2D random walk double for loop

Question: Consider a particle which starts from the origin, and it moves in a random direction in each timestep: (∆x,∆y) = (dcosθ,dsinθ) where d = 0.01 and θ is a random number between 0 and 2π. Plot the positions of Np = 2000 independent random particles at timestep 2000 in the x-y plane.

I have managed to plot the path of 1 particle walking for 2000 steps (it was the previous part of this question) but I don't seem to be able to create a double for loop correctly to plot the final position of 2000 particles. The program just keeps running and nothing happens.

Where did I make a mistake?

clear % clear variables and functions from memory

d=0.01 % initial condition

for j=1:2000 % Repeat for 2000 particles

for i=1:2000 % Time-evolution of a single particle

theta = 2*pi*rand(2000,1); % theta= random angle between 0 and 2pi

% for 2000 steps

x(1)=0 % initial condition x=0

y(1)=0 % initial condition y=0

x(i+1) = x(i)+d*cos(theta(i,1)); % define i-th element of x vector

y(i+1) = y(i)+d*sin(theta(i,1)); % define i-th element of y vector

end

xfinal(j)=x(2001); % the position of the j-th particle

yfinal(j)=y(2001);

rfinal(j)=sqrt(x(2001)^2+y(2001)^2); % the distance from the origin

end

plot(xfinal,yfinal,"bo") % plots final position

axis equal % sets the aspect ratio so that equal tick mark

% increments on the x and y axis are equal in size.

xlabel('X','FontSize',20) % X-axis label

ylabel('y','FontSize',20) % Y-axis label

grid on % adds grid

grid minor % adds finer grid

Answer 1

[Agnish Dutta]

I used the following method to generate the x and y coordinates od 2000 points moving randomly in 2D cartesian space. I was then able to use the "plot" function to track their movement.

pos_x = zeros(1, 2000);
pos_y = zeros(1, 2000);
d = 0.01;
 
for i = 1:2000
theta = 2*pi*rand(1, 2000);
pos_x(end + 1, :) = pos_x(end) + d.*cos(theta);
pos_y(end + 1, :) = pos_y(end) + d.*sin(theta);
end
 
% pos_x(i, j) = X-cooridnate of the jth particle at instance 'i'.
% pos_y(i, j) = Y-cooridnate of the jth particle at instance 'i'.
 

The next thing would be to plot the particle's movements in the cartesian plane.

for i = 1:2000
plot(pos_x(:, i), pos_y(:, i));
hold on;
end

Plotting all the 2000 points on the same figure can get messy though. I suggest plotting 3-5 of them at a time.

Here is some additional material I found related to visualizing random walks:

https://www.mathworks.com/videos/visualizing-random-walk-data-part-1-97175.html

[ane4kina]

Thanks for your help!