An invited talk at Talkboctopus: A Virtual Complex Systems & Data Science Seminar Series, Vermont Complex Systems Center, University of Vermont, March 17, 2022, Burlington, VT / online.
4. Von Neumann’s Question
• Natural biological systems seem to have increased their
complexity through evolution
• Artificial systems seem to be able to make only products that
are less complex than themselves
Can artificial systems make products equally complex to, or
more complex than, themselves?
Von Neumann, J., (1966). Theory of Self-Reproducing Automata (edited by A. W. Burks). University of Illinois Press. 4 / 60
5. Von Neumann’s Automaton: Theoretical Design
A : universal constructor
B : tape duplicator
C : controller
ID=A+B+C : description tape
A + IX → A + IX + X
B + IX → B + IX + IX
(A + B + C) + IX
→ (A + B + C) + IX + X + IX
(A + B + C) + IA+B+C
→ (A + B + C) + IA+B+C
+ (A + B + C) + IA+B+C
* This is also deeply related to A. Turing’s proof of the halting problem’s undecidability.
Sayama, H. (2008). Construction theory, self‐replication, and the halting problem. Complexity, 13(5), 16-22.
5 / 60
6. If there is a change in the description …, the system
will produce, not itself, but a modification of itself.
Whether the next generation can produce anything or
not depends on where the change is. …
… So, while this system is exceedingly primitive, it
has the trait of an inheritable mutation, even to the
point that a mutation made at random is most
probably lethal, but may be non-lethal and
inheritable.
-- John von Neumann (1949)
6 / 60
9. Von Neumann’s Self-Reproducing Cellular Automata
(Completed by A. W. Burks)
• 29-state 5-
neighbor CA
• Construction-
universal,
potentially
evolvable
• Computationally
expensive to
simulate
Von Neumann, J., (1966). Theory of Self-Reproducing Automata (edited by A. W. Burks). University of Illinois Press.
9 / 60
Simulator:
http://golly.sourceforge.net/
10. Codd’s Self-Reproducing Cellular Automata
• 8-state 5-
neighbor CA
• Construction-
universal,
potentially
evolvable
• Computationally
more expensive
to simulate
Codd, E. (1968). Cellular Automata. Academic Press.
Hutton, T. J. (2010). Codd's self-replicating computer. Artificial Life, 16(2), 99-117. 10 / 60
11. Game of Life
• Created by J. H. Conway;
popularized by M. Gardner
• State transition rule:
• 0 turns into 1 if and only
if exactly three 1’s
surround it
• 1 remains 1 if and only if
two or three other 1’s
surround it (otherwise it
turns into 0)
• The most complex yet
parsimonious in its rule
family
Gardner, M. (1970). Mathematical games: The
fantastic combinations of John Conway's new
solitaire game "life". Scientific American, 223,
120-123.
Peña, E., & Sayama, H. (2021). Life worth
mentioning: Complexity in life-like cellular
automata. Artificial Life, 27(2), 105-112. 11 / 60
12. Langton’s Loops
• Simplified model of self-reproduction
based on a part of Codd’s automata
• No ability of universal construction
• First practical demonstration of self-
reproduction with genotype-phenotype
distinction
Langton, C. G. (1984). Self-reproduction in cellular automata. Physica D:
Nonlinear Phenomena, 10(1-2), 135-144. 12 / 60
13. If we could populate a large area with multiple copies
of such reproducing colonies, and introduce variation
into at least the portion of the description that codes
for the extra machinery, we would have all of the raw
material necessary for natural selection to operate
among variants and hence we would have a
sufficient basis for the process of evolution.
-- Christopher G. Langton (1986)
13 / 60
14. Artificial Life (1987-)
• Interdisciplinary field founded by Christopher
Langton
• International Society for Artificial Life (ISAL;
2001-) https://alife.org
• Artificial Life journal (MIT Press)
https://direct.mit.edu/artl
• ALIFE (ECAL) conferences
https://alife.org/conferences/
+ IEEE ALIFE, AROB, etc.
14 / 60
15. “Artificial Life”
• “... is a field of study devoted to understanding life by
attempting to abstract the fundamental dynamical
principles underlying biological phenomena, and
recreating these dynamics in other physical media ―
such as computers ― making them accessible to new
kinds of experimental manipulation and testing.”
• “... In addition to providing new ways to study the
biological phenomena associated with life here on Earth,
life-as-we-know-it, Artificial Life allows us to extend our
studies to the larger domain of "bio-logic" of possible
life, life-as-it-could-be.”
Langton, C.G. (1992). Preface. Artificial Life II (pp. xiii-xviii). Addison-Wesley. 15 / 60
17. “Digital
Ecosystem”
Approaches
• Related to, but quite
different from, typical
evolutionary computation
• Heredity, variation and
selection are not given a
priori as built-in
mechanisms, but they
naturally emerge from
interactions among
microscopic components
(e.g., codes, neurons,
individuals)
17 / 60
18. From “Core War” to Artificial Life Research
Jones, D. G. & Dewdney, A. K. (1984).
Core War Guidelines.
Ray, T. S. (1991). An approach to the synthesis of
life. Artificial life II, 371-408. Addison-Wesley.
Rasmussen, S., Knudsen, C., Feldberg, R., & Hindsholm, M.
(1990). The coreworld: Emergence and evolution of
cooperative structures in a computational chemistry.
Physica D: Nonlinear Phenomena, 42(1-3), 111-134.
Coreworld
(Venus) Tierra
18 / 60
19. • Template-based
addressing achieved
robust functioning of
mutated codes and non-
trivial “parasitic”
interactions
• Programs became shorter
yet more sophisticated
through interactions with
adversaries
Ray, T. S. (1991). An approach to the synthesis of
life. Artificial life II, 371-408. Addison-Wesley. 19 / 60
Emergence of Parasitic
Interactions in Tierra
20. Variations and Further Developments
Avida
Adami, C. & Brown, C. T. (1994). Evolutionary
learning in the 2D artificial life system “Avida”.
Artificial Life IV (pp. 377-381). MIT Press.
Pargellis, A. N. (1996). The evolution of self-
replicating computer organisms. Physica D:
Nonlinear Phenomena, 98(1), 111-127.
Amoeba
PolyWorld
Yaeger, L. (1993). Computational genetics, physiology, metabolism,
neural systems, learning, vision, and behavior or PolyWorld: Life in a
new context. Artificial Live III (pp. 263-298). Addison-Wesley.
Geb
Channon, A. D., & Damper, R. I.
(1998). Evolving novel
behaviors via natural selection.
Artificial Life VI (pp. 384-388).
MIT Press.
20 / 60
21. 3D Equivalent: Karl Sims’ “Blockies”
Ito, T., Pilat, M. L., Suzuki, R., & Arita, T. (2016). Population and
evolutionary dynamics based on predator–prey relationships in a
3D physical simulation. Artificial Life, 22(2), 226-240.
Sims, K. (1994). Evolving 3D morphology
and behavior by competition. Artificial Life,
1(4), 353-372.
21 / 60
23. Evolution in Cellular Automata?
How to create basic processes of evolution from local rules?
• Organisms, self-reproduction, heredity, variation, selection
Early attempts:
• Emergence and evolution of
“symbioorganisms” by Barricelli
(first computational experiments of logical
self-reproduction and artificial evolution)
• Sexually reproducing CA by Vitányi
Barricelli, N. A. (1962). Numerical testing of evolution theories.
Part I. Theoretical introduction and basic tests. Acta
Biotheoretica, XVI(1/2): 69–98.
Barricelli, N. A. (1963). Numerical testing of evolution theories.
Part II. Preliminary tests of performance. Symbiogenesis and
terrestrial life. Acta Biotheoretica, XVI(3/4): 99–126.
Taylor, T., & Dorin, A. (2020). Rise of the Self-Replicators.
Springer.
Vitányi, P. M. (1973). Sexually reproducing cellular automata.
Mathematical Biosciences, 18(1-2), 23-54. 23 / 60
24. “Death” Introduced in
Chou & Reggia’s Loops
Chou, H. H., & Reggia, J. A. (1997). Emergence of self-replicating structures in a cellular automata space. Physica
D: Nonlinear Phenomena, 110(3-4), 252-276.
Chou, H. H., & Reggia, J. A. (1998). Problem solving during artificial selection of self-replicating loops. Physica D:
Nonlinear Phenomena, 115(3-4), 293-312.
Death is important in evolution!!
Sayama, H. (1998). Introduction of structural dissolution
into Langton's self-reproducing loop. Artificial Life VI
(pp. 114-122). MIT Press.
Veenstra, F., de Prado Salas, P. G., Stoy, K., Bongard, J., &
Risi, S. (2020). Death and progress: How evolvability is
influenced by intrinsic mortality. Artificial Life, 26(1), 90-
111.
24 / 60
25. Evoloops
(Or How Hiroki Obtained His PhD with Weird Research)
• Redesigned Langton’s loops with:
• Death (structural dissolution)
• Robustness against perturbations
• Minor modification of initial shape
Sayama, H. (1998). Constructing Evolutionary Systems
on a Simple Deterministic Cellular Automata Space.
PhD Dissertation, University of Tokyo.
Sayama, H. (1999). A new structurally dissolvable self-
reproducing loop evolving in a simple cellular
automata space. Artificial Life, 5(4), 343-365. 25 / 60
26. Detailed Gene Sequencing of Evoloops
Salzberg, C., & Sayama, H. (2004). Complex genetic evolution of artificial self‐replicators in cellular automata.
Complexity, 10(2), 33-39.
26 / 60
27. Diverse Macroscopic Morphologies
27 / 60
Salzberg, C., & Sayama, H. (2004). Complex genetic evolution of artificial self‐replicators in cellular automata.
Complexity, 10(2), 33-39.
28. Evolutionary Exploration in Genotype Space
Salzberg, C., Antony, A., & Sayama, H. (2006). Visualizing evolutionary dynamics of self-replicators:
A graph-based approach. Artificial Life, 12(2), 275-287.
28 / 60
29. Salzberg, C., & Sayama, H. (2004). Complex genetic evolution of artificial self‐replicators in
cellular automata. Complexity, 10(2), 33-39. 29 / 60
30. Other Examples of
Evolving CA
• Shape-encoding self-replicators
• Sexyloops
Sayama, H. (2000). Self-replicating worms that increase
structural complexity through gene transmission.
Artificial life VII (pp. 21-30). MIT Press.
Suzuki, K., & Ikegami, T. (2006). Spatial-pattern-induced evolution of a
self-replicating loop network. Artificial Life, 12(4), 461-485.
Oros, N., & Nehaniv, C. L. (2007). Sexyloop: Self-
reproduction, evolution and sex in cellular
automata. IEEE Symposium on Artificial Life (pp.
130-138). IEEE.
30 / 60
32. Artificial
Chemistry
• A sub-field of Artificial
Life where models of
artificial chemical
reactions are used to
study the emergence
and evolution of life
from non-living
elements
Banzhaf, W., & Yamamoto, L. (2015).
Artificial Chemistries. MIT Press.
32 / 60
33. Self-Replication of Artificial Molecules/Cells
(Not Quite Evolving)
• Self-replicating strings by
complementary matching
• Self-replicating cells made of
logical particles
Hutton, T. J. (2002). Evolvable self-replicating
molecules in an artificial chemistry. Artificial
Life, 8(4), 341-356.
Smith, A., Turney, P., & Ewaschuk, R. (2003).
Self-replicating machines in continuous space
with virtual physics. Artificial Life, 9(1), 21-40.
Hutton, T. J. (2007). Evolvable self-reproducing cells in a two-
dimensional artificial chemistry. Artificial Life, 13(1), 11-30.
33 / 60
35. Making Swarm
Chemistry Evolvable
• Recipe transmission
(with errors) between
particles
• Environmental
perturbation to break
status quo
Sayama, H. (2011). Seeking open-ended
evolution in Swarm Chemistry. IEEE
Symposium on Artificial Life (pp. 186-
193). IEEE.
Sayama, H., & Wong, C. (2011).
Quantifying evolutionary dynamics of
Swarm Chemistry. ECAL (pp. 729-730).
MIT Press.
35 / 60
36. Automatically Identified Best Runs
• http://YouTube.com/ComplexSystem/
Sayama, H., & Wong, C. (2011). Quantifying evolutionary dynamics of Swarm Chemistry.
ECAL (pp. 729-730). MIT Press. 36 / 60
38. FYI: Evolution Slows Down in 3D Space
3D
2D
Sayama, H. (2012). Evolutionary Swarm Chemistry in three-dimensions. Artificial Life 13 (pp.576-577). MIT Press. 38 / 60
39. Automated
Object
Harvesting
Sayama, H. (2018, July). Seeking open-
ended evolution in Swarm Chemistry II:
Analyzing long-term dynamics via
automated object harvesting. ALIFE 2018
(pp. 59-66). MIT Press.
39 / 60
49. Picbreeder
• Evolution of visual patterns
using NEAT and human-
computer interaction
• Human users serve as the
dynamically changing
environment for evolvers
Secretan, J., Beato, N., D Ambrosio, D. B.,
Rodriguez, A., Campbell, A., & Stanley, K. O.
(2008). Picbreeder: Evolving pictures
collaboratively online. Proceedings of the
SIGCHI Conference on Human Factors in
Computing Systems (pp. 1759-1768). ACM.
49 / 60
50. Novelty Search
Lehman, J., & Stanley, K. O. (2011). Evolving a
diversity of virtual creatures through novelty
search and local competition. Proceedings of
the 13th Annual Conference on Genetic and
Evolutionary Computation (pp. 211-218). ACM.
Such, F. P., Madhavan, V., Conti, E., Lehman, J.,
Stanley, K. O., & Clune, J. (2017). Deep
neuroevolution: Genetic algorithms are a
competitive alternative for training deep neural
networks for reinforcement learning. NeurIPS
Deep Reinforcement Learning Workshop / arXiv
preprint arXiv:1712.06567.
50 / 60
51. Lenia
Chan, B. W. C. (2019). Lenia: Biology of artificial
life. Complex Systems, 28(3), 251–286.
Chan, B. W. C. (2020). Lenia and expanded
universe. ALIFE 2020: The 2020 Conference on
Artificial Life (pp. 221-229). MIT Press.
51 / 60
56. How to Make Things Evolve
• “How Things Evolve” ≠ “How to Make Things Evolve”
• Key ingredients:
Identity of an “organism”
Replication with heredity
Variation
Selection (death); natural selection preferrable
Co-evolution (incl. “adversarial” approaches)
Dynamic, non-stationary environment
Accessibility to vast possibility space
Formation of higher-order entities
Spatial parallelism
Observation and detection
Recreational/entertainment spirit!!
56 / 60
57. Beyond
Artificial Life
57 / 60
• “How to Make Things
Evolve” is applicable to
many other scenarios
• Society
• Product design &
innovation
• Idea generation &
decision making
• Sustainability (i.e.,
“endless” existence)
Dionne, S. D., Sayama, H., & Yammarino, F.
J. (2019). Diversity and social network
structure in collective decision making:
Evolutionary perspectives with agent-
based simulations. Complexity, 7591072.
58. Future Directions:
Von Neumann’s Ultimate Challenge
• How to create kinematic evolutionary
systems?
Freitas, R. A., & Merkle, R. C. (2004). Kinematic
Self-Replicating Machines. Landes Bioscience.
Freitas, R. A., & Space Initiative. (1982). Advanced Automation for
Space Missions. NASA Conference Publication 2255. 58 / 60
59. Let’s Make Xenobots Evolve!!
59 / 60
Kriegman, S., Blackiston, D., Levin, M., & Bongard, J. (2021). Kinematic self-replication in
reconfigurable organisms. Proceedings of the National Academy of Sciences, 118(49),
e2112672118.
