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Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton

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  • Anamarija Fofonjka

    (University of Geneva
    SIB Swiss Institute of Bioinformatics)

  • Michel C. Milinkovitch

    (University of Geneva
    SIB Swiss Institute of Bioinformatics)

Abstract

We previously showed that the adult ocellated lizard skin colour pattern is effectively generated by a stochastic cellular automaton (CA) of skin scales. We additionally suggested that the canonical continuous 2D reaction-diffusion (RD) process of colour pattern development is transformed into this discrete CA by reduced diffusion coefficients at the borders of scales (justified by the corresponding thinning of the skin). Here, we use RD numerical simulations in 3D on realistic lizard skin geometries and demonstrate that skin thickness variation on its own is sufficient to cause scale-by-scale coloration and CA dynamics during RD patterning. In addition, we show that this phenomenon is robust to RD model variation. Finally, using dimensionality-reduction approaches on large networks of skin scales, we show that animal growth affects the scale-colour flipping dynamics by causing a substantial decrease of the relative length scale of the labyrinthine colour pattern of the lizard skin.

Suggested Citation

  • Anamarija Fofonjka & Michel C. Milinkovitch, 2021. "Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
  • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-22525-1
    DOI: 10.1038/s41467-021-22525-1
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    Cited by:

    1. Yanming Liu & He Tian & Fan Wu & Anhan Liu & Yihao Li & Hao Sun & Mario Lanza & Tian-Ling Ren, 2023. "Cellular automata imbedded memristor-based recirculated logic in-memory computing," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

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