Localized states with nontrivial symmetries: Localized labyrinthine patterns

The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with nontrivial symmetries such as labyrinthine patterns are observed in different physical contexts. Here we report stable localized disordered patterns in spatially extended dissipative systems. These two- and three-dimensional localized structures consist of an isolated labyrinth embedded in a homogeneous steady state. Their partial bifurcation diagram allows us to explain this phenomenon as a manifestation of a pinning-depinning transition. We illustrate our findings on the Swift-Hohenberg-type of equations and other well-established models for plant ecology, nonlinear optics, and reaction-diffusion systems.