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It is widely believed that evolutionary dynamics of artificial self-replicators realized in cellular automata (CA) Key Words: cellular automata; self-replication; genetic evolution; diversity; adaptation S ince von Neumann's work on self-reproducing automata [1], artificial self-replication models based on cellular automata (CA) have formed one of the mainstreams in artificial life [2][3][4][5]. Recent developments indicate that simple CA with fixed rules can reproduce natural selection among different self-replicating structures [6,7], yet their evolutionary dynamics are considered quite limited in both diversity and adaptive behavior [8,9]. Contrary to these earlier observations, we show that genetic adaptation and diversification processes may occur in such simple CA. We investigate a system of evolving self-replicating loops, or evoloops [7], in which replication, variation and selection emerge solely from fixed local rules. Applying new tools for detailed genetic identification and genealogy tracing [10], we uncovered a genotypic permutation space that expands combinatorially with replicator size, within which loops exhibit significant diversity in macro-scale morphologies and mutational biases. Populations undergo nontrivial genetic adaptation, maximizing colony density while enhancing sustainability against other species. We also identified a set of nonmutable subsequences in the evoloop genetics, with which one can carry out genetic operations to alter fitness differentials and promote long-term evolutionary exploration. This effect is further manifested when populations are introduced to a hostile environment. These results demonstrate a unique example of genetic evolution that traverses multiple scales, hierarchically emerging from local interactions between elements much smaller than individual replicators.

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.

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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.

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