgVE9ET1MgRSBRVUFJU1FVRVIgRElSRUlUT1MgREUgUkVWSVPDg08gQ09NTyBUQU1Cw4lNIEFTIERFTUFJUyBPQlJJR0HDh8OVRVMgRVhJR0lEQVMgUE9SIENPTlRSQVRPIE9VIEFDT1JETy4KCkEgVW5pdmVyc2lkYWRlIFByZXNiaXRlcmlhbmEgTWFja2VuemllIHNlIGNvbXByb21ldGUgYSBpZGVudGlmaWNhciBjbGFyYW1lbnRlIG8gc2V1IG5vbWUgKHMpIG91IG8ocykgbm9tZShzKSBkbyhzKSBkZXRlbnRvcihlcykgZG9zIGRpcmVpdG9zIGF1dG9yYWlzIGRhIHRlc2Ugb3UgZGlzc2VydGHDp8OjbywgZSBuw6NvIGZhcsOhIHF1YWxxdWVyIGFsdGVyYcOnw6NvLCBhbMOpbSBkYXF1ZWxhcyBjb25jZWRpZGFzIHBvciBlc3RhIGxpY2Vuw6dhLgo=Biblioteca Digital de Teses e Dissertaçõeshttp://tede.mackenzie.br/jspui/PRI |
dc.title.por.fl_str_mv |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
title |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
spellingShingle |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore Rocha, Felipe Gonçalves da autômatos celulares bidimensionais conservabilidade vizinhança de Moore vizinhança de Moore equivalência dinâmica composição de regras decomposição de regras por divisão e perturbação CNPQ::ENGENHARIAS |
title_short |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
title_full |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
title_fullStr |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
title_full_unstemmed |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
title_sort |
Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore |
author |
Rocha, Felipe Gonçalves da |
author_facet |
Rocha, Felipe Gonçalves da |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Oliveira, Pedro Paulo Balbi de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/9556738277476279 |
dc.contributor.referee1.fl_str_mv |
Ruivo, Eurico Luiz Prospero |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/5918644808671007 |
dc.contributor.referee2.fl_str_mv |
Mendonça, José Ricardo Gonçalves de |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/8792749813872106 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/2322148521706681 |
dc.contributor.author.fl_str_mv |
Rocha, Felipe Gonçalves da |
contributor_str_mv |
Oliveira, Pedro Paulo Balbi de Ruivo, Eurico Luiz Prospero Mendonça, José Ricardo Gonçalves de |
dc.subject.por.fl_str_mv |
autômatos celulares bidimensionais conservabilidade vizinhança de Moore vizinhança de Moore equivalência dinâmica composição de regras decomposição de regras por divisão e perturbação |
topic |
autômatos celulares bidimensionais conservabilidade vizinhança de Moore vizinhança de Moore equivalência dinâmica composição de regras decomposição de regras por divisão e perturbação CNPQ::ENGENHARIAS |
dc.subject.cnpq.fl_str_mv |
CNPQ::ENGENHARIAS |
description |
Number conserving cellular automata can represent or model equally conservative realworld dynamics. In the literature, this property has been extensively addressed for the one-imensional case and for the two-dimensional von Neumann neighbourhood. The present work aimed at a computational exploration in the space of two-dimensional rules with Moore neighbourhood of unit radius. As such, the main related concepts were revisited, such as number conservation in the elementary space and in the two-dimensional case with von Neumann neighbourhood; the general conditions for number conservation in hyper-rectangular neighbourhoods; the composition of conservative rules; and the decomposition algorithm of division and disturbance rules. From this, it was possible to derive a regular expression for the identity and displacement rules; propose a method to list the traffic rules of the space at issue; and introduce a heuristic to obtain rules in the desired space, based on the composition of one-dimensional conservative rules. Additionally, when applying the split-and-perturb decomposition algorithm, the conservative rules in Moore neighbourhood obtained were revealed to be the same as those in von Neumann’s 4-dimensional neighbourhood. The conservative rules obtained were analysed from a phenomenological point of view, which led to their grouping into classes, and revealed a rich variety of patterns of temporal evolution. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-12-08 |
dc.date.accessioned.fl_str_mv |
2021-12-18T21:44:23Z |
dc.date.available.fl_str_mv |
2021-12-18T21:44:23Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
ROCHA, Felipe Gonçalves da. Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore. 2020. 82 f. Dissertação ( Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo, 2020. |
dc.identifier.uri.fl_str_mv |
https://dspace.mackenzie.br/handle/10899/28608 |
identifier_str_mv |
ROCHA, Felipe Gonçalves da. Explorando o espaço de autômatos celulares conservativos binários com vizinhança de Moore. 2020. 82 f. Dissertação ( Engenharia Elétrica) - Universidade Presbiteriana Mackenzie, São Paulo, 2020. |
url |
https://dspace.mackenzie.br/handle/10899/28608 |
dc.language.iso.fl_str_mv |
por |
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por |
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Universidade Presbiteriana Mackenzie |
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Engenharia Elétrica |
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UPM |
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Brasil |
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Escola de Engenharia Mackenzie (EE) |
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Universidade Presbiteriana Mackenzie |
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