Random path coordinates in 2D within a unit square

Hi all, I want to generate a random path within a unit square and get the x,y coordinates of 1000 points on it. Can you suggest a way to do it?

start point and the end point should lie diagonally on the opposite corners. For example, if the starting point is (0,0), end point should be (1,1). and if the starting point is (0,1), end point should be (1,0)

I would like to generate random path like this and obtain the coordinates along the path. Please see the attached figure.

Answer 1

[James Tursa]

Any restrictions on the path? E.g., would 1000 random points suffice:

mypath = rand(1000,2);  % <-- each row is an (x,y) point in a unit square

[KalMandy]

Hi, thanks for the answer.

mypath = rand(1000,2);

xp=mypath(:,1); yp=mypath(:,2);

plot(xp,yp)

I tried this. But the plot gives a mesh-like path. The path should be smooth with a small deviation from the line connecting the starting point and the ending point.

[James Tursa]

Please give more details on the path restrictions.

[KalMandy]

I would like to generate random path like this and obtain the coordinates along the path. Please see the attached figure.

[David Goodmanson]

Hi KM, what is the relation between the start and end points and the unit square? From your example, the two points can't be diagonally opposite corners of the square.

[KalMandy]

start point and the end point should lie diagonally on the opposite corners. For example, if the starting point is (0,0), end point should be (1,1). and if the starting point is (0,1), end point should be (1,0)

[David Goodmanson]

except that in the example, some of the paths stray outside the unit square and your original question specifies "within" a unit square. So is outside the unit square all right?

[John D'Errico]

If the first point and the last point are known, then they are not random. But all that means is you really need to generate 998 random points and then append the first and last point.

[KalMandy]

@David I want to have all of the path inside the unit square.

[KalMandy]

@John yes you are right.

Answer 2

[Image Analyst]

See my attached random walk programs and adapt as needed.

[KalMandy]

Thank you, I will check it.