2D Random path within a unit square

Hi all, I want to generate a random path within a unit square and get the x,y coordinates of n=1000 points on it. start point and the end point can be picked up from the vertices of the unit square, i.e, (0,0), (0,1),(1,0),(1,1).

The code I have up to now is given as follows. But it does not restrict the path to lie inside the unit square. How can I solve this?

n=1000;

mypath = rand(n,2);

xp=mypath(:,1);

xp_s=cumsum(xp);

yp=mypath(:,2);

yp_s=cumsum(yp);

plot(xp_s,yp_s)

Answer 1

[Andrei Bobrov]

n=1000;
mypath = rand(n,2);
m = cumsum(mypath);
mout = m./m(end,:);                 % MATLAB >= R2016b
mout = bsxfun(@rdivide,m,m(end,:)); % MATLAB <  R2016b

Answer 2

[Image Analyst]

I have a number of random walk demos and I've attached them. Feel free to use them however you wish.

[KalMandy]

sorry, I could not find the solution with this.

[Image Analyst]

In your loop, simply don't add the next random step if it would take you outside the unit box. Just get another step instead.