Four different outputs keep ending up with the same "answer" when I don't believe they're supposed to.

I am trying to plot the path of 1 particle for 100 steps, running 100 runs, with the option for it to go up,down,left, or right randomly. I want to find the root mean square distance (square root of the number of steps) and final position. My distance, distances, rootmeansquared, and meandistance all keep coming up as the same value and I'm not sure why. Any help is appreciated.

Homework question: Write a simulation of a random walk in two dimensions, in which the particle stands at an intersection and chooses to go left, right, up, or down. The average final position is zero, and the root mean squared distance is the square root of the number of steps. Try it with 100 steps and with 1000 steps, and run the simulation 100 times. Make sure that the final position and root mean square distance are what you expect. Show a plot of the particle’s path for each run of the simulation.

pos=[0 0]
distances= [ ]
coinx = 0
coiny = 0

figure
for j=1:1
    for i=1:100
        coinx=rand;
        coiny=rand;
        if coinx>0.5
            pos(1)=pos(1)+1;
        else
            pos(1)=pos(1)-1;
        end
        if coiny>0.5
            pos(2)=pos(2)+1;
        else
            pos(2)=pos(2)-1;
        end
        plot(pos(1),pos(2),'ro');
        hold on
    end
    distance=sqrt(pos(1)^2+sqrt(pos(2)^2))
    distances=[distances distance]
    hold on
    pos=[0 0];
end

rootmeansquared=rms(distances)
meandist=mean(distances) %This is the final position

Thank you.

[DGM]

Two things:

The reason why your mean and rms distances are the same is because the variable distances is a scalar. The reason it's a scalar and not a vector is because the outer loop is only set to run one pass.

Second, the way the explanation reads, you're to to find the RMS distance, and the mean position. So you'll need to log the final x,y positions as well.

[Kristin Aldridge]

I'm having trouble finding how to log the x and y positions. Below is what I came up with but I'm missing what to put in the code itself, and where. I've been trying pos1(end) and pos2(end) and then having empty vectors for pos1(end)=[ ] and pos2(end)=[ ] but it keeps telling me "The end operator must be used within an array index expression".

Answer 1

[DGM]

Something like this:

numsteps = 100;
numtrials = 10;

distances = zeros(numtrials,1);
finalpos = zeros(numtrials,2);
for j = 1:numtrials
    pos = [0 0];
    for i = 1:numsteps
        % this does the same as the if statements
        pos = pos + 2*round(rand(1,2)) - 1;
        
        plot(pos(1),pos(2),'ro');
        hold on
    end
    distances(j) = sqrt(pos(1)^2+sqrt(pos(2)^2)); % this doesn't look right
    finalpos(j,:) = pos; % store final position
end
rootmeansquared = rms(distances)
meandist = mean(finalpos,1) % This is the mean end position

I'm not really sure what the requirements actually are here. It kind of sounds like you're supposed to get the RMS distance estimate, which would just be sqrt(N) -- which is something that's known from the start.