Complex Genetic Evolution of Self-Replicating Loops Chris Salzberg 1,2 , Antony Antony 3 and Hiroki Sayama 1 1 Department of Human Communication, University of Electro-Communications, Tokyo 182-8585, Japan 2 Graduate School of Arts and Sciences, University of Tokyo, Tokyo 153-8904, Japan 3 Section Computational Science, Universiteit van Amsterdam, 1098 SJ Amsterdam, the Netherlands chris@cx.hc.uec.ac.jp antony@phenome.org sayama@hc.uec.ac.jp Abstract It is generally believed that self-replication models con- structed on cellular automata have quite limited evolutionary dynamics in both diversity and adaptative behavior. Contrary to this view, we show that complex genetic diversification and adaptation processes may occur in self-replicating loop popu- lations. Applying newly developed tools for detailed genetic identification and genealogy tracing to evoloop populations, we uncovered a genotypic permutation space that expands combinatorially with replicator size. Within this space popu- lations demonstrate broad behavioral diversity and non-trivial genetic adaptation, maximizing colony density while enhanc- ing sustainability against other species. We also found a set of non-mutable subsequences enabling genetic operations that alter fitness differentials and promote long-term evolutionary exploration. These results reveal the amazing potential of cel- lular automata to re-create complex genetic evolution of self- replicators in a simple, deterministic framework. Introduction Since von Neumann’s seminal work on self-reproducing automata (von Neumann 1966), models of artificial self- replicators based on cellular automata (CA) have formed one of the mainstreams in Artificial Life (Langton 1984; Reg- gia et al. 1993; Sipper 1998). Recent developments indi- cate that simple CA systems can reproduce natural selec- tion processes occuring on different self-replicating struc- tures (Sayama 1999). Their evolutionary dynamics, how- ever, are generally believed to be quite limited in both di- versity and adaptative behavior (Sayama 1999; McMullin 2000; Suzuki et al. 2003). Previous results point to a seem- ingly well-defined fitness landscape in which optimization converges to a single global maximum: homogeneous pop- ulations dominated by a single species of the smallest size and shortest replication time. Contrary to these earlier observations, here we show that complex genetic diversification and adaptation processes may occur in such simple CA. We investigate a system of evolving self-replicating loops (evoloops) (Sayama 1999) in which replication, variation and natural selection emerge solely from local rules. Applying newly developed tools ca- pable of sophisticated genetic identification and genealogy tracing to evoloop populations (Salzberg 2003; Salzberg, in press), we uncovered a genotypic permutation space that ex- pands combinatorially with replicator size. Within this space populations demonstrate broad behavioral diversity and non- trivial genetic adaptation, maximizing colony density while enhancing sustainability in the presence of other competing species. Such adaptation was observed even within species of the same size, thought to be of equal fitness in previ- ous treatment. Intriguing genetic features were also found that may parallel issues in molecular genetics, including the discovery of non-mutable subsequences enabling genetic operations that alter relative fitness differentials. Simula- tions with such “genetically modified organisms” demon- strate continuously changing, long-lasting evolutionary be- havior. These results reveal the amazing potential of CA to re-create complex genetic evolution of self-replicators in a simple, deterministic framework. Model The evoloop (Sayama 1999) we investigate is a determinis- tic nine-state 2D CA model with von Neumann neighbor- hoods, designed after Langton’s self-replicating loop (Lang- ton 1984). An evoloop individual contains an identifiable modular structure describing the shape of offspring (geno- type) and an external structure of its own body (phenotype). The former is a sequence of moving signal states (genes) and the latter is a looped sheath of square or rectangular shape, with an arm thrust outward [Fig. 1(a)]. A viable gene sequence contains several ‘7’ states for straight growth of the arm and a pair of consecutive ‘4’ states to control left turning of the arm. In a process of self-replication, cyclic propagation of signal states coordinates the external arm to create a new structural entity. The growing arm is guided through three successive turns and eventually meets its own root, causing tip and root to bond together to form a new, separate loop [Fig. 1(b)]. The truncated arm then retracts, completing the self-replication process. Loops are destroyed by the appearance and propagation of the dissolver state ‘8’ through contiguous loop structures. Triggered by local configurations non-integral to the normal self-replication cycle, this process of structural dissolution typically arises from shortage of space due to overcrowd- ing and exhibits highly complex dynamics. Its spread is af-