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on 10 Oct 2021
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%-----------------------------------------------------
%% GRAY-SCOTT REACTION-DIFFUSION MODEL (Slime-growth)
%-----------------------------------------------------
%% system parameters
f=.055; % slime feedrate
k=.062; % slime killrate
N=128; % gridsize (N=128)
M=64; % middle (M=64)
%% initial conditions
x = meshgrid(1:N);
u = 0*x+1;
v = 0*u;
v(M,M) = 1; % center seeding
%% petri-dish filter
w = (sqrt((x-M).^2 + (x.'-M).^2) <= .9*M);
%% numerical PDE solver
j = 0;
while j < 2e4
u = u+w.*((del2(u,2))-u.*v.^2+f.*(1-u));
v = v+w.*((del2(v,2))/2+u.*v.^2-(f+k).*v);
j = j + 1;
end
%% plotting magic ;)
surf(x,x.',w.*u)
colormap(summer)
shading interp
axis off
view(20,85)
%% References:
% [1] A. M. Turing, The chemical basis of morphogenesis, Philosophical Transactions of the
% Royal Society of London (Biological Sciences), 237: 37-72, 1952.
% [2] K. Käfer and M. SchulzGray, Gray-Scott Model of a Reaction-Diffusion System Pattern Formation
% https://itp.uni-frankfurt.de/~gros/StudentProjects/Projects_2020/projekt_schulz_kaefer/
% (Accessed at October, 2021).
%% Notes:
% i) Please check the references for other f,k parameters!
% ii) Yes, indeed. THE "Alan Turing" studied these dynamic models ;o
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