Existence and box dimension of general recurrent fractal interpolation functions

Authors

  • H.-J. Ruan
  • J.-C. Xiao
  • B. Yang

Keywords:

box dimension, iterated function systems, recurrent fractal interpolation functions, strongly connected component

Abstract

The notion of recurrent fractal interpolation functions (RFIFs) was introduced by Barnsley, Elton and Hardin in 1989. Roughly speaking, the graph of an RFIF is the invariant set of a recurrent iterated function system on $\mathbb{R}^2$. In this paper, we generalize the definition of RFIFs in the following sense: iterated functions in the recurrent system need not to be contractive with respect to the first variable. We also obtain the box dimensions of all self-affine RFIFs in our general setting.

Published

2021-03-10

Issue

Vol. 103 No. 2 (2021)

Section

Articles
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