1. Heredity, Complexity and Surprise: Embedded Self-Replication and Evolution in CA Chris Salzberg 1,2 and Hiroki Sayama 1 1 Dept. of Human Communication, University of Electro-Communications, Japan 2 Graduate School of Arts and Sciences, University of Tokyo, Japan

2. Summary Introduction:  History of embedded models of self-replication in cellular automata Concepts:  Embeddedness  Explicitness  Heredity  Evolutionary growth of complexity Evolvable self-replicators in CA Conclusions

3. Introduction

4. Self-replication and ALife Self-replication is one of the main themes of research in Artificial Life. In the past, research has mainly targeted regulated behavior:  Universal construction,  Self-replication,  Self-inspection,  Functionality. Behavior oriented toward pre-defined goals.

5. von Neumann’s theory von Neumann was inspired by the many increases of “complication” observed in natural organisms. His “Theory of Self-Reproducing Automata”:  proved that such increases could in principle be realized in artificial automata,  outlined a concrete example of such a constructive automata in a 29-state CA.

6. Some key features Uses a discrete cellular space with local rules (as suggested by S. Ulam) Introduces separation between passive tape and active machine:  evolution occurs via mutations to tape,  construction pathways exist from simpler to more complex types (McMullin,2000). CA rules are fixed during evolution.

7. The key issue System is computationally intractable:  requires 29 states and a highly complex set of transition rules,  occupies an estimated 50,000 to 200,000 CA cells (Sipper,1998). Extremely sensitive to perturbations (non-robust, brittle). Only recently simulated for the first time (Pesavento,1995).

8. Solutions to this “problem” Demand so-called “non-trivial” self- reproduction (rather than universality):  some minimal level of structural complexity, and  a translation/transcription process that is highly explicit. These criteria make no demands on heredity.

9. A Popular Example Langton (Langton,1984) designed the self- reproducing loop (SR Loop):  uses a much smaller set of rules,  requires only a few hundred cells, and  is readily realizable. However, the SR loop cannot accommodate mutations. Hence, it cannot evolve (no heredity).

10. von Neumann’s definition “[S]elf-reproduction includes the ability to undergo inheritable mutations as well as the ability to make another organism like the original” (von Neumann,1949). The capacity to withstand viable hereditary mutations was central to von Neumann’s formal theory.

11. “Marginal” heredity? Do there exist simple CA-based self- replicating structures that:  span an infinite and diverse space of possible genotypes/phenotypes,  are able to withstand viable hereditary mutations, and  evolve spontaneously via physical laws rather than any explicit mutation operator?

12. Concepts

13. Embeddedness Quantifies the extent to which state information of an individual is expressed in the arena of competition. Embeddedness enables “the very structure of the individual to be modified”, likely a necessary condition for open-ended evolution (Taylor,1999).

14. Embeddedness of systems CA are highly embedded:  They do not “hide” any information (except the transition rules), and  allow for direct and unrestricted interactions between cells. Systems of evolutionary computer programs (e.g. (Ray,1991)) are less so:  Most information is hidden in auxiliary non- interactive locations (memory).

15. Embeddedness and materiality Self-replicators embedded in CA share an important feature with biological organisms:  Both are built up from, and interact through, a common material structure grounded in physical laws (i.e. CA rules). This makes them “messy” to analyze. But also potentially rich in dynamics.

16. Explicitness Degree to which a self-replication process is governed by an environment rather than an object in that environment (Taylor,1999). e.g. explicitness of translation and transcription (Langton,1984). Often used as criterion for non-trivial self- replication (somewhat arbitrary).

17. Heredity Heredity is a more appropriate criteria:  Distinguishes simple replicators (e.g. SR Loop) from potentially evolvable machines (e.g. von Neumann’s UC).  Focuses on static descriptions rather than translation/transcription process,  Potentially enables “reproduction without degeneration in size or level of organization” (von Neumann,1949).

18. Growth of complexity Principle conditions for the “evolutionary growth of complexity” (McMullin,2000):  Exhibit a concrete class of machines that are “purely mechanistic”,  “show that they span a significant range of complexity”, and  “demonstrate that there are construction pathways leading from the simplest to the most complex”.

19. von Neumann’s insight von Neumann discovered a system which satisfies these conditions, but:  It is extremely complicated, and  It is extremely fragile/brittle. In addition:  It enables a mutational growth of complexity (construction pathways), but  It does not necessarily enable a Darwinian growth of complexity.

20. Practical alternatives Can we find simpler CA-based self- replicators of marginal hereditary and structural complexity, which concretely realize these criteria? What evolutionary complexity growth, if any, do we observe in these CA?

21. Evolvable self-replicators in cellular automata

22. Marginal CA Replicators Many self-replicating structures have been implemented in CA. Most of these CA target regulated behavior (functional or computational capabilities). A small subset, however, were designed with the aim of studying the evolutionary process itself.

23. Outline of observations Observed behaviors:  Emergence of self-replicators from a “soup” of parts (Chou & Reggia,1997)  Spontaneous evolution (Sayama,1999)  Genetic diversity, complex genealogy, complexity-increase (Salzberg et al.,2004)  Structural variability & complexity-increase (Suzuki & Ikegami, 2003)  Spontaneous evolution of robust self-replicators (Azpeitia and Ibanez, 2002)  Template-based replication (Hutton, 2003)

24. Categorization of self-reps To categorize CA models, we use a method by Taylor (Taylor,1999):  2D visualization scheme  x-axis = copy process (explicit/implicit)  y-axis = heredity (limited/indefinite) Central region represents self-replicators of marginal hereditary and structural complexity.

25. Categorization of self-reps Heredity Copying Process limited indefinite explicit (structure-based) implicit (physics-based) minimal self-reps (Langton ‘84, etc.) emergent self-reps (Chou & Reggia, ‘97) evoloop (Sayama, ‘99) robust self-inspection cellular replicators (Azpeitia et al., 2002) von Neumann’s self-rep Automata (1950s) template-based self-reps in CA (Hutton ‘02, etc.) interaction-based evolving loops (Suzuki et al., ‘03) gene-transmitting worms (Sayama, ‘00) symbioorganisms (Barricelli ‘57) ‘trivial’ self-reps)

26. Conclusions Complexity-increase of a limited kind is possible in practice. Marginal replicators can realize:  High levels of hereditary variability  Structural robustness  Spontaneous (Darwinian) evolution Such models constitute the first step towards von Neumann’s original goal of complexity-increase in CA.

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