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.
[1]
E. Szathmáry,et al.
A classification of replicators and lambda-calculus models of biological organization
,
1995,
Proceedings of the Royal Society of London. Series B: Biological Sciences.
[2]
Henk Barendregt,et al.
The Lambda Calculus: Its Syntax and Semantics
,
1985
.
[3]
W. Fontana,et al.
“The arrival of the fittest”: Toward a theory of biological organization
,
1994
.
[4]
Bruce J. MacLennan,et al.
Functional programming - practice and theory
,
1990
.
[5]
Christopher G. Langton,et al.
Computation at the edge of chaos: Phase transitions and emergent computation
,
1990
.