分形插值曲线的MATLAB实现

0Mandelbrot(1983),。、、、、、Euclid。。。MATLAB、、。1(IteratedFunctionSystemIFS),,。1.1{(xi,yi)∈R2,i=0,1,2,…N}x0x1……xNf(xi)=yi,i=0,1,2,…Nf:[x0,xN]→R。1.2IFSI=[x0,xN]Ii=[xj-1,xj]LjLj:I→Ij,j=0,1,2,…N,Lj(x0)=xj-1Lj(xN)=xj。FjFj:K奂I×R→[a,b]a,bFj(x0,y0)=yj-1,Fj(xN,yN)=yj。Wj(x,y)=(Lj(x),Fj(x,y))j=1,2……N,IFSGG:f:I→[a,b],f(xi)=yi,i=0,1,2……N。IFS{R2:wn,n=1,2……N}wn:MATLABFractalInterpolatedCurveAchievedbytheMATLABLanguageZhouChengxinChenHuiqin,330029(DeparmentofElectrical&MechanicalServices,JiangxiBlueSkyUniversityJiangxiNanchang330029)Euclid,。(IFS),,IFS。MATLAB。,。:MATLABTP31A1671-4792-(2009)3-0119-02Abstract:Inthenaturemanyphenomenaexiststhefractalcharacteristic,thetraditionalEuclid’sspacesimulatethefractalcharacteristicnatureshapetohavecertaindifficulty.Regardingthisreason,mayusethefractalinterpolationtofitthenatureshape.ThefractalinterpolatedfunctionisrealizedbytheIteratedFunctionSystem(IFS),usingthediscretedatapointconstructsfractalinterpolatedfunction,itmayprovethatthefrac-talinterpolatingfunctionistheIFS’ssoleattractor.UsingtheMATLABmatrixoperationandthegraphplanfunctionmayrealizethediscretedatapointtothefractalinterpolationfitting.Thetestresultindicatedthatthisalgorithmhasthesimpleandintuitivecharacteristic.Keywords:FractalInterpolated;IteratedFunctionSystem;MATLABArithmeticMATLAB11192009.3,1DnDnDn1IFS。2MATLAB:1a)(xi,yi)i=0,1,2……NN+1b)dnn=1,2……NNd=rand(1,N)c)L(L≥1),mm=1nwnn=1d)x[x0,xN]e)wnXY=[]23an、cn、en、fn3(1)n≤N3(4)m=m+1m≤L3(5)XY,。31,22,2.53,44,65,35x,y=(3.56.5),L=4,。4,,。。[1],.[M].:,2002.[2].MATLAB6.x.[M].2002.[3].[J].,2002,(3).[4].[][D].,2006,3.[5].[J].(),2002,23(5):1-4.1970—,,1980—,,。23;120