title: Scale-invariance in reaction-diffusion models of spatial pattern formation.
abstract: We propose a reaction-diffusion model of spatial pattern formation whose solutions can exhibit scale-invariance over any desired range for suitable choices of parameters in the model. The model does not invoke preset polarity or any other ad hoc distinction between cells and provides a solution to the French flag problem without sources at the boundary. Furthermore, patterns other than the polar pattern that usually arises first in a growing one-dimensional system described by Turing's model can be obtained. Evidence is given that suggests that the model may apply in the slug stage of Dictyostelium discoideum.
mesh_terms: D002454:Cell Differentiation; D004023:Dictyostelium / Q000166:cytology; D004058:Diffusion; D008962:Models, Theoretical; D009024:Morphogenesis