Numerical Examples of Evolutionary Processes [English translation of “Esempi Numerici di Processi di Evoluzione” (1954)]

Publication details

Numerical Examples of Evolutionary Processes [English translation of “Esempi Numerici di Processi di Evoluzione” (1954)]

Nils Aall Barricelli

2026

Abstract

Some consequences of the Darwinian principle of evolution by survival of the fittest are analyzed. Considering that this principle reduces evolution to a purely statistical phenomenon, we draw the conclusion that it may apply not only to living organisms but also to elements of any kind able to reproduce and to undergo hereditary changes (mutations). By applying the Darwinian principle to the most primitive elements with the required properties, viruses or artificially constructed elements (for instance, numbers), we show that the Darwinian principle alone is not sufficient to explain the origin of an evolutionary process like the biological one. At least one additional principle is needed in order to explain the origin of such an evolutionary process. We suggest that the theory of gene symbiosis may serve as this complementary principle. By using numerical elements with reproduction rules that make symbiosis (or utilitarian association) necessary, we show that evolutionary processes with promising properties are likely to arise. In the last part of the paper, we describe an evolutionary process obtained with numerical elements during a series of experiments performed by the electronic computer at the Institute for Advanced Study, Princeton, NJ, USA, in the spring of 1953.

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Reference

Barricelli, N. A. (2026). Numerical Examples of Evolutionary Processes [English translation of “Esempi Numerici di Processi di Evoluzione” (1954)] (G. Bianchi & T. Taylor, Trans.). Artificial Life, X(X), XX-XX. https://doi.org/10.1162/artl_X_XXXXX

BibTeX

@article{barricelli2026experiments,
  author = {Barricelli, Nils Aall},
  translator = {Bianchi, Giulia and Taylor, Tim},
  title = {Numerical Examples of Evolutionary Processes [English translation of ``Esempi Numerici di Processi di Evoluzione'' (1954)]},
  journal = {Artificial Life},
  year = {2026},
  volume = {X},
  number = {X},
  pages = {XX-XX},
  publisher = {{MIT} Press Journals},
  doi = {10.1162/artl_X_XXXXX},
  issn = {1530-9185},
  category = {journal},
  keywords = {history, selfrep, oee}
}

Related publications

Taylor, T., & Bianchi, G. (2026). A Commentary on Nils Aall Barricelli’s “Esempi Numerici di Processi di Evoluzione” (1954). Artificial Life, X(X), XX-XX. https://doi.org/10.1162/artl_X_XXXXX
Full details
```
@article{taylor2026commentary,
  author = {Taylor, Tim and Bianchi, Giulia},
  title = {A Commentary on Nils Aall Barricelli's ``Esempi Numerici di Processi di Evoluzione'' (1954)},
  journal = {Artificial Life},
  year = {2026},
  volume = {X},
  number = {X},
  pages = {XX-XX},
  publisher = {{MIT} Press Journals},
  doi = {10.1162/artl_X_XXXXX},
  issn = {1530-9185},
  category = {journal},
  keywords = {history, selfrep, oee}
}
```
Channon, A., Bedau, M., Packard, N., & Taylor, T. (2024). Editorial Introduction to the 2024 Special Issue on Open-Ended Evolution. Artificial Life, 30(3), 300–301. https://doi.org/10.1162/artl_e_00445
PDF Full details
```
@article{channon2024editorial,
  author = {Channon, Alastair and Bedau, Mark and Packard, Norman and Taylor, Tim},
  title = {Editorial Introduction to the 2024 Special Issue on Open-Ended Evolution},
  journal = {Artificial Life},
  year = {2024},
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  number = {3},
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}
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PDF Full details
```
@article{taylor2024afterword,
  author = {Taylor, Tim},
  title = {An Afterword to "Rise of the Self-Replicators": Placing John A. Etzler, Frigyes Karinthy, Fred Stahl, and Others in the Early History of Thought About Self-Reproducing Machines},
  journal = {Artificial Life},
  year = {2024},
  volume = {30},
  number = {1},
  pages = {91-105},
  publisher = {{MIT} Press Journals},
  doi = {10.1162/artl_a_00424},
  issn = {1530-9185},
  category = {journal},
  keywords = {history, selfrep}
}
```
Taylor, T. (2021). Evolutionary Innovation Viewed as Novel Physical Phenomena and Hierarchical Systems Building. Presented at the Fourth Workshop on Open-Ended Evolution (OEE4) at the 2021 Conference on Artificial Life (ALIFE 2021). Retrieved from https://arxiv.org/abs/2107.09669
PDF Full details
```
@article{taylor2021evolutionary,
  author = {Taylor, Tim},
  title = {Evolutionary Innovation Viewed as Novel Physical Phenomena and Hierarchical Systems Building},
  journal = {Presented at the Fourth Workshop on Open-Ended Evolution (OEE4) at the 2021 Conference on Artificial Life (ALIFE 2021)},
  year = {2021},
  month = jul,
  url = {https://arxiv.org/abs/2107.09669},
  category = {workshop},
  keywords = {oee}
}
```
Taylor, T. (2020). The Importance of Open-Endedness (For the Sake of Open-Endedness). In J. Bongard, J. Lovato, L. Hebert-Dufrésne, R. Dasari, & L. Soros (Eds.), ALIFE 2020: Proceedings of the Artificial Life Conference 2020 (pp. 578–580). https://doi.org/10.1162/isal_a_00257
PDF Full details
```
@inproceedings{taylor2020importance,
  author = {Taylor, Tim},
  title = {The Importance of Open-Endedness (For the Sake of Open-Endedness)},
  booktitle = {ALIFE 2020: Proceedings of the Artificial Life Conference 2020},
  editor = {Bongard, Josh and Lovato, Juniper and Hebert-Dufrésne, Laurent and Dasari, Radhakrishna and Soros, Lisa},
  year = {2020},
  publisher = {{MIT} Press},
  pages = {578-580},
  doi = {10.1162/isal_a_00257},
  category = {conference},
  keywords = {oee}
}
```

Taylor, T. (2020). What Am I For? Self-Purpose and Self-Reproduction in Rossum’s Universal Robots (Samoúčelnost a samoreprodukce u Rossumových univerzálních robotů). In J. Čejková (Ed.), ROBOT 100: Sto rozumů (pp. 178–180). Prague: Kosmas.

PDF Full details

@incollection{taylor2020what,
  author = {Taylor, Tim},
  title = {What Am I For? Self-Purpose and Self-Reproduction in Rossum's Universal Robots (Samoúčelnost a samoreprodukce u Rossumových univerzálních robotů)},
  booktitle = {ROBOT 100: Sto rozumů},
  editor = {\v{C}ejkov\'{a}, Jitka},
  year = {2020},
  pages = {178-180},
  isbn = {978-80-7592-062-1},
  publisher = {Kosmas},
  address = {Prague},
  category = {chapter},
  keywords = {selfrep, agency},
  note = {Centenary edition of Karel \v{C}apek's Rossum's Universal Robots. In Czech.}
}

Taylor, T., & Dorin, A. (2020). Rise of the Self-Replicators: Early Visions of Machines, AI and Robots That Can Reproduce and Evolve. Cham: Springer.
Full details
```
@book{taylor2020rise,
  title = {Rise of the Self-Replicators: Early Visions of Machines, AI and Robots That Can Reproduce and Evolve},
  author = {Taylor, Tim and Dorin, Alan},
  publisher = {Springer},
  year = {2020},
  isbn = {978-3-030-48233-6},
  address = {Cham},
  category = {book},
  keywords = {history, selfrep}
}
```
Taylor, T. (2019). Evolutionary Innovations and Where to Find Them: Routes to Open-Ended Evolution in Natural and Artificial Systems. Artificial Life, 25(2), 207–224. https://doi.org/10.1162/artl_a_00290
PDF Full details
```
@article{taylor2019evolutionary,
  author = {Taylor, Tim},
  title = {Evolutionary Innovations and Where to Find Them: Routes to Open-Ended Evolution in Natural and Artificial Systems},
  journal = {Artificial Life},
  year = {2019},
  volume = {25},
  number = {2},
  pages = {207--224},
  publisher = {{MIT} Press Journals},
  doi = {10.1162/artl_a_00290},
  issn = {1064-5462},
  category = {journal},
  keywords = {oee}
}
```
Packard, N., Bedau, M., Channon, A., Ikegami, T., Rasmussen, S., Stanley, K., & Taylor, T. (2019). An Overview of Open-Ended Evolution: Editorial Introduction to the Open-Ended Evolution II Special Issue. Artificial Life, 25(2), 93–103. https://doi.org/10.1162/artl_a_00291
PDF Full details
```
@article{packard2019overview,
  author = {Packard, Norman and Bedau, Mark and Channon, Alastair and Ikegami, Takashi and Rasmussen, Steen and Stanley, Kenneth and Taylor, Tim},
  title = {An Overview of Open-Ended Evolution: Editorial Introduction to the Open-Ended Evolution II Special Issue},
  journal = {Artificial Life},
  year = {2019},
  volume = {25},
  number = {2},
  pages = {93--103},
  publisher = {{MIT} Press Journals},
  doi = {10.1162/artl_a_00291},
  issn = {1064-5462},
  category = {journal},
  keywords = {oee}
}
```
Packard, N., Bedau, M., Channon, A., Ikegami, T., Rasmussen, S., Stanley, K., & Taylor, T. (2019). Open-Ended Evolution and Open-Endedness: Editorial Introduction to the Open-Ended Evolution I Special Issue. Artificial Life, 25(1), 1–3. https://doi.org/10.1162/artl_e_00282
PDF Full details
```
@article{packard2019openended,
  author = {Packard, Norman and Bedau, Mark and Channon, Alastair and Ikegami, Takashi and Rasmussen, Steen and Stanley, Kenneth and Taylor, Tim},
  title = {Open-Ended Evolution and Open-Endedness: Editorial Introduction to the Open-Ended Evolution I Special Issue},
  journal = {Artificial Life},
  year = {2019},
  volume = {25},
  number = {1},
  pages = {1--3},
  publisher = {{MIT} Press Journals},
  doi = {10.1162/artl_e_00282},
  issn = {1064-5462},
  category = {journal},
  keywords = {oee}
}
```
Taylor, T., & Dorin, A. (2018). Past Visions of Artificial Futures: One Hundred and Fifty Years under the Spectre of Evolving Machines. In T. Ikegami, N. Virgo, O. Witkowski, M. Oka, R. Suzuki, & H. Iizuka (Eds.), ALIFE 2018: Proceedings of the Artificial Life Conference 2018 (pp. 91–98). https://doi.org/10.1162/isal_a_00022
PDF Full details
```
@inproceedings{taylor2018past,
  author = {Taylor, Tim and Dorin, Alan},
  title = {Past Visions of Artificial Futures: One Hundred and Fifty Years under the Spectre of Evolving Machines},
  booktitle = {ALIFE 2018: Proceedings of the Artificial Life Conference 2018},
  editor = {Ikegami, Takashi and Virgo, Nathaniel and Witkowski, Olaf and Oka, Mizuki and Suzuki, Reiji and Iizuka, Hiroyuki},
  year = {2018},
  publisher = {{MIT} Press},
  pages = {91--98},
  doi = {10.1162/isal_a_00022},
  category = {conference},
  keywords = {history, selfrep}
}
```
Taylor, T. (2018). Routes to Open-Endedness in Evolutionary Systems. Presented at the Third Workshop on Open-Ended Evolution (OEE3) at the 2018 Conference on Artificial Life (ALIFE 2018). Retrieved from https://arxiv.org/abs/1806.01883v3
PDF Full details
```
@article{taylor2018routes,
  author = {Taylor, Tim},
  title = {Routes to Open-Endedness in Evolutionary Systems},
  journal = {Presented at the Third Workshop on Open-Ended Evolution (OEE3) at the 2018 Conference on Artificial Life (ALIFE 2018)},
  year = {2018},
  month = jul,
  url = {https://arxiv.org/abs/1806.01883v3},
  category = {workshop},
  keywords = {oee}
}
```

Taylor, T., Bedau, M., Channon, A., Ackley, D., Banzhaf, W., Beslon, G., … Wiser, M. (2016). Open-Ended Evolution: Perspectives from the OEE Workshop in York. Artificial Life, 22(3), 408–423. https://doi.org/10.1162/artl_a_00210

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@article{taylor2016openended,
  author = {Taylor, Tim and Bedau, Mark and Channon, Alastair and Ackley, David and Banzhaf, Wolfgang and Beslon, Guillaume and Dolson, Emily and Froese, Tom and Hickinbotham, Simon and Ikegami, Takashi and McMullin, Barry and Packard, Norman and Rasmussen, Steen and Virgo, Nathaniel and Agmon, Eran and Clark, Edward and McGregor, Simon and Ofria, Charles and Ropella, Glen and Spector, Lee and Stanley, Kenneth O. and Stanton, Adam and Timperley, Christopher and Vostinar, Anya and Wiser, Michael},
  title = {Open-Ended Evolution: Perspectives from the {OEE} Workshop in {Y}ork},
  journal = {Artificial Life},
  year = {2016},
  publisher = {{MIT} Press Journals},
  volume = {22},
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  keywords = {oee}
}

Taylor, T. (2015). Requirements for Open-Ended Evolution in Natural and Artificial Systems. Presented at the EvoEvo Workshop at the European Conference on Artificial Life 2015 (ECAL 2015). Retrieved from https://arxiv.org/abs/1507.07403
PDF Full details
```
@article{taylor2015requirements,
  author = {Taylor, Tim},
  title = {Requirements for Open-Ended Evolution in Natural and Artificial Systems},
  journal = {Presented at the EvoEvo Workshop at the European Conference on Artificial Life 2015 (ECAL 2015)},
  year = {2015},
  month = jul,
  url = {https://arxiv.org/abs/1507.07403},
  category = {workshop},
  keywords = {oee}
}
```
Taylor, T., Dorin, A., & Korb, K. (2014). Digital Genesis: Computers, Evolution and Artificial Life. Presented at the 7th Munich-Sydney-Tilburg Philosophy of Science Conference: Evolutionary Thinking, University of Sydney, 20-22 March 2014. Retrieved from https://arxiv.org/abs/1512.02100
PDF Full details
```
@article{taylor2014digital,
  author = {Taylor, Tim and Dorin, Alan and Korb, Kevin},
  title = {Digital Genesis: Computers, Evolution and Artificial Life},
  journal = {Presented at the 7th Munich-Sydney-Tilburg Philosophy of Science Conference: Evolutionary Thinking, University of Sydney, 20-22 March 2014},
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  url = {https://arxiv.org/abs/1512.02100},
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  keywords = {history}
}
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Taylor, T. (2014). Evolution in virtual worlds. In M. Grimshaw (Ed.), The Oxford Handbook of Virtuality (pp. 526–548). https://doi.org/10.1093/oxfordhb/9780199826162.013.044
PDF Full details
```
@inbook{taylor2014evolution,
  title = {Evolution in virtual worlds},
  author = {Taylor, Tim},
  year = {2014},
  doi = {10.1093/oxfordhb/9780199826162.013.044},
  language = {English},
  isbn = {9780199826162},
  pages = {526--548},
  editor = {Grimshaw, Mark},
  booktitle = {The Oxford Handbook of Virtuality},
  publisher = {Oxford University Press},
  address = {United Kingdom},
  category = {chapter},
  keywords = {oee}
}
```
Taylor, T. (2012). Exploring the Concept of Open-Ended Evolution. In C. Adami, D. M. Bryson, C. Ofria, & R. T. Pennock (Eds.), Artificial Life 13: Proceedings of the Thirteenth International Conference on the Simulation and Synthesis of Living Systems (pp. 540–541). MIT Press.
PDF Full details
```
@inproceedings{taylor2012exploring,
  author = {Taylor, Tim},
  title = {Exploring the Concept of Open-Ended Evolution},
  booktitle = {Artificial Life 13: Proceedings of the Thirteenth International Conference on the Simulation and Synthesis of Living Systems},
  year = {2012},
  editor = {Adami, Christoph and Bryson, David M. and Ofria, Charles and Pennock, Robert T.},
  pages = {540--541},
  publisher = {{MIT} Press},
  category = {conference},
  keywords = {oee}
}
```
Taylor, T. (2004). Redrawing the Boundary between Organism and Environment. In J. Pollack, M. A. Bedau, P. Husbands, R. A. Watson, & T. Ikegami (Eds.), Artificial Life IX: Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems (pp. 268–273). https://doi.org/10.7551/mitpress/1429.003.0045
PDF Full details
```
@inproceedings{taylor2004redrawing,
  author = {Taylor, Tim},
  title = {Redrawing the Boundary between Organism and Environment},
  booktitle = {Artificial Life IX: Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems},
  year = {2004},
  editor = {Pollack, Jordan and Bedau, Mark A. and Husbands, Phil and Watson, Richard A. and Ikegami, Takashi},
  pages = {268-273},
  address = {Cambridge, MA},
  publisher = {{MIT} Press},
  doi = {10.7551/mitpress/1429.003.0045},
  category = {conference},
  keywords = {evoca, oee, meaning, agency}
}
```
Taylor, T. (2003). Evolving Interaction in Artificial Systems: An historical overview and future directions. In P. McOwan, K. Dautenhahn, & C. L. Nehaniv (Eds.), Abstracts from the Evolvability and Interaction Symposium, held at Queen Mary, University of London, UK, in October 2003. University of Hertfordshire Computer Science Technical Report No. 393.
Full details
```
@incollection{taylor2003evolving,
  author = {Taylor, Tim},
  title = {Evolving Interaction in Artificial Systems: An historical overview and future directions},
  booktitle = {Abstracts from the Evolvability and Interaction Symposium, held at Queen Mary, University of London, UK, in October 2003},
  publisher = {University of Hertfordshire Computer Science Technical Report No.~393},
  year = {2003},
  month = oct,
  editor = {McOwan, Peter and Dautenhahn, Kerstin and Nehaniv, Chrystopher L.},
  category = {workshop},
  keywords = {evoca, history, oee}
}
```
Taylor, T. (2001). Creativity in Evolution: Individuals, Interactions and Environments. In P. J. Bentley & D. W. Corne (Eds.), Creative Evolutionary Systems (pp. 79–108). https://doi.org/10.1016/b978-155860673-9/50037-9
PDF Full details
```
@incollection{taylor2001creativity,
  author = {Taylor, Tim},
  title = {Creativity in Evolution: Individuals, Interactions and Environments},
  booktitle = {Creative Evolutionary Systems},
  editor = {Bentley, Peter J and Corne, David W},
  chapter = {1},
  pages = {79--108},
  publisher = {Morgan Kaufmann},
  year = {2001},
  doi = {10.1016/b978-155860673-9/50037-9},
  category = {chapter},
  keywords = {creativity, oee}
}
```
McMullin, B., Taylor, T., & von Kamp, A. (2001). Who Needs Genomes? Proceedings of the Atlantic Symposium on Computational Biology and Genome Information Systems and Technology, CBGIST 2001, 250–254. Duke University, USA.
PDF Full details
```
@inproceedings{mcmullin2001who,
  author = {McMullin, Barry and Taylor, Tim and {von Kamp}, Axel},
  title = {Who Needs Genomes?},
  booktitle = {Proceedings of the Atlantic Symposium on Computational Biology and Genome Information Systems and Technology, CBGIST 2001},
  year = {2001},
  pages = {250-254},
  month = mar,
  address = {Duke University, USA},
  category = {conference},
  keywords = {selfrep}
}
```
Taylor, T. (2000). Some Representational and Ecological Aspects of Evolvability. In C. L. Nehaniv (Ed.), Proceedings of the Evolvability Workshop at the the Seventh International Conference on the Simulation and Synthesis of Living Systems (Artificial Life 7) (pp. 41–44). Retrieved from http://homepages.herts.ac.uk/ comqcln/al7ev/cnts.html
PDF Full details
```
@inproceedings{taylor2000some,
  author = {Taylor, Tim},
  title = {Some Representational and Ecological Aspects of Evolvability},
  booktitle = {Proceedings of the Evolvability Workshop at the the Seventh International Conference on the Simulation and Synthesis of Living Systems (Artificial Life 7)},
  year = {2000},
  editor = {Nehaniv, Chrystopher L.},
  pages = {41-44},
  url = {http://homepages.herts.ac.uk/~comqcln/al7ev/cnts.html},
  month = aug,
  category = {workshop},
  keywords = {selfrep, oee}
}
```

Taylor, T. (1999). On Self-Reproduction and Evolvability. In D. Floreano, J.-D. Nicoud, & F. Mondada (Eds.), Advances in Artificial Life. ECAL 1999 (pp. 94–103). https://doi.org/10.1007/3-540-48304-7_15

PDF Full details

@inproceedings{taylor1999selfreproduction,
  title = {On Self-Reproduction and Evolvability},
  author = {Taylor, Tim},
  year = {1999},
  booktitle = {Advances in Artificial Life. ECAL 1999},
  series = {Lecture Notes in Computer Science},
  volume = {1674},
  pages = {94-103},
  editor = {Floreano, Dario and Nicoud, Jean-Daniel and Mondada, Francesco},
  doi = {10.1007/3-540-48304-7_15},
  publisher = {Springer},
  address = {Berlin},
  category = {conference},
  keywords = {selfrep, cosmos}
}

Taylor, T. J. (1999). From Artificial Evolution to Artificial Life (PhD thesis). School of Informatics, College of Science and Engineering, University of Edinburgh.
PDF Full details
```
@phdthesis{taylor1999artificial,
  author = {Taylor, Timothy John},
  title = {From Artificial Evolution to Artificial Life},
  school = {School of Informatics, College of Science and Engineering, University of Edinburgh},
  year = {1999},
  uri = {http://hdl.handle.net/1842/361},
  category = {dissertation},
  keywords = {selfrep, oee, cosmos}
}
```
Taylor, T. (1998). Nidus Design Document (Departmental Working Paper No. 269). Department of Artificial Intelligence, University of Edinburgh.
PDF Full details
```
@techreport{taylor1998nidus,
  author = {Taylor, Tim},
  title = {Nidus Design Document},
  institution = {Department of Artificial Intelligence, University of Edinburgh},
  year = {1998},
  type = {Departmental Working Paper},
  number = {269},
  month = jun,
  category = {techreport},
  keywords = {oee}
}
```
Taylor, T., & Hallam, J. (1997). Studying Evolution with Self-Replicating Computer Programs. In P. Husbands & I. Harvey (Eds.), Fourth European Conference on Artificial Life (pp. 550–559). Cambridge, MA: MIT Press.
PDF Full details
```
@inproceedings{taylor1997studying,
  title = {Studying Evolution with Self-Replicating Computer Programs},
  author = {Taylor, Tim and Hallam, John},
  pages = {550--559},
  booktitle = {Fourth European Conference on Artificial Life},
  editor = {Husbands, Phil and Harvey, Inman},
  publisher = {MIT Press},
  address = {Cambridge, MA},
  isbn = {0262581574},
  year = {1997},
  category = {conference},
  keywords = {cosmos, selfrep}
}
```