Research game 04 · 5–8 min
The Copy Garden
What does tomorrow inherit from today?
Optional advanced workshop: Descriptive and normative publication ↓
Optional advanced workshop · Descriptive and normative publication
What is happening? · The idea and the research
The garden has a finite population of short texts. Every text uses the same frame, “The garden holds ___.” Only the final noun is modelled; the fixed frame is not counted or generated. There are eight possible nouns and no grammar or meaning model.
With neutral copying, the next generation samples its nouns independently from the current counts. No word is penalised, yet rare words can miss a generation entirely. Once lost, they have zero probability of returning unless another source reintroduces them.
Precisely what is computed
Neutral: qᵢ = pᵢ
Favour: qᵢ = wᵢpᵢ / Σⱼ wⱼpⱼ, with chosen w = 3 and other w = 1
Archive: qᵢ = 0.85pᵢ + 0.15pᵢ(initial)
Next counts ∼ Multinomial(M, q)
Each generation replaces all M positions. For one word, its new neutral count is Binomial(M,p), with expected frequency p, variance of frequency p(1−p)/M, and exact dropout probability (1−p)ᴹ. This is the full-replacement unigram Wright–Fisher process, the tractable neutral case of the manuscript’s Theorem 1. The app offers M = 32, 64, or 256, and at most 30 generations per phase.
Selection is a toy one-token acceptance rule: accept the favoured word with probability 1 and others with probability 1/3, then condition on acceptance. It does not look ahead or test correctness. The archive is a separate illustrative external-input extension. Neither is a demonstration of the paper’s higher-order fixed-point or depth claims.
Word entropy is −Σ pᵢ log₂ pᵢ, in bits. It measures frequency diversity, not quality. The many-garden comparison uses 200 seeded pseudorandom trajectories per rule; the survival fractions and Wilson intervals are estimates. The one-step dropout formula is analytic. A shared seed makes a run reproducible, not empirical.
Research connection, exact source, and scope
Søren Riis, Drift and selection in LLM text ecosystems (preprint). The model choice was checked against the 41-page inspected manuscript (included unchanged) Drift_and_Selection.pdf: main Theorem 1(a), Appendix 1.9–1.10, and the acceptance-conditioned law in Appendix 4.3. The local review notes record the exact SHA-256 of the inspected file; this bundled copy is the inspected version.
Classical Wright–Fisher drift comes from population genetics. The optional workshop also compares exact binary-trigram laws under descriptive recycling and fixed-target normative publication. Both browser models are deliberately much smaller than the paper’s text experiments. It uses no LLM, no literary corpus, no semantic quality score, no lookahead, and no evidence about deployed AI ecosystems.