Increasingly, biologists are emphasising the cell as the most fundamental unit of life, and importantly, a view of the cell as an emergent, dynamic object irreducible to its molecular composition — “greater than the sum of its parts.” But what makes a cell itself living? Most answers to this question are unsatisfactory: lists of properties or behaviours that always have exceptions. Moreover, there is a lack of consensus that does not appear to be near resolution.

The theory of autopoiesis offers a potential solution here, providing an operational definition of the organisation of a cell, independent of what molecules compose it. Autopoietic theory allows us to answer questions about when a cell dies, and how it can behave. However, for it to realise this utility, rigorous theories need to be developed for specific models of emergent individuals. Beer (2020b) has previously used the Game of Life cellular automaton as one such model, and developed a mathematical theory of autopoiesis that can predict the behaviour and death of an emergent individual (Beer, McShaffrey, & Gaul, 2024).

This thesis extends and reformulates this work to a broader class of cellular automata, called Larger than Life (LtL) (Evans, 1996). I then further extend the LtL theory to a Euclidean automata, called RealLife (Pivato, 2007), and provide evidence of the convergence of autopoiesis in LtL to RealLife. I also introduce a method for deriving automata rules from the organisation of an individual.

Finally, I discuss the implications autopoietic theory has for our understanding of life and cognition, including a reevaluation of the relation between autopoiesis and the enactive approach to cognition (Di Paolo, 2005; Varela et al., 2017).

PDF/TeX

Gaul, T. M. (2025). Biological Organisation and Viability: A Theory of Autopoiesis in Cellular and Euclidean Automata. [Undergraduate Honors Thesis, Indiana University Bloomington].

@mastersthesis{Gaul2025,
  author = {Gaul, Thomas M},
  date = {2025-05-09},
  title = {Biological Organisation and Viability},
  subtitle = {A Theory of Autopoiesis in Cellular and Euclidean Automata},
  institution = {Indiana University Bloomington},
  type = {Honor's Thesis},
  language = {English}
}

Commentary

This is my undergraduate thesis for Departmental Honors in the Cognitive Science Program at Indiana Univeristy. None of the work contained in it has been published, as of October 28, 2026.

October 28, 2026: The source code for the project is currently available on GitLab, though I plan on migrating it to either GitHub (as a part of the Computational Neuroethology Lab organization) or to SourceHut, where I now host all of my projects. If anybody finds any of this code of interest, keep in mind that it is very bad. This was my first time using Rust, and my general programming ability was still quite poor. If you have any questions, feel free to reach out (see my contact information on the home page).

October 29, 2026: While I have not thoroughly reviewed this work in some time, I want to point out a few things that I feel are worth mentioning to any potential reader.

First, there are many, many grammatical errors, though I hope they are minor enough to not get in the way of understanding.

Second, the explanation of graphons is not very good, and so I recommend reading some introductory literature on the topic before tackling Chapter 3 or sections A.2-3 of the Appendix.

Third, I use the mathematical term “metric” incorrectly a number of times, though I don’t depend on any metric-theoretic results (as far as I’m aware), so the underlying mathematics should still be correct.