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Morphogenetic patterns are highly sophisticated dissipative structures. Are they governed by the same general mechanisms as chemical and hydrodynamic patterns? Turings symmetry breaking and Wolperts signalling provide alternative mechanisms. The current evidence points out that the latter is more relevant but reality is still far more complicated.
The Nikolaevskiy equation has been proposed as a model for seismic waves, electroconvection and weak turbulence; we show that it can also be used to model transverse instabilities of fronts. This equation possesses a large-scale Goldstone mode that s
Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications, encompassin
We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review general co
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern formation near
The surface pattern formation on a gelation surface is analyzed using an effective surface roughness. The spontaneous surface deformation on DiMethylAcrylAmide (DMAA) gelation surface is controlled by temperature, initiator concentration, and ambient