This repository contains the MATLAB files to reproduce the data and figures from 'Approximate Localised Dihedral Patterns Near a Turing Instability' by Dan J. Hill, Jason J. Bramburger and David J.B. Lloyd (2022).

A copy of the paper can be found here: http://arxiv.org/abs/2203.09363

For the numerical continuation of localised dihedral patterns in the planar quadratic-cubic Swift-Hohenberg equation, see the folder 'Continuation'.

For the recreation of Figure 1 b) (Convergence of a localised hexagon patch in the von Hardenberg vegetation model) using exponential time-steppers, see the folder 'Exp_Time_Step'

For the verification of our computer-assisted proof of Theorem 5.8, see the folder 'Integral-Equation-Proof-Code'.