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% Nick Lowery and Tristan Ursell
% 2018
%
% Structured environments fundamentally alter dynamics and stability of ecological communities
% https://www.biorxiv.org/content/early/2018/07/10/366559
% 
% This script generates pillar lattices with random noise added to the pillar
% sizes and/or spacings.  Sample grids used in the paper are provided at 
% https://github.com/nick-lowery/ecological_simulations/jittered_grids/
% Grids are manually curated to make sure pillars do not overlap or are spaced
% too closely for the diffusion process to function properly.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% define relevant parameters
D = 15;
R = 30;
dx = 5*R;
sy = 500;
sx = 500;
L = 500;

var_R = 0;  % max ~ 0.5
var_dx = 0; % relative to R; depends on dx

% construct center-distance matrix
Xmat = ones(sy,1)*(1:sx);
Ymat = (1:sy)'*ones(1,sx);
dist_mat = sqrt((Xmat - sx/2).^2 + (Ymat - sy/2).^2);

%form hexagonal grid position arrays
x_cent0 = 0:dx:(L + dx);
y_cent0 = [0:(sqrt(3)/2*dx):(L + dx*sqrt(3)/2)] + R;

x_cent = zeros(length(y_cent0), length(x_cent0));
for i = 1:length(y_cent0)
    if mod(i,2) == 1
        x_cent(i,:) = x_cent0 + dx/4;
    else
        x_cent(i,:) = x_cent0 - dx/4;
    end
end

y_cent = zeros(size(x_cent));
for j = 1:length(x_cent0)
    y_cent(:,j) = y_cent0';
end

%%% jitter pillar placement %%%

% select random angle
theta = 360*rand(size(x_cent));

% generate random displacement within +/- var_dx
d = var_dx .* rand(size(x_cent)) * R; 

x_jitt = x_cent + d .* cosd(theta);
y_jitt = y_cent + d .* sind(theta);

%create pillars
filt_all = ones(size(Xmat));
for i = 1:length(x_cent0)
    for j = 1:length(y_cent0)
        R_jitter = (-var_R + 2*var_R .* rand(1))*R + R;
        if R_jitter <= D/2
            R_jitter = D/2 + 0.1;
        end
        filt_temp = ((Xmat - x_jitt(j,i)).^2 + (Ymat - y_jitt(j,i)).^2) >= R_jitter^2;
        filt_all = filt_all .* filt_temp;
    end
end

dbound = -L/2;
filt_all_temp = zeros(size(filt_all));
filt_all_temp(1:round(L/2) - dbound,:) = filt_all(1:round(L/2) - dbound,:);
filt_all_temp(round(L/2) - dbound + 1:end,:) = 1;
filt_all = filt_all_temp;

%%% plot pillar mask for manual validation %%%

imagesc(filt_all)

%%% write file %%%

%id number for grid - don't forget to change when saving!
grid_num = 1;

save(['jitter_grid_R-' num2str(R) '_dx-' num2str(dx) '_vR-' num2str(var_R) ...
            '_vdx-' num2str(var_dx) '_num-' num2str(grid_num) '.mat'], 'filt_all')