Table Of ContentSpringer Proceedings in Mathematics & Statistics
Christoph Bandt · Michael Barnsley
Robert Devaney · Kenneth J. Falconer
V. Kannan · Vinod Kumar P.B. Editors
Fractals,
Wavelets,
and their
Applications
Contributions from the International
Conference and Workshop on Fractals
and Wavelets
Springer Proceedings in Mathematics & Statistics
Volume 92
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Christoph Bandt • Michael Barnsley
Robert Devaney • Kenneth J. Falconer
V. Kannan • Vinod Kumar P.B.
Editors
Fractals, Wavelets,
and their Applications
Contributions from the International
Conference and Workshop on Fractals
and Wavelets
123
Editors
ChristophBandt MichaelBarnsley
InstitutfürMathematikundInformatik MathematicalSciencesInstitute
UniversitätGreifswald AustralianNationalUniversity
Greifswald,Mecklenburg-Vorpomm. Canberra,Australia
Germany
KennethJ.Falconer
RobertDevaney MathematicalInstitute
MathDepartment UniversityofStAndrews
BostonUniversity StAndrews,Fife,UK
Boston,MA,USA
VinodKumarP.B.
V.Kannan DepartmentofBasicSciences
DepartmentofMathematics andHumanities
andStatistics RajagiriSchoolofEngineering
UniversityofHyderabad andTechnology
Hyderabad,India Kerala,India
ISSN2194-1009 ISSN2194-1017(electronic)
ISBN978-3-319-08104-5 ISBN978-3-319-08105-2(eBook)
DOI10.1007/978-3-319-08105-2
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2014949263
MathematicsSubjectClassification(2010):28A80,81Q35,42C40,65T60
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Preface
Fractalgeometryisayoungfield.Itwasinitiallydevelopedinthe1980s,drivenby
the motivationto modelrough phenomenain nature, and by new opportunitiesof
computervisualization.Towardstheendofthe1980s,waveletswereintroducedfor
theneedsofsignalandimageprocessing.Today,thefieldoffractalsandwavelets
has grown into a respected mathematical discipline with specific concepts and
techniques,andwithplentyofapplicationsinsideandoutsidemathematics.
InNovember2013aworkshopandthefirstInternationalConferenceonFractals
andWaveletsinIndiatookplaceatRajagiriSchoolofEngineeringandTechnology,
Kochi,Kerala.
In the workshop, from November 9 to 12, leading experts from all over the
world gave comprehensive survey lectures on the state of the art in their areas.
In the International Conference from November 13 to 16, new research results
were presented by mathematiciansfrom ten countries. There were more than 100
participants from India, revealing that research in fractals and wavelets has taken
rootatmanyIndianuniversities,with an emphasison applicationsto engineering,
medicine,Internettraffic,hydrology,andotherfields.
This volume contains all invited lectures of the workshop as well as selected
contributions to the conference. Providing readable surveys, it can be used as a
referencebookforthosewhowanttostartworkinthefield.Itdocumentsthepresent
state of research in the area, both in India and abroad, and can help to develop
cooperationamongwidelyscatteredgroups.
TheorganizersoftheconferencewouldliketothankthemanagementofRajagiri
SchoolofEngineeringandTechnology,Cochin,Kerala,Indiafortheinspirationand
supportprovidedtoconducttheconference.
The organizers acknowledge the financial support given by the International
Centre for Theoretical Physics, the International Mathematical Union, the Inter-
national Council for Industrial and Applied Mathematics, the National Board for
Higher Mathematics India, the Department of Science & Technology India, the
DefenceResearch&DevelopmentOrganisationIndia,theIndianNationalScience
Academy, the Kerala State Council for Science Technology & Environment, and
TheSouthIndianBankLimited.
v
Contents
PartI FractalTheory
IntroductiontoFractals......................................................... 3
ChristophBandt
GeometryofSelf-similarSets................................................... 21
ChristophBandt
AnIntroductiontoJuliaandFatouSets....................................... 37
ScottSutherland
ParameterPlanesforComplexAnalyticMaps............................... 61
RobertL.Devaney
MeasurePreservingFractalHomeomorphisms .............................. 79
MichaelF.Barnsley,BrendanHarding,andMiroslavRypka
TheDimensionTheoryofAlmostSelf-affineSetsandMeasures........... 103
KárolySimon
CountableAlphabetNon-autonomousSelf-affineSets ...................... 129
MariuszUrban´ski
OnTransverseHyperplanestoSelf-similarJordanArcs.................... 147
AndreyTetenov
FractalsinProductFuzzyMetricSpace....................................... 157
R.UthayakumarandA.Gowrisankar
SomePropertiesonKochCurve................................................ 165
R.UthayakumarandA.NalayiniDevi
ProjectionsofMandelbrotPercolationinHigherDimensions.............. 175
KárolySimonandLajosVágó
SomeExamplesofFiniteTypeFractalsinThree-DimensionalSpace..... 191
MaiTheDuy
vii
viii Contents
FractalsinPartialMetricSpaces............................................... 203
S.MiniraniandSunilMathew
PartII WaveletTheory
FramesandExtensionProblemsI ............................................. 219
OleChristensen
FramesandExtensionProblemsII ............................................ 235
OleChristensen,HongOhKim,andRaeYoungKim
LocalFractalFunctionsandFunctionSpaces................................ 245
PeterR.Massopust
SomeHistoricalPrecedentsoftheFractalFunctions........................ 271
M.A.NavascuésandM.V.Sebastián
ANewClassofRationalQuadraticFractalFunctionswith
PositiveShapePreservation..................................................... 283
A.K.B.Chand,P.Viswanathan,andM.A.Navascués
IntervalWaveletSetsDeterminedbyPointsontheCircle .................. 303
DivyaSingh
InverseRepresentationTheoremforMatrixPolynomialsand
MultiscalingFunctions .......................................................... 319
M.MubeenandV.Narayanan
ARemarkonReconstructionofSplines fromTheir Local
WeightedAverageSamples...................................................... 341
P.DevarajandS.Yugesh
C1-RationalCubic FractalInterpolation Surface Using
FunctionalValues ................................................................ 349
A.K.B.ChandandN.Vijender
OnFractalRationalFunctions ................................................. 369
P.ViswanathanandA.K.B.Chand
PartIII ApplicationsofFractalsandWavelets
InnovationontheTortuousPath:FractalElectronics....................... 385
NathanCohen
PermutationEntropyAnalysisof EEG of Mild Cognitive
ImpairmentPatientsDuringMemoryActivationTask...................... 395
LeenaT.Timothy,BinduM.Krishna,MuraliKrishnaMenon,
andUshaNair
Contents ix
AMultifractal-BasedImageAnalysisforCervicalDysplasia
Classification...................................................................... 407
P.Singh,J.Jagtap,C.Pantola,A.Agarwal,andA.Pradhan
Self-SimilarNetworkTrafficModellingUsingFractalPoint
Process-MarkovianApproach.................................................. 413
RajaiahDasari,RameshRenikunta,andMallaReddyPerati
ValidationofVarianceBasedFittingforSelf-similarNetworkTraffic .... 427
Ramesh Renikunta, Rajaiah Dasari, Ranadheer Donthi,
andMallaReddyPerati
Self-Similar Network Traffic Modeling Using Circulant
MarkovModulatedPoissonProcess ........................................... 437
Ranadheer Donthi, Ramesh Renikunta, Rajaiah Dasari,
andMallaReddyPerati
InvestigationofPriorityBasedOpticalPacketSwitchUnder
Self-Similar Variable Length Input Traffic Using Matrix
QueueingTheory................................................................. 445
RaviKumarGudimallaandMallaReddyPerati
Computationally Efficient Wavelet Domain Solver for
FlorescenceDiffuseOpticalTomography ..................................... 457
K.J.FrancisandI.Jose
ImplementationofWaveletBasedandDiscreteCosineBased
AlgorithmonPanchromaticImage ............................................ 471
JyotiSarup,JyotiBharti,andArpitaBaronia
Trend,TimeSeries,andWaveletAnalysisofRiverWaterDynamics...... 479
KulwinderSinghParmarandRashmiBhardwaj
An Efficient Wavelet Based Approximation Method to
Film-PoreDiffusionModelArisinginChemicalEngineering .............. 491
PandyPirabaharan,R.DavidChandrakumar,andG.Hariharan
ANewWavelet-BasedHybridMethodforFisherTypeEquation.......... 501
R.RajaramandG.Hariharan
