The relationship between structure and function is explored via a system of labeled directed graph structures upon which a single elementary read/write rule is applied locally. Boundaries between static (information-carrying) and active (information-processing) objects, imposed by mandate of the rules or physics in earlier models, emerge instead as a result of a structure-function dynamic that is reflexive: objects may operate directly on their own structure. A representation of an arbitrary Turing machine is reproduced in terms of structural constraints by means of a simple mapping from tape squares and machine states to a uniform medium of nodes and links, establishing computation universality. Exploiting flexibility of the formulation, examples of other unconventional “self-computing” structures are demonstrated. A straightforward representation of a kinematic machine system based on the model devised by Laing is also reproduced in detail. Implications of the findings are discussed in terms of their relation to other formal models of computation and construction. It is argued that reflexivity of the structure-function relationship is a critical informational dynamic in biochemical systems, overlooked in previous models but well captured by the proposed formulation.

We present a general approach for evaluating and visualizing evolutionary dynamics of self-replicators using a graph-based representation for genealogy. Through a transformation from the space of species and mutations to the space of nodes and links, evolutionary dynamics are understood as a flow in graph space. A formalism is introduced to quantify such genealogical flows in terms of the complete history of localized evolutionary events recorded at the finest level of detail. Represented in a multidimensional viewing space, collective dynamical properties of an evolving genealogy are characterized in the form of aggregate flows. We demonstrate the effectiveness of this approach by using it to compare the evolutionary exploration behavior of self-replicating loops under two different environmental settings.