% Model of a discrete form of the heat equation

function heat

d=0.1;
num_steps=5;
num_sects=11;
state = zeros(1,num_sects);


    function set_state(the_state)
       for n=1:num_sects
           state(n)=1-n/num_sects;
       end
    end


    function new_sect =step_section(the_state, n)
        % ... a b c ..., we are stepping b

        if(n==1)
            b=the_state(n);
            c=the_state(n+1);
            new_sect= d*c+(1-2*d)*b;
        elseif(n==num_sects)
            a=the_state(n-1);
            b=the_state(n);
            new_sect=(1-2*d)*b+d*a;
        else
            a=the_state(n-1);
            b=the_state(n);
            c=the_state(n+1);
            new_sect= d*c+(1-2*d)*b+d*a;
        end
    end

    function new_state=step(the_state)
        new_state = zeros(1,num_sects);
        for x=1:num_sects
            new_state(x)=step_section(the_state,x);
        end
    end



%MAIN FUNCTION HERE
    set_state(state)
    for k=1:num_steps
        state=[state;step(state(k,:))];
    end
    state
    mesh(state);
end