REVERSE ITERATED FUNCTION SYSTEM AND DIMENSION OF DISCRETE FRACTALS

Abstract

AbstractA reverse iterated function system is defined as a family of expansive maps {T1,T2,…,Tm} on a uniformly discrete set $M\subset \Bbb {R}^d$. An invariant set is defined to be a nonempty set $F\subseteq M$ satisfying F=⋃ j=1mTj(F). A computation method for the dimension of the invariant set is given and some questions asked by Strichartz are answered.