Representation of discrete sequences with N-dimensional iterated function systems in tensor form

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piecewise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piecewise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the multi-dimensional piecewise hidden variable fractal model. This new model uses a "mapping partial derivative" and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore the result is very general. Moreover, the piecewise hidden-variable fractal model in tensor form is more terse than in the usual matrix form.