Preliminary Investigation of Random SKI-Combinator Trees

SKI-combinator trees are a simple model of computation, which are computationally complete (in a Turing sense), but are suggestive of basic biochemical processes and can be used as a vehicle for understanding processes of biological (and prebiotic) self-organization. After a brief overview of SKI-combinator trees, we describe the results of a series of preliminary experiments exploring the statistical properties of populations of random SKI-combinator trees. We show that in such populations a signiicant fraction of the trees will exhibit complex, non-terminating growth patterns, suggestive of biological processes. Further, we show that the fraction of S-combinators in such trees is an important parameter deening a sharp phase transition between (uninteresting) terminating behavior and (interesting) nonterminating growth. (This is related to the \edge of chaos" investigated by Chris Langton.) Finally, we discuss some of the follow-on investigations suggested by these exploratory experiments. support is gratefully acknowledged. This report is in the public domain and may be used for any non-proot purpose provided that the source is credited.