In this paper we derive a simple parametrization of the cycling method
developed by us in our earlier work. The new method, called renormali
zation group (RG) mapping, consists of a series of carefully tuned APE
-smearing steps. We study the relation between cycling and RG mapping.
We also investigate in detail how smooth instantons and instanton-ant
i-instanton pairs behave under the RG mapping transformation. We use t
he RG-mapping technique to study the topological susceptibility and in
stanton size distribution of SU(2) gauge theory. We find scaling in bo
th quantities in a wide range of coupling values. Our result for the t
opological susceptibility, chi(1/4) = 220(6) MeV, agrees with our earl
ier results. (C) 1998 Elsevier Science B.V.