An Inductive Formalization of Self Reproduction in Dynamical Hierarchies

Formalizing self reproduction in dynamical hierarchies is one of the important problems in Artificial Life (AL) studies. We study, in this paper, an inductively defined algebraic framework for self reproduction on macroscopic organizational levels under dynamical system setting for simulated AL models and explore some existential results. Starting with defining self reproduction for atomic entities we define self reproduction with possible mutations on higher organizational levels in terms of hierarchical sets and the corresponding inductively defined `meta' - reactions. We introduce constraints to distinguish a collection of entities from genuine cases of emergent organizational structures.