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Reaktiodiffuus, or reaction-diffusion, refers to a class of mathematical models that describe how the concentration of chemical species changes in space and time due to local chemical reactions and diffusion. These systems are typically expressed by partial differential equations that include a reaction term and a diffusion term, capturing how substances transform into each other and spread through space.

In the simplest two-species form, the concentrations u(x,t) and v(x,t) evolve according to

∂u/∂t = Du ∇^2 u + f(u,v),

∂v/∂t = Dv ∇^2 v + g(u,v),

where Du and Dv are diffusion coefficients and f, g describe the reaction kinetics. Patterns can arise when diffusion interacts with nonlinear reactions to destabilize a homogeneous steady state, a phenomenon known as diffusion-driven or Turing instability. Critical factors include the existence of a stable steady state without diffusion and a sufficiently large difference between the diffusion rates of the involved species.

Common theoretical models include activator-inhibitor systems, the Schnakenberg model, and the Brusselator. These models, and their variations, can generate a range of spatial structures such as spots, stripes, or labyrinth patterns, depending on parameters, geometry, and boundary conditions. Reaction-diffusion systems also underpin studies of biological morphogenesis, chemical oscillations, and ecological pattern formation.

Historical context notes that Alan Turing proposed reaction-diffusion as a mechanism for biological pattern formation in 1952, laying groundwork later supported by experiments and simulations. While powerful for explaining spatial organization, real-world applications require careful consideration of parameter choices, noise, boundary effects, and model simplifications, which can limit direct predictive power in living systems.