No repeated coordinates in random walker ensemble

Question

i'm simulating an ensemble of random walkers in 2D in python, I set [x,y] coordinates of my walkers to be gaussian in a 2D grid, then use a rand array of -1 and +1 to move up down left right:

N=20 #number of walkers

Coor[:,1]=100*random(N) #X's coordinates
Coor[:,2]=100*random(N) #Y's coordinates

To do the simulation more realistic I want to impose that none of the walkers could have the same X Y coordinates as another at the same time, so as example if at certain time after random moves my coordinates array looks like this:

Coor[:,1]=([1,3,5,7,7,8,....]) 
Coor[:,2]=([4,8,3,2,2,9,....]) 

then the 4th and 5th elements have the same coordinates in X and Y so How I find when that happens and change one of the values to don't be in that situation?

Answer 1

Instead of updating the coordinates by adding a randomized vector of -1 and +1 to them, you could simply iterate over walkers and select a random direction from the currently available ones. This way your system never gets into invalid state so no extra checks are needed. I cannot prove it but I suspect that pure vectorized solution for the problem might not even exist.

Also, your current solution only gives the walkers 4 possible directions (the diagonals) to move to. I'm not sure if this was the intention.