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1、Whatisit?ItisabranchofmathsonthefrontiersofmedicalresearchinarainforestinwirelesscommunicationsinthemoviesYoucanfinditWHEREISIT?thejagged,repeatingformcalledaFractal分形Broccoli西兰花ThesurfaceofthemoonveinsleafTheFatherofFractalaFrenchandAmericanmathematician12EmeritusatYaleUniversity
2、3IBMFellowEmeritusattheThomasJ.WatsonResearchCenter4SterlingProfessorofMathematicalSciencesBenoîtMandelbrotCantorsetTheGermanmathematicianGeorgCantorcreatedthefirstofthemonstersin1883.Takeastraightline,breakthislineintothirds,erasethemiddlethird,twolinesateachendareleft.Takethoset
3、wolines,takeoutthemiddlethird,andwe'lldoitoverandoveragain.I'vethrowneverythingaway,Mostpeoplewouldthink,eventually,there'snothingleft.Notthecase.There'snotjustonepointleft.There'snotjusttwopointsleft.There'sinfinitelymanypointsleft.Engineersweretransmittingcomputerdataoverphoneli
4、nes.Butsometimes,theinformationwasnotgettingthrough.thenoisedataCantorsetinlife插入视频：15’09—15’21VonKochSnowflakeAKochsnowflakeisconstructedbymakingprogressiveadditionstoasimpletriangle.Theadditionsaremadebydividingtheequilateraltriangle’ssidesintothirds,thencreatinganewtriangleonea
5、chmiddlethird.Thus,eachframeshowsmorecomplexity,buteverynewtriangleinthedesignlooksexactlyliketheinitialone.Bluetoothwalkie-talkieWi-FiSierpinskiTriangle3D1Startwithanequilateraltriangle2Shrinkthetriangleto½heightand½width,makethreecopies,andpositionthethreeshrunkentrianglessothat
6、eachtriangletouchesthetwoothertrianglesatacorner3Repeatstep2witheachofthesmallertrianglesAlthoughitstopologicaldimension(拓扑维度)is2,it’sHausdorff-Besicovitchdimensionislog(3)/log(2)~1.58插入视频：19’37—19’48Itisasetofpointsinthecomplexplane,theboundaryofwhichformsafractal.MandelbrotSetHo
7、wLongIstheCoastofBritain?Themeasuredlengthofastretchofcoastlinedependsonthescaleofmeasurement.Empiricalevidencesuggeststhatthesmallertheincrementofmeasurement,thelongerthemeasuredlengthbecomes.Ifoneweretomeasureastretchofcoastlinewithayardstick,onewouldgetashorterresultthanifthesa
8、mestretchweremeasuredwitharuler.T
