1. ABOUT THE DATASET -------------------- Title: Dataset for 'Spatiotemporal Chaos Driven by Nonlinear Interactions with Two Critical Wavenumbers' Creator(s): Laura Pinkney[1], Alastair M. Rucklidge[1], Cédric Beaume[1] Organisation(s): 1. School of Mathematics, University of Leeds, Leeds LS2 9JT, UK Rights-holder(s):Unless otherwise stated, Copyright 2026 University of Leeds Publication Year: 2026 Description: The dataset contains the data for generating the figures in the paper. The code directory contains the python codes required to generate the figures. The remaining two directories contain the files required to execute these codes. To generate the figures, only PDE_pattern_classification.py needs to be executed. This imports data from 'output_files' to do this. However, if the user would like to generate data given in 'output_files' themselves, then the other python codes are required. The files in 'input_files' are required to execute ETD4RK.py for the first value of Q_1 (Q_1=-1.4). For the remaining values of Q_1 a different initial condition will need to be imported (to generate the same figures presented in the paper). This initial condition will be the final solution generated for the previous value of Q_1, which should be saved as 'new_U_ic.txt' (this is saved by default when executing ETD4RK.py). The files in 'output_files' can be generated by executing loadandplot_newcriteria.py (after executing ETD4RK.py) for a range of values of Q_1 which are named in the subdirectories of 'output_files'. The data within these subdirectories are the inputs for PDE_pattern_classification.py which generates the figures in the paper. A sample file tree to describe the paths defined within the codes is also included. Cite as:  Laura Pinkney, Alastair M. Rucklidge, Cédric Beaume (2026): Dataset for 'Spatiotemporal Chaos Driven by Nonlinear Interactions with Two Critical Wavenumbers'. University of Leeds. [Dataset] https://doi.org/10.5518/1819. Related publication: Laura Pinkney, Alastair M. Rucklidge, Cédric Beaume: Spatiotemporal Chaos Driven by Nonlinear Interactions with Two Critical Wavenumbers (in preparation). Contact: mm18lp@leeds.ac.uk, a.m.rucklidge@leeds.ac.uk, C.M.L.Beaume@leeds.ac.uk 2. TERMS OF USE --------------- A standard copyright notice and licence statement with URL can be used, e.g. Copyright [publication year] [University of Leeds, name of other rights-holder(s)]. Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/. 3. PROJECT AND FUNDING INFORMATION ---------------------------------- Title: Three-Wave Interactions with Two Length Scales Dates: 2022-2026 Funding organisation: University of Leeds: Leeds Doctoral Scholarship Grant no.: 4. CONTENTS ----------- File listing Directory output_files: Data to generate Figure 9. There are six subdirectories, one for each value of Q_1 used. Subdirectories: Q1_-1.4 -- data for Figure 9a. Q1_-1.2 -- data for Figure 9b. Q1_-1.01 -- data for Figure 9c. Q1_-0.9 -- data for Figure 9d. Q1_-0.8 -- data for Figure 9e. Q1_-0.6 -- data for Figure 9f. Within each of these, there are three data files criteria_values.txt patterncodenew.txt patterncodepatch.txt There are 18 plain text data files in all. In criteria_values.txt there are five space-separated columns of numbers: mu, nu, \mathcal{C}_1, \mathcal{C}_2, \mathcal{C}_3. Where the \mu and \nu are the linear growth rates for the k=1 and k=q modes. \mathcal{C} values correspond to the three classification criteria values for the PDE solution for that pair (\mu,\nu). In patterncodenew.txt there are 12 space-separated columns of numbers: mu, nu, P_1, P_q, p_1, p_q, E, S, F, SV, SSC, LSC Where: P_1 : number of peaks in k=1 annulus. P_q : number of peaks in k=q annulus. p_1 : small amplitude contributions to k=1 annulus (True/False). p_q : small amplitude contributions to k=q annulus (True/False). E : equilibrium solution (True/False). S : slow time-dependent solution (True/False). F : fast time-dependent solution (True/False). SV : small variations in time derivative (True/False). SSC : small spatial change (True/False). LSC : large spatial change (True/False). The boolean variables are marked numerically with 1/0 for True/False respectively. This is the classification criteria for the PDE solution for a given (\mu,\nu) pair. In patterncodepatch.txt there are 7 space-separated columns of numbers: mu,nu, patch_number, P_1, P_q, p_1, p_q Which gives the patch analysis where we count the number of peaks and small contributions in each annulus for three different small patches of the solution (in real space). Therefore, patch_number will be one of 1, 2 or 3. Directory input_files: Files needed to be provided for codes (specifically parameters.py). There are three files in this directory: paramlist.txt -- list of (r,\chi) values ((\mu,\nu) in polar co-ordinates: \mu = r\cos\chi, \nu = r \sin\chi) to simulate on. Used in Figures 9, 10, 13, 14 and 17. paramlistwedge.txt -- different list of (r,\chi) values, a smaller but more dense mesh. Used in Figure 19. random_U_ic.txt -- a presaved random initial condition, used as the initial condition for Figure 9a. Directory code: Example Python codes to solve the PDE for a set of parameter values. There are five different python scripts: ETD4RK.py functions.py loadandplot_newcriteria.py parameters.py PDE_pattern_classification.py PDE_pattern_classification.py is the code used to generate Figure 9. This code loads in the patterncode.txt and patterncodepatch.txt files for a given value of Q_1 and produces the PDE diagram shown in Figure 9. The remaining four codes are provided in case the user would like to generate the text files patterncode.txt, patterncodepatch.txt and criteria_values.txt themselves: parameters.py should be edited to specify the chosen PDE parameters and type of initial condition to be used. This code is written with the purpose of executing using HPC via task-arrays (by loading paramlist.txt or paramlistwedge.txt), however, the code will run locally too. The values currently entered into parameters.py includes Q_1=-1.4 and importing in the presaved initial condition random_U_ic.txt, corresponding to Figure 9a. functions.py contains defined functions used in ETD4RK.py and does not need to be edited. ETD4RK.py performs the time integration of the PDE (importing the preferences set in parameters.py). This code generates various outputs which are required to execute loadandplot_newcriteria.py. loadandplot_newcriteria.py creates plots of the solution and generates the three text files criteria_values.txt, patterncodenew.txt and patterncodepatch.txt which are the inputs for PDE_pattern_classification.py. loadandplot_newcriteria.py should be run for each (\mu,\nu) pair (each simulation), where the results are appended to these three text files. Since these codes rely on saving and loading multiple textfiles, a file tree has been provided in directory_tree.txt which explains where all the input files need to be and where the output files are saved. The user must create the directories 'Subplots', 'Peaks_New', 'Peaks_Patch', 'run_outputs', 'pythonfiles' and 'submissionfiles' before executing the ETD4RK.py and loadandplot_newcriteria.py codes. 5. METHODS ---------- The details of the pattern classification method are given in the paper.