Random Walk Simulation for Multiple Particles

Im trying to perform a randown walk for 1000 particles, simuating each for 20 steps. Im then supposed to calcualte and plot the mean square displacement but im not sure how. Here's what i have so far...

% Simulation of a random walk (delta = 1, tau = 1)
rng('Shuffle')                         

nSteps = 20;                          
positionArray = zeros(nSteps+1, 1);     
stepNumber = 0:nSteps;                  


position = 0;                          

for index = 1:nSteps

    randomMove = rand;                  % random number between 0 and 1; used to decide direction of random move

    if (randomMove <= 0.5)
        position = position+1;          % move right
    else
        position = position-1;          % move left
    end
    
    positionArray(index+1) = position;  % store position

end

plot(stepNumber,positionArray,'k')      % plot the position as a function of step number
set(gca,'FontSize',10);
xlabel('number of steps','FontSize',10)
ylabel('position','FontSize',10)

Answer 1

[Alan Stevens]

Do you mean like this:

% Simulation of a random walk (delta = 1, tau = 1)
rng('Shuffle')                         

trials = 1000;

nSteps = 20;                          
positionArray = zeros(nSteps+1, 1);     
stepNumber = 0:nSteps;    

meansquaredisplacement = zeros(trials,1);

for trial = 1:trials
    squareposn = 0;
    position = 0;                          

    for index = 1:nSteps

        randomMove = rand;                  % random number between 0 and 1; used to decide direction of random move

        if (randomMove <= 0.5)
            position = position+1;          % move right
        else
            position = position-1;          % move left
        end

    end
    squareposn = squareposn + position^2;
    meansquaredisplacement(trial) = squareposn/nSteps;
end
 

plot(1:trials,meansquaredisplacement,'k')      % plot the msd as a function of step number
set(gca,'FontSize',10);
xlabel('trial','FontSize',10)
ylabel('mean square displacement','FontSize',10)