Fractal Interpolation Of Parametric Form

This paper discusses fractal interpolating problem of parametric form (PFIP).At first,it clearly provides the definition of PFIP,introduces fractal interpolating space of parametric form ,and points out the basic properties on the space. And then ,this paper gives three kinds of new methods on FIP-affine fractal interpolation IFS of parametric form , holographic fractal interpolation IFS of parametric form, intergraphic fractal inter-polation IFS of parametric form on the base of affine fractal interpolation IFS of Barnsley and the holographic fractal interpolation IFS and the intergraphic fractal interpolation IFS of ShengzhongPing. This paper also gives the hyperbolic conditions of the three forms of IFS,at the same time,it proves that the attractor A of the fractal interpolation IFS of parametric form is the graph G[f] of the continuous vector-valued function f.