Title: Heredity, Complexity and Surprise: Embedded Self-Replication and Evolution in CA
1Heredity, 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
2Summary
- 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
3Introduction
4Self-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.
5von 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.
6Some 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.
7The 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).
8Solutions 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.
9A 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).
10von 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.
11Marginal 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?
12Concepts
13Embeddedness
- 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).
14Embeddedness 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).
15Embeddedness 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.
16Explicitness
- 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).
17Heredity
- 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).
18Growth 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.
19von 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.
20Practical 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?
21Evolvable self-replicators in cellular automata
22Marginal 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.
23Outline 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)
24Categorization 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.
25Categorization 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
26Conclusions
- 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.
27References
- 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.