An application of neural networks to fractal function interpolation
Abstract
When processing experimental information (for instance, some spectrometric data), often we have to deal with ragged shapes more suited to be approximated by fractal structures rather than by ordinary differentiable functions. Given a set of data points { x_{i}, f( x_{i})) i = 0,1,…, N}, x_{0} < x_{1} < … < x_{N}, it is possible to construct a socalle Hyperbolic Iterated Function SystemF = { R^{2};f _{1},f _{2},…,f _{N}} , where f_{i} is a shear transformation, whose attractor is the graph of the fractal interpolation function interpolating the data. Do not only iterated function systems describe fractals, but they also permit to build the synaptic weight matrix of an asymmetric binary neural network realizing the dynamics of the iterated function system. So we can use such neural networks to build fractal sets and fractal interpolation functions.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 February 1997
 DOI:
 10.1016/S01689002(97)001447
 Bibcode:
 1997NIMPA.389..255S