GENERAL FRACTAL PRESERVING LINEAR AND NONLINEAR TRANSFORMATIONS

In this paper the most general fractal nature preserving linear transf ormation is derived starting from the most general linear lossless inh omogeneous transformation, that is the Special Affine Fourier Transfor m, (SAFT). It is known that the SAFT is simply related to paraxial opt ical signal processing operations. The transformation's properties are discussed in relation to recent optics literature regarding linear tr ansformations, fractal functions and self-reciprocal functions. It is indicated how these results further generalise results previously pres ented in the literature regarding some non-linear transforms of fracta ls and prefractals.