The Holographic Method And Intergraphic Method For The Fractal Interpolating Problem

The Holographic Method and Intergraphic Method for the Fractal Interpolating ProblemSun Mingyan (Department of Mathematics, Northeast Normal University)Abstract .- This paper discusses the fractal interpolating problem (FIP). At first, it clearly provides the strict definition of FIP, introduces the fractal interpolating space, and points out the basic properties on the space. Secondly, using the above mathematical language, it makes a summary of the classical affine IPS fractal interpolating method. And then, it puts forward the concepts of holographic self-similarity and intergraphic self-similarity, the holographic self-similarity means that the local is similar to the global; the intergraphic self-similarity means that the local is similar to the local. Responding to the word holographic (or: holograph, hologram), the word intergraphic (or: Intergraph, intergram) is made by us. Hence, this paper gives two kinds of new methods on FIP梩he holographic method and the intergraphic method, and provides some examples for the two methods,, The main results are as follows.1. Introduces the holographic IFS of FIP, proves that the holographic IFS is contractive, and obtains the following generalresults.Theorem A. Let {w(}"=1 be a holographic IPS of FIP ?Assume {(x,,.y,)},10 is the interpolating data group , [a,b] is the interpolating interval, and D = {(x,y)e. R2 :a ,=r~'w,r (/= 1,2,...,?, then {co,}'^ is the holographic IPS of the other FIP, where the micro interpolating condition is its interpolating condition, the if/ isits shape curve, and the (p is its base curve. Moreover,Vlllto,(x,y) = (*,_, + a,(x-x0),ip,(x) + d,(y-