Reaksjondiffusjonssystemer

Reaksjondiffusjon, or reaction-diffusion, describes processes in which chemical reactions and diffusion interact to produce evolving spatial patterns in a reacting medium. Diffusion causes substances to spread from regions of high concentration to low concentration, while chemical reactions convert species into others, potentially altering diffusion behavior. When these processes couple, the system can settle into steady patterns or exhibit dynamic behavior such as waves.

Mathematical models of reaction-diffusion systems typically use coupled partial differential equations that describe the concentrations of chemical species as functions of time and space. For two interacting species, the equations express the time rate of change of each concentration as the sum of a diffusion term—diffusion coefficient times the spatial Laplacian—and a nonlinear reaction term depending on the concentrations. The interplay between diffusion and reaction can destabilize a uniform state and produce patterns known as Turing patterns, oscillations, or traveling waves depending on parameters and boundary conditions.

Historically, the concept was introduced by Alan Turing in 1952 as a potential mechanism for biological morphogenesis, explaining how organisms develop spatially ordered structures. Since then, reaction-diffusion theory has influenced biology, chemistry, and materials science, guiding studies of chemical oscillations, pattern formation, and the design of reactive materials and reactors. Common examples include the Belousov-Zhabotinsky reaction and various computational models such as the Gray-Scott system, which generate spots, stripes, spirals, and other complex patterns. The field continues to inform approaches in synthetic biology and engineering, where controlled diffusion and reaction enable spatial patterning and temporal dynamics.