How can I plot x,y,z position of particles over time from a multidimensional array?

Hi everyone,

I'm trying to simulate the positions of a number of molecules in free space over time, occasionally being hit by helium atoms (random velocity) and photons (uniform velocity). I have it set up to work through a number of steps, each time changing the velocity of the particular molecule based on a helium kick and then a photon kick. It then creates a position array, of dimensions (#molecules, 3, #steps). Those mechanics all seem to work. My problem comes when trying to plot the position over time. I'd like to plot each molecule's [x,y,z] position coordinate across the total number of steps, but the code below returns some sort of strange triangular graph in three dimensions that I'm not sure how to interpret. When I had this code set up for one dimension, it worked just fine.

So is there a way to plot an individual row of each "page" of the 3d array across the total number of steps?

numParticles = 10;
numSteps = 100;
HeliumThreshold = 0.1;
PhotonThreshold = .49999;
PhotonKick = [.0005193164, 0, 0];
Sigmav = .000005193164*eye(3);

v = zeros(numParticles, 3, numSteps);
x = zeros(numParticles, 3, numSteps);

for stepNumber = 2 : numSteps
    for p = 1 : numParticles
        HeliumProb = rand;
        PhotonProb = rand;
        Deltav = [0, 0, 0; 0, 0, 0];
        if HeliumProb > HeliumThreshold
            HeliumKick = mvnrnd([0, 0, 0], Sigmav, 1);
            Deltav(1, :) = HeliumKick;
        else
            Deltav = Deltav;
        end
        if PhotonProb > PhotonThreshold
            Deltav(2, :) = HeliumKick + PhotonKick;
        else
            Deltav = Deltav;
        end
        v(p, :, stepNumber) = v(p, :, stepNumber - 1) + Deltav(2, :);
        x(p, :, stepNumber) = x(p, :, stepNumber - 1) + v(p, :, stepNumber);
        X=reshape(x,[],3);
        plot3(X(:,1),X(:,2),X(:,3));
        hold on
    end
    hold off
end

Also, here's a picture of the plot:

Answer 1

[Cris LaPierre]

Based on my understanding, here's how I would approach this. I swapped your for loops so that it selects a particle, and then works through all the steps. At the conclusion of the inner loop, I can now plot the path of that particle. Rather than reshape, I use indexing to select the 'page' to plot, and use squeeze to remove the singleton dimension (otherwise you'll get an error when plotting).

Let me know if you have any questions.

numParticles = 10;
numSteps = 100;
HeliumThreshold = 0.1;
PhotonThreshold = .49999;
PhotonKick = [.0005193164, 0, 0];
Sigmav = .000005193164*eye(3);

v = zeros(numParticles, 3, numSteps);
x = zeros(numParticles, 3, numSteps);

for p = 1 : numParticles
    for stepNumber = 2 : numSteps
        HeliumProb = rand;
        PhotonProb = rand;
        Deltav = [0, 0, 0; 0, 0, 0];
        if HeliumProb > HeliumThreshold
            HeliumKick = mvnrnd([0, 0, 0], Sigmav, 1);
            Deltav(1, :) = HeliumKick;
        else
            Deltav = Deltav;
        end
        if PhotonProb > PhotonThreshold
            Deltav(2, :) = HeliumKick + PhotonKick;
        else
            Deltav = Deltav;
        end
        v(p, :, stepNumber) = v(p, :, stepNumber - 1) + Deltav(2, :);
        x(p, :, stepNumber) = x(p, :, stepNumber - 1) + v(p, :, stepNumber);
        
    end
    X = squeeze(x(p,:,:));
    plot3(X(1,:),X(2,:),X(3,:),'DisplayName',num2str(p));
    hold on
end
hold off
legend

[Michael Rainville]

I just tried your changes, and everything works beautifully! Swapping the for loops made it faster by something like an order of magnitude as well. Thank you so much!