Fractal Patterns Created by Ulam's Cellular Automaton

Ulam's cellular automaton, a nonlinear two-dimensional cellular automaton, was introduced by Stanislaw Ulam for emulating crystalline growths. In this paper we give two numerical results in which the particular orbit of the automaton has some fractal structures. First result is that the boundar...

Full description

Saved in:
Bibliographic Details
Published in2014 Second International Symposium on Computing and Networking pp. 484 - 486
Main Author Kawaharada, Akane
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2014
Subjects
Automata
Educational institutions
Equations
fractal pattern
Fractals
Lebesgue's singular function
Mathematical model
Orbits
Ulam's cellular automaton
Online AccessGet full text
ISSN2379-1888
DOI10.1109/CANDAR.2014.51

Cover

Abstract Ulam's cellular automaton, a nonlinear two-dimensional cellular automaton, was introduced by Stanislaw Ulam for emulating crystalline growths. In this paper we give two numerical results in which the particular orbit of the automaton has some fractal structures. First result is that the boundaries of the spatio patterns are fractal curves as time approaches infinity. Second, we study the number of cells consisting the spatio patterns for each time step. We show that the dynamics of the number can be represented by Lebesgue's singular function.
AbstractList Ulam's cellular automaton, a nonlinear two-dimensional cellular automaton, was introduced by Stanislaw Ulam for emulating crystalline growths. In this paper we give two numerical results in which the particular orbit of the automaton has some fractal structures. First result is that the boundaries of the spatio patterns are fractal curves as time approaches infinity. Second, we study the number of cells consisting the spatio patterns for each time step. We show that the dynamics of the number can be represented by Lebesgue's singular function.
Author Kawaharada, Akane
Author_xml – sequence: 1
  givenname: Akane
  surname: Kawaharada
  fullname: Kawaharada, Akane
  email: akwhrd@u-shizuoka-ken.ac.jp
  organization: Dept. of Math., Hiroshima Univ., Higashi-Hiroshima, Japan
BookMark eNotj01Lw0AURUeoYFu7deMmO1eJ781HZ2YZolWhqIhdl5fmBSKTRCbTRf-9BXs3B87iwF2I2TAOLMQdQoEI_rEq35_Kr0IC6sLglVigtt5rNFLOxFwq63N0zt2I1TT9AICSoGGt5sJsIh0SheyTUuI4TFkVmRI3WX3KdoH6h7PhEI6BYlYe09hTGodbcd1SmHh14VLsNs_f1Wu-_Xh5q8pt3inElFt0Zg2KgYBad7C6qb1WwL5uWUuuLcgGrW3rxpAhC85i3Z4nCaRxhtVS3P93O2be_8aup3jaWzjfUqj-ABawRlI
CODEN IEEPAD
ContentType Conference Proceeding
DBID 6IE
6IL
CBEJK
RIE
RIL
DOI 10.1109/CANDAR.2014.51
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEL
IEEE Proceedings Order Plans (POP All) 1998-Present
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISBN 1479941522
9781479941520
EndPage 486
ExternalDocumentID 7052231
Genre orig-research
GroupedDBID 6IE
6IF
6IL
6IN
AAWTH
ABLEC
ADZIZ
ALMA_UNASSIGNED_HOLDINGS
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CBEJK
CHZPO
IEGSK
OCL
RIE
RIL
ID FETCH-LOGICAL-i311t-7185603e0a0af8c74db9430e9bfe42eb702d177fbd5a5a70871bffff2a02585e3
IEDL.DBID RIE
ISSN 2379-1888
IngestDate Wed Aug 27 02:03:08 EDT 2025
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-i311t-7185603e0a0af8c74db9430e9bfe42eb702d177fbd5a5a70871bffff2a02585e3
PageCount 3
ParticipantIDs ieee_primary_7052231
PublicationCentury 2000
PublicationDate 2014-12
PublicationDateYYYYMMDD 2014-12-01
PublicationDate_xml – month: 12
  year: 2014
  text: 2014-12
PublicationDecade 2010
PublicationTitle 2014 Second International Symposium on Computing and Networking
PublicationTitleAbbrev candar
PublicationYear 2014
Publisher IEEE
Publisher_xml – name: IEEE
SSID ssj0003204063
ssj0001967840
Score 1.5792025
Snippet Ulam's cellular automaton, a nonlinear two-dimensional cellular automaton, was introduced by Stanislaw Ulam for emulating crystalline growths. In this paper we...
SourceID ieee
SourceType Publisher
StartPage 484
SubjectTerms Automata
Educational institutions
Equations
fractal pattern
Fractals
Lebesgue's singular function
Mathematical model
Orbits
Ulam's cellular automaton
Title Fractal Patterns Created by Ulam's Cellular Automaton
URI https://ieeexplore.ieee.org/document/7052231
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3PS8MwFA5zJ09TN_E3OQheTJcm6bIcx3QMYWOIg91GsryAOFqZ7UH_epO220Q8mFOTU0he-r6XvO97CN1KLaURwhGXcEmEBEGUBU6cEkZrbYwu-RWTaW88F0-LZNFA9zsuDACUyWcQhc_yLd9mqyJclXUl9WghkKYPvJlVXK39fYryv91atyT0OfPmWRZSY1wqEvtIr9ZsjKnqDgfTh8FzyOwSUXij_FFZpXQsoxaabKdU5ZO8RUVuotXXL7XG_875CHX2FD482zmnY9SA9AS1tjUccH2k2ygZBZqUXuNZKbSZfuBhgJFgsfnEc28ud34E1uuQrYoHRZ55hJulHTQfPb4Mx6QupUBeeRznxHsgD204UE2166-ksCboroMyDgQDIymzsZTO2EQnWlIfRhnnG9MeE_UT4KeomWYpnCFsmE18DEK5ZUooZlUM0HfMWsN7Wjp6jtphFZbvlVrGsl6Ai7-HL9Fh2IQqQeQKNfNNAdfezefmptzfbzwupBY
linkProvider IEEE
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3PT8IwGG0IHvSECsbf7mDixULXdpQeCUpQgRADCTfS0q-JkWxGt4P-9bbbAGM8uNPWU9Mfe9_Xvvc-hK6FEkJzbrGNmMBcAMfSAMNWcq2U0lrl-orRuD2Y8cd5NK-g240WBgBy8hk0_Wt-l2-SZeaPylqCuGjBi6Z3HO7zqFBrbU9UpPvxls4l_ptRt0DzUmqUCYlDl-uVro0hka1ed3zXffbcLt70t5Q_aqvk0NKvodG6UwWj5LWZpbq5_Prl1_jfXu-jxlbEF0w28HSAKhAfotq6ikNQbuo6ivpeKKVWwSS32ow_gp4PJMEE-jOYuQVz41pgtfJ81aCbpYmLcZO4gWb9-2lvgMtiCviFhWGKHQa54IYBUUTZzlJwo73zOkhtgVPQglATCmG1iVSkBHGJlLbuocpFRZ0I2BGqxkkMxyjQ1EQuCyHMUMklNTIE6FhqjGZtJSw5QXU_Cou3wi9jUQ7A6d_NV2h3MB0NF8OH8dMZ2vMTUtBFzlE1fc_gwoF-qi_zuf4GCjanYw
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=2014+Second+International+Symposium+on+Computing+and+Networking&rft.atitle=Fractal+Patterns+Created+by+Ulam%27s+Cellular+Automaton&rft.au=Kawaharada%2C+Akane&rft.date=2014-12-01&rft.pub=IEEE&rft.issn=2379-1888&rft.spage=484&rft.epage=486&rft_id=info:doi/10.1109%2FCANDAR.2014.51&rft.externalDocID=7052231
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2379-1888&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2379-1888&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2379-1888&client=summon