Labyrinthine versus straight-striped patterns generated by two-dimensional Turing systems

Hiroto Shoji, Yoh Iwasa

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


Striped patterns are often observed on fish skin. Such patterns have been accounted for by reaction-diffusion (RD) Turing-type models, in which two substances can spontaneously form a spatially heterogeneous pattern in a homogeneous field. Among the striped patterns generated by Turing-type models, some are "straight-striped patterns," with many stripes running in parallel, while others are "labyrinthine patterns," in which the stripes often change direction, merge with each other, and frequently branch out. RD models differ in terms of their tendency to generate either labyrinthine or straight-striped patterns. Here, we studied the conditions under which either a labyrinthine or straight-striped pattern would emerge. First, we defined an index for stripe clearness, Sh. Straight-striped patterns (large Sh) are formed if only a narrow range of spatial periods corresponds to an unstable mode. Labyrinthine patterns (small Sh) are formed when a wide range of spatial periods is unstable. More specifically, labyrinthine patterns are formed when the maximum spatial period of unstable modes is more than twice that of the minimum spatial period of unstable modes; otherwise, straight-striped patterns are formed. We then examined RD models with nonlinear reaction terms, including both activator-inhibitor and substrate-depletion models, and we demonstrated that the same conclusions hold with respect to the conditions required for labyrinthine versus straight-striped patterns.

Original languageEnglish
Pages (from-to)104-116
Number of pages13
JournalJournal of Theoretical Biology
Issue number1
Publication statusPublished - Nov 7 2005

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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