Approximation and Designing of Fractal Images by Complex Neural Networks

Abstract

Complex neural networks (C.N.N.) with their complex back-propagation learning algorithm are useful in processing complex signals. As the characteristics of the C.N.N., the learning and generalization abilities with respect to affine transformation on a complex space are known. This paper is concerned with applications of these C.N.N.’s characteristics to generation of fractal images by constructing iterated function systems (IFS) with the C.N.N.’s input and output relations. The simulations for several examples demonstrate effectiveness of the C.N.N. to coding fractal images in the prospect of designing the desired fractal images.