GPT tut interaction 20110530 second edit

Back to tutoral on the interaction function details The green comments have not been removed in this copy - to allow you to see the context in which the new code has been placed.

There are two submodels. The first has isotropic growth and the second has anisotropic growth. The choice of submodel (1 or 2) is made on the line highlighted in RED.

Section 1

    function m = gpt_tut_interaction_20110530( m )
        %m = gpt_tut_interaction_20110530( m )
        %   Morphogen interaction function.
        %   Written at 2011-05-30 09:42:07.
        %   GFtbox revision 0, .

        % The user may edit any part of this function between delimiters
        % of the form "USER CODE..." and "END OF USER CODE...".  The
        % delimiters themselves must not be moved, edited, deleted, or added.

        if isempty(m), return; end

        fprintf( 1, '%s found in %s\n', mfilename(), which(mfilename()) );

        try
            m = local_setproperties( m );
        catch
        end

        realtime = m.globalDynamicProps.currenttime;

Section 2
        %%% USER CODE: INITIALISATION

        % In this section you may modify the mesh in any way whatsoever.
        if (Steps(m)==0) && m.globalDynamicProps.doinit % First iteration
            % Zero out a lot of stuff to create a blank slate.
            % If no morphogens are set in the GUI it may be useful to
            % zero some arrays by uncommenting the following.
            % m.morphogens(:) = 0;
            % m.morphogenclamp(:) = 0;
            % m.mgen_production(:) = 0;
            % m.mgen_absorption(:) = 0;
            % m.seams(:) = false;
            % m.mgen_dilution(:) = false;

            % Set up names for variant models.  Useful for running multiple models on a cluster.
            m.userdata.ranges.modelname.range = { 'MODEL1', 'MODEL2' };  % CLUSTER
             m.userdata.ranges.modelname.index = 2;                       % CLUSTER
        end
        modelname = m.userdata.ranges.modelname.range{m.userdata.ranges.modelname.index};  % CLUSTER
        disp(sprintf('\nRunning %s model %s\n',mfilename, modelname));
        switch modelname
            case 'MODEL1'
                % Set up the parameters (e.g. mutations) for this model here.
            case 'MODEL2'
                % Set up the parameters (e.g. mutations) for this model here.
            otherwise
                % If you reach here, you probably forgot a case.
        end

        % More examples of code for all iterations.

        % Set priorities for simultaneous plotting of multiple morphogens, if desired.
        % m = leaf_mgen_plotpriority( m, {'MGEN1', 'MGEN2'}, [1,2], [0.5,0.75] );

        % Set colour of polariser gradient arrows.
        % m = leaf_plotoptions(m,'highgradcolor',[0,0,0],'lowgradcolor',[1,0,0]);

        % setup a multiplot of the following morphogens
        % m = leaf_plotoptions( m, 'morphogen', {'V_PROFILE1','V_PROFILE2','KAPAR','S_LEFTRIGHT'});

        % to plot polariser on the A side and resultant areal growth rate on the B side:
        % m = leaf_plotoptions( m, 'morphogenA', 'POLARISER', ...
        %                      'outputquantityB', 'resultantgrowthrate', ...
        %                      'outputaxesB', 'areal' );

        % monitor properties of vertices must be done here - so that it reports newly equilibrated levels
        % m=leaf_profile_monitor(m,... % essential
        %         'REGIONLABELS',{'V_PROFILE1','V_PROFILE2'},... % essential
        %         'MORPHOGENS',{'S_LEFTRIGHT','S_CENTRE'},... % optional  (one element per REGIONLABEL)
        %         'VERTLABELS',false,'FigNum',1,'EXCEL',true,'MODELNAME',modelname); % optional (file in snapshots directory')


        %%% END OF USER CODE: INITIALISATION

Section 3
        %%% SECTION 1: ACCESSING MORPHOGENS AND TIME.
        %%% AUTOMATICALLY GENERATED CODE: DO NOT EDIT.

        if isempty(m), return; end

        setGlobals();
        global gNEW_KA_PAR gNEW_KA_PER gNEW_KB_PAR gNEW_KB_PER
        global gNEW_K_NOR gNEW_POLARISER gNEW_STRAINRET gNEW_ARREST
        dt = m.globalProps.timestep;
        polariser_i = gNEW_POLARISER;
        P = m.morphogens(:,polariser_i);
        [kapar_i,kapar_p,kapar_a,kapar_l] = getMgenLevels( m, 'KAPAR' );
        [kaper_i,kaper_p,kaper_a,kaper_l] = getMgenLevels( m, 'KAPER' );
        [kbpar_i,kbpar_p,kbpar_a,kbpar_l] = getMgenLevels( m, 'KBPAR' );
        [kbper_i,kbper_p,kbper_a,kbper_l] = getMgenLevels( m, 'KBPER' );
        [knor_i,knor_p,knor_a,knor_l] = getMgenLevels( m, 'KNOR' );
        [strainret_i,strainret_p,strainret_a,strainret_l] = getMgenLevels( m, 'STRAINRET' );
        [arrest_i,arrest_p,arrest_a,arrest_l] = getMgenLevels( m, 'ARREST' );
        [id_plusorg_i,id_plusorg_p,id_plusorg_a,id_plusorg_l] = getMgenLevels( m, 'ID_PLUSORG' );
        [id_negorg_i,id_negorg_p,id_negorg_a,id_negorg_l] = getMgenLevels( m, 'ID_NEGORG' );
        [id_a_i,id_a_p,id_a_a,id_a_l] = getMgenLevels( m, 'ID_A' );
        [id_b_i,id_b_p,id_b_a,id_b_l] = getMgenLevels( m, 'ID_B' );

        % Mesh type: circle
        %          centre: 0
        %       circumpts: 48
        %       coneangle: 0
        %         dealign: 0
        %          height: 0
        %        innerpts: 0
        %      randomness: 0.1
        %           rings: 6
        %         version: 1
        %          xwidth: 0.2
        %          ywidth: 0.2

        %            Morphogen   Diffusion   Decay   Dilution   Mutant
        %            -------------------------------------------------
        %                KAPAR        ----    ----       ----     ----
        %                KAPER        ----    ----       ----     ----
        %                KBPAR        ----    ----       ----     ----
        %                KBPER        ----    ----       ----     ----
        %                 KNOR        ----    ----       ----     ----
        %            POLARISER        ----    ----       ----     ----
        %            STRAINRET        ----    ----       ----     ----
        %               ARREST        ----    ----       ----     ----
        %           ID_PLUSORG        ----    ----       ----     ----
        %            ID_NEGORG        ----    ----       ----     ----
        %                 ID_A        ----    ----       ----     ----
        %                 ID_B        ----    ----       ----     ----


        %%% USER CODE: MORPHOGEN INTERACTIONS

        % In this section you may modify the mesh in any way that does not
Section 4
        % alter the set of nodes.

        if (Steps(m)==0) && m.globalDynamicProps.doinit  % Initialisation code.
            % Put any code here that should only be performed at the start of
            % the simulation, for example, to set up initial morphogen values.
            % m.nodes is the set of vertex positions, an N by 3 array if there
            % are N vertices.  Row number K contains the X, Y, and Z
            % coordinates of the Kth vertex. To obtain a list of the X
            % coordinates of every vertex, write m.nodes(:,1).  The Y
            % coordinates are given by m.nodes(:,2) and the Z coordinates by
            % m.nodes(:,3).

            % Set up a morphogen promoter (_p suffix) region where x values are minimum
            % id_prox_p(m.nodes(:,1)==min(m.nodes(:,1)))=1;
            % if the morphogen level (_l suffix) is to be used in this iteration
            % set the level using the morphogen activity (_a suffix).
            % id_prox_l=id_prox_p * id_prox_a; % when a mutation is specified in the GUI
            % the activity (_a) is set to zero

            id_a_p(m.nodes(:,1)<-0.03)=1; % setup region for A where identity factor A is represented by id_a_p
            id_b_p(m.nodes(:,2)<-0.01)=1; % setup region for B

            % One way to set up a morphogen gradient is by ...
            % Setting up a gradient by clamping the ends (execute only once)
            P((m.nodes(:,1)<-0.05)&(m.nodes(:,2)>0.03))=1;
            m.morphogenclamp( P==1, polariser_i ) = 1;
            m = leaf_mgen_conductivity( m, 'POLARISER', 0.01 );  %specifies the diffusion rate of polariser
            m = leaf_mgen_absorption( m, 'POLARISER', 0.1 );     % specifies degradation rate of polariser

            % Fixing vertices, i.e. fix z for the base to prevent base from moving up or down
            % m=leaf_fix_vertex(m,'vertex',find(id_prox_p==1),'dfs','z');

            % To cut the mesh, set a temporary morphogen to 1 in places to cut
            % seams=zeros(size(P));
            % seams(indexes to places to cut)=1;
            % m=leaf_set_seams(m,seams);

        end

Section 5
        % Second way to generate a gradient
        % generating (+) and sinking (-) a diffusing signal (in this case polariser)
        % m.mgen_production( :, polariser_i ) = + 5*s_spur_p - P .* id_dist_p;

        % Monitor growth by scattering discs that deform over time (c.f. inducing biological clones)
        % (CARE - if the canvas is flat ensure that Plot:Hide Thickness is true,
        % because a quirk of the Matlab z-buffer means that they can get hidden by mistake)
        %    if (340>realtime-dt) && (340<realtime+dt) % discs to be added at realtime==340
        %        m = leaf_makesecondlayer( m, ...  % This function adds discs that represent transformed cells.
        %            'mode', 'each', ...  % Make discs randomly scattered over the canvas.
        %            'relarea', 1/16000, ...   % Each discs has area was 1/16000 of the initial area of the canvas.
        %            'probpervx', 'V_FLOWER', ... % induce discs over whole canvas (V_FLOWER is 1 over whole canvas)
        %            'numcells',4500,...%number of discs (that will become ellipses)
        %            'sides', 6, ...  % Each discs is approximated as a 6-sided regular polygon.
        %            'colors', [0.5 0.5 0.5], ...  % Default colour is gray but
        %            'colorvariation',1,... % Each disc is a random colour
        %            'add', true );  % These discs are added to any discs existing already
        %    end

Section 6
        % Directives for creating latex representation directly from Matlab code
        % not fully implemented yet but will use @@ directives
        % @@at t
        % @@before t
        % @@after t
        % @@between t1 t2

Section 7
        %     % If you want to define different phases according to the absolute
        %     % time, create a morphogen for each phase and modulate
        %     % expressions using the morphogen
        %     % like.  For example:
        %     if (realtime < 10)  % first growth phase
        %         f_firstgrowth_p = 1;
        %     else
        %         f_firstgrowth_p = 0;
        %     end
        %     if (realtime >= 10) % second growth phase
        %         f_secondgrowth_p = 1;
        %     else
        %         f_secondgrowth_p = 0;
        %     end
        %
        %     % If you want one morphogen to affect others only during a certain
        %     % phase, write something like:
        %
        %     mgen_a_p = f_firstgrowth_p .* (various terms); % will zero except in firstgrowth

Section 8
        % Code common to all models.
        % @@PRN Polariser Regulatory Network
        % Every equation to be formatted should end with an at-at Eqn N comment.
        % @@GRN Gene Regulatory Network
        % Every equation to be formatted should end with an at-at Eqn N comment.
        % @@KRN Growth Regulatory Network
        % Every equation to be formatted should end with an at-at Eqn N comment.

Section 9
        % Code for specific models.
        switch modelname
Section 10
            case 'MODEL1'  % @@model MODEL1
                % @@PRN Polariser Regulatory Network
                % Every equation to be formatted should end with an at-at Eqn N comment.
                % P(:) = ...  % @@ Eqn xx
                % @@GRN Gene Regulatory Network
                % Every equation to be formatted should end with an at-at Eqn N comment.
                % @@KRN Growth Regulatory Network
                % Every equation to be formatted should end with an at-at Eqn N comment.
                % kapar_p(:) = 0;  % @@ Eqn xx
                % kaper_p(:) = 0;  % @@ Eqn xx
                % kbpar_p(:) = 0;  % @@ Eqn xx
                % kbper_p(:) = 0;  % @@ Eqn xx
                % knor_p(:)  = 0;  % @@ Eqn xx
                kapar_p(:) = id_a_l .* inh(1,id_b_l); % growth rate
                kaper_p(:) = kapar_p; % isotropic growth
                kbpar_p(:) = kapar_p; % same on both sides of the sheet
                kbper_p(:) = kapar_p; % same
                knor_p(:)  = 0;       % thickness not growing
Section 11
            case 'MODEL2'  % @@model MODEL2
                % @@PRN Polariser Regulatory Network
                % Every equation to be formatted should end with an at-at Eqn N comment.
                % P(:) = ...  % @@ Eqn xx
                % @@GRN Gene Regulatory Network
                % Every equation to be formatted should end with an at-at Eqn N comment.
                % @@KRN Growth Regulatory Network
                % Every equation to be formatted should end with an at-at Eqn N comment.
                % kapar_p(:) = 0;  % @@ Eqn xx
                % kaper_p(:) = 0;  % @@ Eqn xx
                % kbpar_p(:) = 0;  % @@ Eqn xx
                % kbper_p(:) = 0;  % @@ Eqn xx
                % knor_p(:)  = 0;  % @@ Eqn xx
                kapar_p(:) = id_a_l .* inh(1,id_b_l); % growth rate
                kaper_p(:) = 0.1*kapar_p; % anisotropic growth
                kbpar_p(:) = kapar_p; % same on both sides of the sheet
                kbper_p(:) = 0.1*kapar_p; % also anisotropic
                knor_p(:)  = 0;       % thickness not growing
            otherwise
                % If this happens, maybe you forgot a model.
        end

Section 12
        %%% END OF USER CODE: MORPHOGEN INTERACTIONS

        %%% SECTION 3: INSTALLING MODIFIED VALUES BACK INTO MESH STRUCTURE
        %%% AUTOMATICALLY GENERATED CODE: DO NOT EDIT.
        m.morphogens(:,polariser_i) = P;
        m.morphogens(:,kapar_i) = kapar_p;
        m.morphogens(:,kaper_i) = kaper_p;
        m.morphogens(:,kbpar_i) = kbpar_p;
        m.morphogens(:,kbper_i) = kbper_p;
        m.morphogens(:,knor_i) = knor_p;
        m.morphogens(:,strainret_i) = strainret_p;
        m.morphogens(:,arrest_i) = arrest_p;
        m.morphogens(:,id_plusorg_i) = id_plusorg_p;
        m.morphogens(:,id_negorg_i) = id_negorg_p;
        m.morphogens(:,id_a_i) = id_a_p;
        m.morphogens(:,id_b_i) = id_b_p;

        %%% USER CODE: FINALISATION

        % In this section you may modify the mesh in any way whatsoever.

Section 13
        % If needed force FE to subdivide (increase number FE's) here
        % if realtime==280+dt
        % m = leaf_subdivide( m, 'morphogen','id_vent',...
        %       'min',0.5,'max',1,...
        %       'mode','mid','levels','all');
        % end
        % Cut the mesh along the seams (see above)
        % if m.userdata.CutOpen==1
        %    m=leaf_dissect(m);
        %    m.userdata.CutOpen=2;
        %    Relax accumulated stresses slowly i.e. 0.95 to 0.999
        %    m = leaf_setproperty( m, 'freezing', 0.999 );
        % end

        %%% END OF USER CODE: FINALISATION

    end


    %%% USER CODE: SUBFUNCTIONS

Section 14
    function m = local_setproperties( m )
        % This function is called at time zero in the INITIALISATION section of the
        % interaction function.  It provides commands to set each of the properties
        % that are contained in m.globalProps.  Uncomment whichever ones you would
        % like to set yourself, and put in whatever value you want.
        %
        % Some of these properties are for internal use only and should never be
        % set by the user.  At some point these will be moved into a different
        % component of m, but for the present, just don't change anything unless
        % you know what it is you're changing.

        %    m = leaf_setproperty( m, 'trinodesvalid', true );
        %    m = leaf_setproperty( m, 'prismnodesvalid', true );
        %    m = leaf_setproperty( m, 'thicknessRelative', 0.020000 );
        %    m = leaf_setproperty( m, 'thicknessArea', 0.000000 );
        %    m = leaf_setproperty( m, 'thicknessMode', 'physical' );
        %    m = leaf_setproperty( m, 'activeGrowth', 1.000000 );
        %    m = leaf_setproperty( m, 'displayedGrowth', 1.000000 );
        %    m = leaf_setproperty( m, 'displayedMulti', [] );
        %    m = leaf_setproperty( m, 'allowNegativeGrowth', true );
        %    m = leaf_setproperty( m, 'usePrevDispAsEstimate', true );
        %    m = leaf_setproperty( m, 'perturbInitGrowthEstimate', 0.000010 );
        %    m = leaf_setproperty( m, 'perturbRelGrowthEstimate', 0.010000 );
        %    m = leaf_setproperty( m, 'perturbDiffusionEstimate', 0.000100 );
        %    m = leaf_setproperty( m, 'resetRand', false );
        %    m = leaf_setproperty( m, 'mingradient', 0.000000 );
        %    m = leaf_setproperty( m, 'relativepolgrad', false );
        %    m = leaf_setproperty( m, 'usefrozengradient', true );
        %    m = leaf_setproperty( m, 'userpolarisation', false );
        %    m = leaf_setproperty( m, 'thresholdsq', 0.000841 );
        %    m = leaf_setproperty( m, 'splitmargin', 1.400000 );
        %    m = leaf_setproperty( m, 'splitmorphogen',  );
        %    m = leaf_setproperty( m, 'thresholdmgen', 0.500000 );
        %    m = leaf_setproperty( m, 'bulkmodulus', 1.000000 );
        %    m = leaf_setproperty( m, 'unitbulkmodulus', true );
        %    m = leaf_setproperty( m, 'poissonsRatio', 0.300000 );
        %    m = leaf_setproperty( m, 'starttime', 0.000000 );
        %    m = leaf_setproperty( m, 'timestep', 0.010000 );
        %    m = leaf_setproperty( m, 'timeunitname',  );
        %    m = leaf_setproperty( m, 'distunitname', 'mm' );
        %    m = leaf_setproperty( m, 'scalebarvalue', 0.000000 );
        %    m = leaf_setproperty( m, 'validateMesh', true );
        %    m = leaf_setproperty( m, 'rectifyverticals', false );
        %    m = leaf_setproperty( m, 'allowSplitLongFEM', true );
        %    m = leaf_setproperty( m, 'longSplitThresholdPower', 0.000000 );
        %    m = leaf_setproperty( m, 'allowSplitBentFEM', false );
        %    m = leaf_setproperty( m, 'allowSplitBio', true );
        %    m = leaf_setproperty( m, 'allowFlipEdges', false );
        %    m = leaf_setproperty( m, 'allowElideEdges', true );
        %    m = leaf_setproperty( m, 'mincellangle', 0.200000 );
        %    m = leaf_setproperty( m, 'alwaysFlat', 0.000000 );
        %    m = leaf_setproperty( m, 'flattenforceconvex', true );
        %    m = leaf_setproperty( m, 'flatten', false );
        %    m = leaf_setproperty( m, 'flattenratio', 1.000000 );
        %    m = leaf_setproperty( m, 'useGrowthTensors', false );
        %    m = leaf_setproperty( m, 'plasticGrowth', false );
        %    m = leaf_setproperty( m, 'totalinternalrotation', 0.000000 );
        %    m = leaf_setproperty( m, 'stepinternalrotation', 2.000000 );
        %    m = leaf_setproperty( m, 'showinternalrotation', false );
        %    m = leaf_setproperty( m, 'performinternalrotation', false );
        %    m = leaf_setproperty( m, 'internallyrotated', false );
        %    m = leaf_setproperty( m, 'maxFEcells', 0 );
        %    m = leaf_setproperty( m, 'inittotalcells', 0 );
        %    m = leaf_setproperty( m, 'bioApresplitproc',  );
        %    m = leaf_setproperty( m, 'bioApostsplitproc',  );
        %    m = leaf_setproperty( m, 'maxBioAcells', 0 );
        %    m = leaf_setproperty( m, 'maxBioBcells', 0 );
        %    m = leaf_setproperty( m, 'colors', (6 values) );
        %    m = leaf_setproperty( m, 'colorvariation', 0.050000 );
        %    m = leaf_setproperty( m, 'colorparams', (12 values) );
        %    m = leaf_setproperty( m, 'freezing', 0.000000 );
        %    m = leaf_setproperty( m, 'canceldrift', false );
        %    m = leaf_setproperty( m, 'mgen_interaction',  );
        %    m = leaf_setproperty( m, 'mgen_interactionName', 'gpt_tut_interaction_20110530' );
        %    m = leaf_setproperty( m, 'allowInteraction', true );
        %    m = leaf_setproperty( m, 'interactionValid', true );
        %    m = leaf_setproperty( m, 'gaussInfo', (unknown type struct) );
        %    m = leaf_setproperty( m, 'stitchDFs', [] );
        %    m = leaf_setproperty( m, 'D', (36 values) );
        %    m = leaf_setproperty( m, 'C', (36 values) );
        %    m = leaf_setproperty( m, 'G', (6 values) );
        %    m = leaf_setproperty( m, 'solver', 'cgs' );
        %    m = leaf_setproperty( m, 'solverprecision', 'double' );
        %    m = leaf_setproperty( m, 'solvertolerance', 0.001000 );
        %    m = leaf_setproperty( m, 'solvertolerancemethod', 'norm' );
        %    m = leaf_setproperty( m, 'diffusiontolerance', 0.000010 );
        %    m = leaf_setproperty( m, 'allowsparse', true );
        %    m = leaf_setproperty( m, 'maxIters', 0 );
        %    m = leaf_setproperty( m, 'maxsolvetime', 1000.000000 );
        %    m = leaf_setproperty( m, 'cgiters', 0 );
        %    m = leaf_setproperty( m, 'simsteps', 0 );
        %    m = leaf_setproperty( m, 'stepsperrender', 0 );
        %    m = leaf_setproperty( m, 'growthEnabled', true );
        %    m = leaf_setproperty( m, 'diffusionEnabled', true );
        %    m = leaf_setproperty( m, 'flashmovie', false );
        %    m = leaf_setproperty( m, 'makemovie', false );
        %    m = leaf_setproperty( m, 'moviefile',  );
        %    m = leaf_setproperty( m, 'codec', 'None' );
        %    m = leaf_setproperty( m, 'autonamemovie', true );
        %    m = leaf_setproperty( m, 'overwritemovie', false );
        %    m = leaf_setproperty( m, 'framesize', [] );
        %    m = leaf_setproperty( m, 'mov', [] );
        %    m = leaf_setproperty( m, 'jiggleProportion', 1.000000 );
        %    m = leaf_setproperty( m, 'cvtperiter', 0.200000 );
        %    m = leaf_setproperty( m, 'boingNeeded', false );
        %    m = leaf_setproperty( m, 'initialArea', 0.031326 );
        %    m = leaf_setproperty( m, 'bendunitlength', 0.176992 );
        %    m = leaf_setproperty( m, 'targetRelArea', 1.000000 );
        %    m = leaf_setproperty( m, 'defaultinterp', 'min' );
        %    m = leaf_setproperty( m, 'readonly', false );
        %    m = leaf_setproperty( m, 'projectdir', 'D:\ab\Matlab stuff' );
        %    m = leaf_setproperty( m, 'modelname', 'GPT_tut_interaction_20110530' );
        %    m = leaf_setproperty( m, 'allowsave', true );
        %    m = leaf_setproperty( m, 'addedToPath', false );
        %    m = leaf_setproperty( m, 'bendsplit', 0.300000 );
        %    m = leaf_setproperty( m, 'usepolfreezebc', false );
        %    m = leaf_setproperty( m, 'dorsaltop', true );
        %    m = leaf_setproperty( m, 'defaultazimuth', -45.000000 );
        %    m = leaf_setproperty( m, 'defaultelevation', 33.750000 );
        %    m = leaf_setproperty( m, 'defaultroll', 0.000000 );
        %    m = leaf_setproperty( m, 'defaultViewParams', (unknown type struct) );
        %    m = leaf_setproperty( m, 'comment',  );
        %    m = leaf_setproperty( m, 'legendTemplate', '%T: %q\n%m' );
        %    m = leaf_setproperty( m, 'bioAsplitcells', true );
        %    m = leaf_setproperty( m, 'bioApullin', 0.142857 );
        %    m = leaf_setproperty( m, 'bioAfakepull', 0.202073 );
        %    m = leaf_setproperty( m, 'interactive', false );
        %    m = leaf_setproperty( m, 'coderevision', 0 );
        %    m = leaf_setproperty( m, 'coderevisiondate',  );
        %    m = leaf_setproperty( m, 'modelrevision', 0 );
        %    m = leaf_setproperty( m, 'modelrevisiondate',  );
        %    m = leaf_setproperty( m, 'savedrunname',  );
        %    m = leaf_setproperty( m, 'savedrundesc',  );
        %    m = leaf_setproperty( m, 'vxgrad', (108 values) );
        %    m = leaf_setproperty( m, 'lengthscale', 0.200000 );
    end

Section 15
    % Here you may write any functions of your own, that you want to call from
    % the interaction function, but never need to call from outside it.
    % Remember that they do not have access to any variables except those
    % that you pass as parameters, and cannot change anything except by
    % returning new values as results.
    % Whichever section they are called from, they must respect the same
    % restrictions on what modifications they are allowed to make to the mesh.

    % For example:

Section 16
    % function m = do_something( m )
    %   % Change m in some way.
    % end

    % Call it from the main body of the interaction function like this:
    %       m = do_something( m );