EXISTENCE AND BOX DIMENSION OF GENERAL RECURRENT FRACTAL INTERPOLATION FUNCTIONS
Huo-Jun Ruan, Jian-Ci Xiao, Yang Bing
Abstract
Abstract The notion of recurrent fractal interpolation functions (RFIFs) was introduced by Barnsley et al. [‘Recurrent iterated function systems’, Constr. Approx. 5 (1989), 362–378]. Roughly speaking, the graph of an RFIF is the invariant set of a recurrent iterated function system on $\mathbb {R}^2$ . We generalise the definition of RFIFs so that iterated functions in the recurrent system need not be contractive with respect to the first variable. We obtain the box dimensions of all self-affine RFIFs in this general setting.
Topics & Concepts
Iterated function systemMathematicsIterated functionAffine transformationFractalInvariant (physics)Interpolation (computer graphics)Pure mathematicsGraphDimension (graph theory)Discrete mathematicsCombinatoricsMathematical analysisImage (mathematics)Artificial intelligenceComputer scienceMathematical physicsMathematical Dynamics and FractalsTheoretical and Computational PhysicsQuantum chaos and dynamical systems