Heredity, Complexity and Surprise:Embedded Self-Replication

and Evolution in CA

Chris Salzberg1,2 and Hiroki Sayama1

1 Dept. of Human Communication, University of Electro-Communications, Japan2 Graduate School of Arts and Sciences, University of Tokyo, Japan

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

Introduction

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.

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.

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.

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).

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.

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).

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.

“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?

Concepts

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).

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).

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.

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).

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).

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”.

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.

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?

Evolvable self-replicators in cellular

automata

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.

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)

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.

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-inspectioncellular replicators(Azpeitia et al., 2002)

von Neumann’s self-repAutomata (1950s)

template-basedself-reps in CA

(Hutton ‘02, etc.)

interaction-basedevolving loops

(Suzuki et al., ‘03)

gene-transmittingworms (Sayama, ‘00)

symbioorganisms(Barricelli ‘57)

‘trivial’self-reps)

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.

References

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