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Title: Heredity, Complexity and Surprise: Embedded Self-Replication and Evolution in CA


1
Heredity, Complexity and SurpriseEmbedded
Self-Replicationand Evolution in CA
  • Chris Salzberg1,2 and Hiroki Sayama1

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

27
References
  • I. Azpeitia and J. Ibanez. Spontaneous emergence
    of robust cellular replicators. In S. Bandini,
    B. Chopard, and M. Tomassini, editors, Fifth
    International Conference on Cellular Automata for
    Research and Industry (ACRI 2002), pages 132-143.
    Springer, 2002.
  • H.H. Chou and J.A. Reggia. Emergence of
    self-replicating structures in a cellular
    automata space. Physica D, 110252-276, 1997.
  • T.J. Hutton. Evolvable self-replicating
    molecules in an artificial chemistry. Arificial
    Life, 8341-356, 2002.
  • C.G. Langton. Self-reproduction in cellular
    automata. Physica D, 10135-144, 1984.
  • B. McMullin. John von Neumann and the
    evolutionary growth of complexity Looking
    backward, looking forward Artificial Life,
    6347-361, 2000.
  • U. Pesavento. An implementation of von Neumanns
    self-reproducing machine. Artifiical Life,
    2335-352, 1996.
  • T.S. Ray. An approach to the synthesis of life.
    In Artificial Life II, volume XI of SFI Studies
    on the Sciences of Complexity, pages 371-408.
    Addison-Wesley Publishing Company, Redwood City,
    California, 1991.
  • C. Salzberg, A. Antony, and H. Sayama.
    Evolutionary dynamics of cellular automata-based
    self-replicators in hostile environments.
    BioSystems. In press.
  • H. Sayama. A new structurally dissolvable
    self-reproducing loop evolving in a simple
    cellular automata space. Artificial Life,
    5343-365, 1999.
  • H. Sayama. Self-replicating worms that increase
    structural complexity through gene transmission.
    In M.A. Bedau, J.S. McCaskill, N.H. Packard, and
    S. Rasmussen, editors, Artificial Life VII
    Proceedings of the Seventh International
    Conference on Artificial Life. MIT Press, 2000.
  • M. Sipper. Fifty years of research on
    self-replication An overview. Artificial Life,
    4237-257, 1998.
  • K. Suzuki and T. Ikegami. Interaction based
    evolution of self-replicating loop structures.
    In Proceedings of the Seventh European Conference
    on Artificial Life, pages 89-93, Dortmund,
    Germany, 2003.
  • T.J. Taylor. From artificial evolution to
    artificial life. PhD thesis, University of
    Edinburgh, 1999.
  • J. von Neumann. Re-evaluation of the problems of
    complicated automata - problems of hierarchy and
    evolution (Fifth Illinois Lecture), December
    1949. In W. Aspray and A. Burks, editors, Papers
    of John von Neumann on Computing and Computer
    Theory, pages 477-490. MIT Press, 1987.
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