How do I make a multidimensional random walk?

So, I have a 2D random walk, but how do I change my code so that it can calculate N dimensions? I will be asking for user input as to the number of dimensions.

 nSteps = input('Enter the number of steps in a single run: ') % Length of the x-axis and random walk.
 nRepeats = input('Enter the number of simulation runs to do: '); % The number of random walks.
 w_position = (1) = 0;
 for i=1:nRepeats
    for j = 1:nSteps % Looping all values of nSteps into w_postion.
        x = sign(randn); % Generates either +1/-1 depending on the sign of RAND.
        w_position(j+1) = w_position(j) + x;
    end
    plot(w_position);
    hold on
 end

Answer 1

[Pratyush Roy]

Hi,

For random walk in higher dimensions we can use a similar approach as mentioned in the code for 2 dimensional random walk. The code snippet below might be helpful to generate random walk in high dimensions:

nSteps = input('Enter the number of steps in a single run: ') % Length of the x-axis and random walk.
nRepeats = input('Enter the number of simulation runs to do: '); % The number of random walks.
nDims = input('Enter the number of Dimensions: '); % Data Dimensionality.
w_position = zeros(nSteps,nDims);
for i=1:nRepeats
   for j = 1:nSteps % Looping all values of nSteps into w_postion.
       x = sign(randn([1,nDims])); % Generates either +1/-1 depending on the sign of RAND.
       w_position(j+1,:) = w_position(j,:) + x;
   end
end

Here w_position stores the position at the ith instant in the ith row.

Hope this helps!