Representation of discrete sequences with three-dimensional iterated function systems

Several recent papers have shown the ability of iterated function system (IFS) models to represent discrete sequences where the attractor of an IFS is self-affine either in R² or R³ or is piece-wise self-affine in R². We extend the piece-wise self-affine IFS model from R² to R³ and we call this model the piece-wise hidden-variable fractal model. This extension permits the representation of discrete sequences with a fractal model that is general and flexible. This new model is presented and a constrained inverse algorithm for identification of the model parameters is given. Examples of this model to seismic data and speech data are then presented