How lineages begin and end in a pattern-forming chemical medium

Lineages in a pattern-forming medium without replicators: the Gray-Scott reaction-diffusion system in three habitats. Four measured results. (i) The medium has a mixing length: two lineages merge below a surface gap of 9 +/- 1 cells, independent of body size. (ii) A fusion is a merger, not a birth: both lineages end on the same step and one body appears under a new identifier. (iii) The outcome is a whole-cell step while the dissolution time spreads before it. (iv) A lineage's end is mostly the loss of its name rather than of its cells, and the habitat that maximises generations is not the one where a lineage survives. The heredity coefficient is measured rather than asserted: the daughter-on-parent slope is 0.9837 [0.9680, 1.0002] and 0.9931 [0.9756, 1.0103], the residual is the mutation rule's own sigma to one per cent, and with the mutation ablated the trait has no variance at all.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23933439
Primary Topic
Cellular Automata and Applications
Type
preprint
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preprint

How lineages begin and end in a pattern-forming chemical medium

Илья Владимиров
Zenodo (CERN European Organization for Nuclear Research)
Cellular Automata and Applications
preprint

How lineages begin and end in a pattern-forming chemical medium

Илья Владимиров
preprint en

Abstract

Lineages in a pattern-forming medium without replicators: the Gray-Scott reaction-diffusion system in three habitats. Four measured results. (i) The medium has a mixing length: two lineages merge below a surface gap of 9 +/- 1 cells, independent of body size. (ii) A fusion is a merger, not a birth: both lineages end on the same step and one body appears under a new identifier. (iii) The outcome is a whole-cell step while the dissolution time spreads before it. (iv) A lineage's end is mostly the loss of its name rather than of its cells, and the habitat that maximises generations is not the one where a lineage survives. The heredity coefficient is measured rather than asserted: the daughter-on-parent slope is 0.9837 [0.9680, 1.0002] and 0.9931 [0.9756, 1.0103], the residual is the mutation rule's own sigma to one per cent, and with the mutation ablated the trait has no variance at all.

Zenodo (CERN European Organization for Nuclear Research)
Cellular Automata and Applications
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