clear;
% This code illustrates possible blurring and deblurring in 1D.
% It is motivated by heat diffusion in 1D.
% Blurring is modeled by diffusion of heat in positive time steps.
% Deblurring is done by diffusion of "heat" in negative time steps.
u = zeros(101,1);
newu = u;
u(30:50) = 10;
u(70:73) = 15;
dt = .00001;
dx = 1/100; 

subplot(1,2,1)      % Forward in "time" or "blurring"
plot(u)
axis([0 101 0 16]);
pause
for k = 1:10
    for i = 2:100
        newu(i) = u(i) + (dt/(dx*dx))*(u(i-1) -2*u(i) + u(i+1));
    end
    plot(newu);
    axis([0 101 0 16]);
    k
    pause;
    u = newu;
end

subplot(1,2,2)      % Backward in "time" or "deblurring"
plot(u)
for k = 1:10
    for i = 2:100
        newu(i) = u(i) - (dt/(dx*dx))*(u(i-1) -2*u(i) + u(i+1));
    end
    plot(newu);
    axis([0 101 0 16]);
    k
    pause;
    u = newu;
end