# Digital Life

What can computational worlds reveal about reproduction, adaptation, ecology and evolutionary novelty? Copying, evaluation and selection may occur within the evolving system or be supplied by its simulator and external optimizer.

## Reproduction and artificial chemistry

- **Self-reproducing automata** - A theoretical constructor uses a description to build a machine and copies that description for its offspring. Separating construction from copying explains how a machine can reproduce its own organization. [von Neumann 1966](<https://search.worldcat.org/title/1085642060> "Theory of Self-Reproducing Automata; University of Illinois Press (edited and completed by Burks)").
- **Langton's loops** - A cellular automaton reproduces a loop containing a circulating construction description. The reduced design separates self-reproduction from the stronger requirement of universal construction. [Langton 1984](<https://doi.org/10.1016/0167-2789(84)90256-2> "Self-reproduction in cellular automata; Physica D").
- **Algorithmic chemistry** - In this computational chemistry, functions act on functions to produce new functions. Random interactions in a fixed-size population form self-maintaining organizations; permitted replication rules change the resulting organization. [Fontana 1991](<https://sites.santafe.edu/~walter/Papers/alchemy92.pdf> "Algorithmic Chemistry; Artificial Life II").
- **Primordial particle systems** - Software particles following a local turning rule form persistent clusters that grow and split from random initial states. Reproduction concerns recurring structures without a genetic instruction tape. [Schmickl et al. 2016](<https://doi.org/10.1038/srep37969> "How a life-like system emerges from a simple particle motion law; Sci. Rep.").
- **Replicator emergence** - Random programs form replicators in designed execution environments. A later BFF study separates first appearance from population takeover and finds that mutation-only walks can also discover replicators. [Agüera y Arcas et al. 2024](<https://arxiv.org/abs/2406.19108v1> "Computational Life: How Well-formed, Self-replicating Programs Emerge from Simple Interaction; arXiv"), [Knierim et al. 2026](<https://arxiv.org/abs/2607.01483v1> "BFF: Simple explanations for complex phenomena; arXiv").

## Digital organisms and ecologies

- **Conway's Game of Life** - Binary cells update simultaneously from eight-neighbor counts. Fixed local rules support stable patterns, oscillators and moving gliders; the initial configuration determines their subsequent evolution. [Gardner 1970](<https://www.scientificamerican.com/article/mathematical-games-1970-10/> "Mathematical Games: The fantastic combinations of John Conway's new solitaire game &quot;life&quot;; Scientific American").
- **Tierra** - Seeded self-replicating programs mutate and compete for processor time and memory. Evolved parasites exploit other programs' replication machinery, turning competition over execution resources into an artificial ecology. [Ray 1991](<https://tomray.me/pubs/alife2/Ray1991AnApproachToTheSynthesisOfLife.pdf> "An approach to the synthesis of life; Artificial Life II").
- **Avida and complex functions** - Digital organisms evolve complex logic functions by reusing instructions that supported simpler rewarded functions. In the reported experiments, no particular intermediate function was indispensable. [Lenski et al. 2003](<https://www.nature.com/articles/nature01568> "The evolutionary origin of complex features; Nature"); [code](<https://github.com/devosoft/avida>).
- **Lenia** - Continuous-state cellular automata use neighborhood kernels and growth functions to sustain localized moving patterns. Rule parameters and initial states shape the repertoire of forms and interactions. [Chan 2019](<https://arxiv.org/abs/1812.05433v3> "Lenia: Biology of Artificial Life; Complex Systems"); [code](<https://github.com/Chakazul/Lenia>), [demo](<https://chakazul.github.io/Lenia/JavaScript/Lenia.html>).
    - **Flow-Lenia** - Conserves mass and localizes rule parameters, allowing differently parameterized patterns to coexist and interact. These changes support persistent individuals; intrinsic evolutionary processes remain untested in this paper. [Plantec et al. 2023](<https://arxiv.org/abs/2212.07906v2> "Flow-Lenia: Towards open-ended evolution in cellular automata through mass conservation and parameter localization; ALIFE"); [code](<https://github.com/erwanplantec/FlowLenia>), [video](<https://sites.google.com/view/flowlenia/videos>).

## Developmental rules and accessible forms

- **Arrival of the frequent** - In RNA-folding evolution simulations, frequently generated forms can fix before fitter, rarely generated alternatives appear. Theory links discovery times to the accessibility of phenotypes. [Schaper and Louis 2014](<https://doi.org/10.1371/journal.pone.0086635> "The Arrival of the Frequent: How Bias in Genotype-Phenotype Maps Can Steer Populations to Local Optima; PLOS ONE").
- **Simplicity bias** - With a simple input-output map and suitable compression estimates, randomly sampled inputs favor simple outputs in tested systems, including RNA folding. The probability bound is one-sided: simple outputs can still be rare. [Dingle et al. 2018](<https://doi.org/10.1038/s41467-018-03101-6> "Input–output maps are strongly biased towards simple outputs; Nat. Commun.").
- **Ruliobiology** - Selecting cellular-automaton rules for long finite lifetimes produces varied space-time forms, correlated traits and conserved early development. Mutation and selection are supplied externally; open-endedness remains a proposal. [Wolfram 2024](<https://writings.stephenwolfram.com/2024/05/why-does-biological-evolution-work-a-minimal-model-for-biological-evolution-and-other-adaptive-processes/> "Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes; author essay"), [Wolfram 2026](<https://writings.stephenwolfram.com/2026/10/endless-forms-most-beautiful-and-most-wonderful-ruliobiology-and-the-theoretical-foundations-of-biological-form/> "&quot;Endless Forms Most Beautiful and Most Wonderful&quot;: Ruliobiology and the Theoretical Foundations of Biological Form; author essay"); [code](<https://resources.wolframcloud.com/FunctionRepository/resources/AdaptiveCellularAutomaton/>).

## Evolution, evolvability and open-endedness

- **Novelty search** - Rewards behavioral difference from previously encountered solutions. It outperforms objective-based search on the paper's deceptive maze and biped tasks; the chosen behavior descriptor defines what counts as novel. [Lehman and Stanley 2011](<https://doi.org/10.1162/EVCO_a_00025> "Abandoning Objectives: Evolution Through the Search for Novelty Alone; Evol. Comput.").
- **Open-ended evolution criteria** - Distinguishes observable hallmarks of continuing innovation from proposed mechanisms that produce them. A single novel adaptation or rise in complexity does not demonstrate an ongoing open-ended process. [Taylor et al. 2016](<https://www.tim-taylor.com/papers/taylor2016openended.pdf> "Open-Ended Evolution: Perspectives from the OEE Workshop in York; Artificial Life").
    - **Routes to evolutionary innovation** - Distinguishes exploratory, expansive and transformational novelty. Asks whether phenotype generation, evaluation and reproduction occur within the evolving system or are supplied externally; proposes routes toward open-endedness. [Taylor 2019](<https://arxiv.org/abs/1806.01883v4> "Evolutionary Innovations and Where to Find Them: Routes to Open-Ended Evolution in Natural and Artificial Systems; Artificial Life").
- **POET** - Coevolves terrain challenges and biped controllers, transferring solutions between environments. Transfer reaches obstacles missed by the tested direct-path curriculum; the environment generator still fixes the kinds of challenges available. [Wang et al. 2019](<https://arxiv.org/abs/1901.01753v3> "Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutions; arXiv"); [code](<https://github.com/uber-research/poet>).
- **Foundation-model-guided search** - ASAL scores simulation videos in a vision-language model's representation space to search for target forms, temporal novelty and diverse behaviors. Demonstrations span five substrates; the learned representation defines the search criterion. [Kumar et al. 2024](<https://arxiv.org/abs/2412.17799v1> "Automating the Search for Artificial Life with Foundation Models; arXiv"); [code](<https://github.com/SakanaAI/asal>), [video](<https://pub.sakana.ai/asal/>).

## Open questions

- What changes when generation, evaluation and reproduction become part of the evolving system rather than fixed simulator services?
- Which measures distinguish sustained innovation from exploration of a fixed repertoire, and how does the conclusion depend on run duration?
- Which apparent signatures of evolution persist when rule encoding, mutation operators and evaluation cutoffs change?

## Related topics

- [Hyperorganism](https://hyperorganism.github.io/)
- [Minimal-cell evolution](https://hyperorganism.github.io/synthetic-life/#minimal-cells-and-engineered-living-constructs) - Adaptation in a wet system provides a comparison without establishing open-endedness.
- [Evolutionary individuality](https://hyperorganism.github.io/collective-life/#evolutionary-individuality) - Changes in reproductive units are distinct from novelty within a fixed representation.
- [Growing neural cellular automata](https://hyperorganism.github.io/morphogenesis/#growth-and-repair) - Learned growth and repair do not by themselves demonstrate heritable evolution.
- [Interactive evolution in art](https://hyperorganism.github.io/systems-aesthetics/#evolution-and-artificial-ecologies) - Human selection is an explicit part of these systems.