A Closer Look at the Evolutionary Dynamics of SelfReproducing Cellular Automata

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A Closer Look at the Evolutionary Dynamics of
Self-Reproducing Cellular Automata

• Antony Antony Chris Salzberg

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Credits

• This project is part of thesis work leading to
  the
• Master of Science degree in Computational
  Science.
• Research is supervised by Dr. Hiroki Sayama
• University of Electro-Communications, Tokyo,
  Japan
• Project to be completed by the end of this year.

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Lecture Plan

• Statement of Problem
• Former works
• A New Dynamic Environment
• Identification and Classification
• Genealogy
• Large-scale Simulations
• Conclusions

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1. Statement of Problem

• Goal
• To study the emergence of complex evolutionary
  phenomena through a simple, abstract model.
• Method
• abstract from the natural self-reproduction
  problem its logical form. (Neumann)
• Synthesize using cellular automata (CA).

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2. Former Works
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Timeline relating current work
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The Self-Reproducing Loop
genes
sheath
arm
tube

• Sheath Outer shell housing gene sequence.
• Genes 7s (straight growth) and 4s (turning).
• Tube 2s within sheath.
• Arm Extensible loop structure for replication.

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State-transition Rules

• Rules take the form CTRLB gt I .
• Local and deterministic.

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Langtons SR Loop

• 8 states
• 5-cell neighbourhood
• Program for self-replication contained in gene
  sequence (genotype)
• Death occurs via functional failure (limited in
  finite space)

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The Evoloop

• 9 states (SR rule set dissolving state)
• 5-cell neighbourhood
• Modifications to SR rule set introduce adaptivity
  leading to evolution.
• Death occurs via structural dissolution.

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Evoloop CA States
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Properties of the Dissolving State

• Appears from undefined configurations.
• Travels along tube to dissolve neighbouring
  states.
• Any contiguous structure is extinguished,
  creating free space for new loops.

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Qualities of the Evoloop CA

• Simple and scalable
• Small rule set (95 59049 rules)
• No central operating system
• Purely deterministic (no stochastic operations in
  rule set).
• Adaptable.
• Realizes an emergent evolutionary process.

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Predictability of the Evoloop

• Continuous self-reproduction leads to
  high-density loop populations (no free space).
• Interaction of phenotypes favours small-sized
  loops.
• Evolution ends with a homogeneous single-species
  population.
• No diversity, no speciation, no evolution.

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Evolution in a Periodic Domain

• Conclusion modify the environment.

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3. A New Dynamic Environment
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The Persistent Dissolving State

• Tenth state added to Evoloop CA.
• Rules nearly identical to dissolving state, but
  persists in time for a finite period N
  (persistence or lifetime).
• Purely part of the environment loops will never
  produce it on their own.

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The Memory Layer

• Memory layer acts as counter, decrementing
  lifetime each iteration if dissolver cell is
  above.
• When lifetime reaches zero, counter is reset and
  dissolver cell is removed.
• Does not directly interact with neighbouring loop
  layer states.

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Persistence and Scale

• The choice of the persistence N imposes a fixed
  scale on the system.
• As domain is expanded (grid size), N can be used
  to scale the population cluster size.

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Persistence and Scale

• Signs of complex evolutionary phenomena.
• Speciation and long-term diversity (phenotype).
• Conclusion to understand whats happening, we
  need better analysis

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4. Identification and Classification
17d55555/13x13
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New Definitions

• Genotype sequence of states 0, 1, 4, and
  7 inside a loops tube structure.
• Phenotype size of inner sheath.
• Birth appearance of state 6 (umbilical cord
  dissolver).
• Death dissolution of any inner sheath state.

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Properties of Loop Species

• Stationary (identification)
• Genotype
• Phenotype
• Reproductive (classification)
• Existence and identity of first-born offspring in
  free space.

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Identification of Loop Species
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Genotype-based Characteristics

• Species of the same phenotype but different
  genotype exhibit distinct dynamics

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Classification of Loop Species

• Stable
• First-born child in free space is identical to
  parent.
• Transitional
• First-born child in free space is different from
  parent.
• Terminal
• Species does not reproduce.

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5. Genealogy
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Genealogy as a Tree

• To track genealogy, ancestral information
  recorded in parent/child form.
• On large grids, results in huge genealogy trees.
• Information missing multiple parents (ancestors)
  for a single child (descendant).
• Conclusion genealogy not tree-based?

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Genealogy as a Graph

• Loop species represented by graph nodes
  (vertices).
• Links (edges) represent ancestral relations.
• Link traversal frequencies both time and
  space-dependent.
• Graph-space size on 3K x 3K run
• 5K nodes
• 10K links

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Classification in Graph-space

• Free-space link graph-space link traversed in
  free space.

• Stable node with free-space self-link
  (buckle).
• Transitional node with free-space to another
  node.
• Terminal node with no free-space links.

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Example of Graph-based Genealogy
A5f541/6x6 B 47d51/6x6 C 27d5/5x5 D
87d5/5x5 E 9f5/4x4 F 41f55/6x6
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Statistics from Graph-Based Genealogy
(3K x 3K run - compiled after 940K iterations)
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6. Large-scale Experiments
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Method

• 3000 x 3000 grid
• Persistence (N) 20,000 time steps.
• Initiated with three loops of species
  17d55555/13x13.
• Block of dissolver cells begin in upper-right
  corner.
• Run for 29 days on DAS II.

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Bottlenecked Life Cycle

• Periodic domain is dynamically partitioned by
  dissolver.
• One species (5f541/6x6) narrowly escapes
  extinction.
• This species is the exclusive ancestor for all
  future generations.
• Predicting this event nearly impossible.

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Bottlenecked Life Cycle
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Evolutionary Stasis

• Between 400K and 1M iterations, two species
  (41f55/6x6, 20fa55/7x7) dominate exclusively.

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Evolutionary Coupling?

• Cycle in graph-space connects dominant species
  (41f55/6x6, 20fa55/7x7).
• System settles in graph-space potential minimum.

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Return of the Giants

• Stasis abruptly ends at 940K iterations.
• Large-sized loops (size 9, 10, 11, 12, 13) make a
  brief return.
• High diversity for very short period (roughly
  80K).
• Punctuated equilibrium (Tierra) ?

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Return of the Giants
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7. Conclusions

• Diversity can be synthesized in a CA space.
• Genealogy can be viewed as a graph.
• Complex evolutionary phenomena can emerge from a
  deterministic CA model
• Evolutionary bottlenecking
• Punctuated Equilibrium
• Describing the past is easier than prescribing
  the future.

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References

• Hiroki Sayama, A new structurally dissolvable
  self-reproducing loop evolving in a simple
  cellular automata space, Artificial Life, vol.5,
  no.4, pp.343-365, 1999.
• Hiroki Sayama Constructing Evolutionary Systems
  on a Simple Deterministic Cellular Automata
  Space, Ph.D. Dissertation, Department of
  Information Science, Graduate School of Science,
  University of Tokyo, December 1998.
• Langton, C. G. Self-reproduction in cellular
  automata, Physica D, 10 pp. 135-144, 1984
• Wolfram S. A New kind of science, Wolfram Media,
  2002.
• Von Neumann, J. edited by Burks Theory of
  Self-Reproducing Automata, 1966.
• Work in progress http//meme.phenome.org.

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Thanks!

• J