We examine the qualitative dynamics of a catalytic self-organizing system o
f binary strings that is inspired by the chemical information processing me
taphor. A string is interpreted in two different ways: either (a) as raw da
ta or (b) as a machine that is able to process another string as data in or
der to produce a third one. This article focuses on the phenomena of evolut
ion whose appearance is notable because no explicit mutation, recombination
, or artificial selection operators are introduced. We call the system self
-evolving because every variation is performed by the objects themselves in
their machine form.