Reaction–Diffusion Solver
Explore the competition between diffusion and logistic reaction in the Fisher–KPP equation. Choose D, reaction rate, grid and time step, then watch an initial profile diffuse and grow toward the carrying state.
How this tool works
The explicit update combines centered diffusion DΔt(uᵢ₋₁−2uᵢ+uᵢ₊₁)/Δx² with the local reaction term rΔt uᵢ(1−uᵢ).
Example
Start from a localized Gaussian with positive reaction rate. Diffusion spreads the profile while the logistic reaction amplifies nonzero values toward u=1.
Common questions
Is this a general reaction–diffusion system?
No. This page solves the scalar Fisher–KPP model, not multi-species systems such as Gray–Scott or Turing models.
What controls the front speed?
For the continuous Fisher–KPP equation, D and r set the characteristic invasion speed. Numerical grid and time-step choices also affect the resolved front.