01 / The question
How do patterns naturally emerge through chemical diffusion in biological systems?
A biological pattern is organised across space, yet its components interact locally. This project explored how reaction and diffusion can generate such organisation without prescribing the final pattern.
02 / The intuition
A mechanism worth testing.
Rather than draw stripes or spots, define local dynamics and let the spatial model evolve. Then ask whether a pattern comes from the model or from the numerical method.
03 / The work
Inside the method.
Explore each part of the approach.
01Write the model
The notes describe Gierer–Meinhardt and Schnakenberg systems, no-flux boundaries and small perturbations of the initial state.
02Compare numerical views
A one-dimensional finite-difference implementation in MATLAB was paired with two-dimensional finite-element simulations in COMSOL.
03Change the domain
Parameter studies and an arbitrary Lagrangian–Eulerian moving mesh explored how domain growth interacts with pattern formation.
∂u/∂t = d∇²u + u²/v − au
∂v/∂t = ∇²v + u² − v
u and v are the coupled fields; d is the relative diffusion coefficient. The report is needed to recover the full parameter and initial-condition specification.
04 / The observations
What emerged.
The project notes describe patterns in one and two dimensions and comparisons with reference figures. They also record stability and parameter studies. The original simulation outputs are not yet attached to this story.
This account is based on recorded project notes. Original reports, figures and datasets are not embedded here.
05 / The limits
Where the evidence stops.
A visually plausible pattern is not sufficient validation. The original meshes, time steps, boundary conditions and convergence results are needed before making quantitative claims.
The academic foundations