High-integrity human intervention in ecosystems: Tracking self-organization modes
Fig 4
Self-organized (SO) modes associated with rhombic pattern.
A nearly asymptotic rhombic pattern in the (x, y) plane (left), resulting from an instability of a stripe pattern, and the corresponding Fourier plane (kx, ky) showing the three SO modes that comprise it (right). See Fig A in S1 Appendix for earlier snapshots. These modes include the original stripe mode with wave-vectors ±(kf, 0) (red squares in right panel), representing periodicity in the x direction as the inset with vertical red stripes in the right panel show. The signature of this mode in the rhombic pattern (left panel) is illustrated by the red lines. The two additional SO modes are a pair of oblique modes with wave-vectors ±(kf/2, ky) and ±(kf/2, −ky) (blue and green squares, respectively, in right panel), which represent slanted stripe patterns as the insets in blue and green in the right panel show. The wave-vector component ky is determined such that the corresponding wave-vector sits on a circle of radius k0—the wavenumber (periodicity) that the natural pattern (in the absence of ground modulations) tends to form. The signatures of the oblique modes in the rhombic pattern (left panel) are illustrated by the slanted blue and green lines.