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Turing patterns with pentagonal symmetry.

J L Aragón1, M Torres, D Gil

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 1-1010, Querétaro 76000, Mexico.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
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Numerical simulations reveal stable fivefold Turing patterns in confined circular domains. This finding offers a mechanism for the fivefold symmetry seen in early echinoid development and can mimic sea urchin patterns.

Area of Science:

  • Developmental Biology
  • Mathematical Biology
  • Pattern Formation

Background:

  • Turing patterns are crucial for biological morphogenesis.
  • Understanding pattern formation in confined geometries is challenging.
  • Fivefold symmetry is observed in various biological structures.

Purpose of the Study:

  • To numerically investigate Turing pattern formation in a confined circular domain.
  • To explore the influence of domain size on pattern symmetry.
  • To propose a mechanism for fivefold symmetry in biological development.

Main Methods:

  • Numerical simulations of reaction-diffusion equations.
  • Analysis of pattern formation in a circular domain with small aspect ratio.
  • Varying disk sizes to observe pattern transitions.

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Main Results:

  • Stable fivefold Turing patterns are formed within a specific range of disk sizes.
  • The formation of fivefold patterns is dependent on the domain's geometry.
  • The simulated patterns can serve as a basis for complex biological structures.

Conclusions:

  • Confined geometries can induce specific symmetries in Turing patterns.
  • The study provides a potential mechanism for fivefold symmetry in echinoderm development.
  • The findings can inform models of sea urchin pigmentation and crinoid plate arrangements.