I have a for loop that makes one particle take 1000 random steps. How do i make this happen for 1000 particles?

I am working on a project where I need to make 1000 particles, starting at the origin, take 1000 random steps and plot said steps. I got the first part which is:

N=1000;
position = zeros(2,N+1);

for i = 2:N+1
    step=2*rand(2,1)-1;    %Creates a random step vector (x,y)
    position(:,i)= position(:,i-1)+step;    %adds step to last position

end;
plot(position(1,2:N+1),position(2,2:N+1))    %Plots steps of particles starting from origin

This all works but now i need to make it work for 1000 particles and i need to plot them all on top of each other on the same graph. Does anyone have any suggestions? Thanks for the help.

Answer 1

[Andrew Newell]

This is a 2D random walk, and it helps to use variable names that reflect this. It is more efficient to generate a lot of random numbers at once and then use cumsum to cumulatively add them:

nSteps = 1000;
nParticles = 1000;
x = cumsum(2*rand(nSteps,nParticles)-1); 
y = cumsum(2*rand(nSteps,nParticles)-1);
plot(x,y)

[ane4kina]

What is you wanted them to start at the origin and only plot the final position of each particle?