This repository contains the main matlab files to reproduce the results from "Lévy flights as an emergent phenomenon in a spatially extended system" by Jiao and Gottwald, Proceedings of the Royal Society A (2023) To simulate the stochastic Landau-Lifshitz-Gilbert SPDE, stochLLG_semiimplicit_with_fitting.m. This simulates a single realisation of the sLLG equation and performs a fitting of the solutions to a combination of sech, tanh and a constant. It requires the subroutine tanhsechconst_phi_w_fit_using_bi_pi.m. The file stochLLG_semiimplicit_angles_ensemble.m generates an ensemble of simulations allowing for the determination of the statistics of the fitted parameters. The associated collective coordinate system of SDEs is solved in collcoord_spherical_with_phi_with_w_Linfinity.m for a single realisation. The ensemble run is solved in collcoord_spherical_ensemble.m.