  In this paper we derive a simple parametrization of the cycling method
developed by us in our earlier work. The new method, called renormalization
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-anti-instanton pairs behave under
the RG mapping transformation. We use the RG mapping technique to study the
topological susceptibility and instanton size distribution of SU(2) gauge
theory. We find scaling in both quantities in a wide range of coupling values.
Our result for the topological susceptibility, chi^1/4=220(6) MeV, agrees with
our earlier results.
