A Monte Carlo Approach for c Placement in Fractal-Dimension Calculations for Waveform Graphs.pdf

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1、203AMonteCarloApproachforcPlacementinFractal-DimensionCalculationsforWaveformGraphsC.A.Pickover“)AbstracthasbeenstudiedextensivelybyB.Mandelbrot.whoManydiverseandcomplicatedobjectsofnatureandcoinedtheword“fractal”(in1975)todescribesuchmathpossessthequalityofself-similarity.andalgo-irreg

2、ularshapes2Fractalobjectshaveincreasingrithmswhichproduceself-similarshapesprovideawayfeaturesrevealedwithincreasingmagnification(unlikeforcomputergraphicstorepresentnaturalstructures.acircle’sedgewhichisfeaturelesswhenmagnified).Foravarietyofstudiesinsignalprocessingandshape-Usingtheco

3、nceptsoffractalgeometry,computerscien-characterization,itisusefultocomparethestructurestistshavegraphicallyportrayedmountainsandterrainofmanydifferent“objects”.Unfortunately,largewithstartlingreali~m.~.~Algorithmsforthegenerationamountsofcomputertimeareneededasprerequisiteofbeautifuland

4、complicatedfractalsbasedoniterativeforrigorousself-similaritycharacterizationandcom-functionsarealsobeingstudied.andtheirpopularityisparison.Thepresentpaperdescribesafastcomputerevidencedbytheproliferatingcomputergraphicsinthetechniqueforthecharacterizationofself-similarshapesscientific

5、andpopularliterat~re.’.~.~.~.~.loandsignalsbaseduponMonteCarlomethods.TheThispresentpaperdescribesafastcomputeralgorithmisspecificallydesignedfordigitizedinputtechniqueforthecharacterizationofself-similarshapes(e.g.pictures,acousticwaveforms,analyticfunctions)ofnatureandmath.Thealgorith

6、misspecificallywheretheself-similarityisnotobviousfromvisualdesignedfordigitizedinput(e.g.pictures,waveforms,inspectionofjustafewsamplemagnifications.Aanalyticfunctions)wheretheself-similarityisnotobvi-speechwaveformgraphisusedasanexample,andousfromvisualinspectionofjustafewsampleadditi

7、onalgraphicsareincludedasavisualaidforcon-magnifications.AspeechwaveformgraphisusedasanceptualizingtheMonteCarloprocesswhenappliedtoexample.Thepotentialbenefitoffractalcharacteriza-speechwaveforms.tionforspeechstudieshasbeendiscussedpreviously,’’andthespeedinherentinthetechniqu