The Random Walker Printer
Matlab, 112
The core idea is generating a list of possible next positions and then uniformly drawing one of them. If we are e.g. at position $l=1$ the possible steps would be [-1,0,1,2,3] Of course if we would chose -1 that would be invalid and we would have to stay at the same position. Thats why we replace the invalid positions with the current position, [1,0,1,2,3], and then randomly chose an element from this updated list.
The OP asked us tho draw the program, so here we go:

The transcription:
function c(n,s);
l=19;                             %initialize position
for k=1:n;                          
    disp([ones(1,l)*32,'.']);     %print the line
    z=(-2:2)+l;                   %get vector of possible next steps (for l=1 we get [-1,0,1,2,3])
    z(z&lt;0)=l;                     %prune invalids: here we just replace the the invalid positions with the current position
    z(z&gt;39)=l;                    %   this ensures the same behaivour as staying in the same spot when going outside of the range
    l=z(randi(5));                %draw random sample of those
    pause(s);
end