Multi-dimensional self-affine fractal interpolation model in tensor form

Iterated Function System (IFS) models have been explored to represent discrete sequences where the attractor of an IFS is self-affine either in R ² or R ³ (R is the set of real numbers). In this paper, the self-affine IFS model is extended from R ³ to R ⁿ (n is an integer and greater than 3), which is called the multi-dimensional self-affine fractal interpolation model. This new model is presented by introducing the defined parameter “mapping partial derivative”. A constrained inverse algorithm is given for the identification of the model parameters. The values of this new model depend continuously on all of the variables. That is, the function is determined by the coefficients of the possibly multi-dimensional affine maps. So the new model is presented as much more general and significant. Moreover, the multi-dimensional self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form.