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Do the wavelengths of the instability have an influence on the type of patterns that we are going to get? Meaning for example in 2D, if the unstable wavelengths are small with respect to the size of the system, we are going to get "dots", small disks, if they are comparable to the size of the system, we are going to get strips (more or less curved) or labyrinth ?

I also wonder whether other parameters enter into account. For example, strips of a typical size contain more matter than disks of radius of the same length, so the initial concentration is supposed to have a role.

Also, do you know any article that deals with that question, meaning how does the system choose his pattern ?

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The keyword here is pattern selection.

The typical wavelength of a pattern may be determined by the system's geometry or be intrinsic, as in reaction-diffusion systems; and, yes, this wavelength affects which patterns are displayed by the system, though, it seems to me, not in a trivial way.

Also play a role in pattern selection, among others:

  • boundaries (which may at least distort 'ideal' patterns)
  • initial conditions (especially important in mixed modes or multistable systems)
  • defects
  • anisotropies
  • system-specific factors.

A quick search for "pattern selection" has several relevant hits, I'd highlight:

De Wit's Spatial Patterns and Spatiotemporal Dynamics in Chemical Systems (e-print).
Cross and Hohenberg's Pattern formation outside of equilibrium (e-print).

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