Multi-Dimensional Piece-Wise Self-Affine Fractal Interpolation Model

Iterated function system (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R² or R³ (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R³ to Rⁿ (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a “mapping partial derivative”, and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in Rⁿ. Therefore, the result is very general. The class of functions obtained is much more diverse because their values depend continuously on all of the variables, with all the coefficients of the possible multi-dimensional affine maps determining the functions.