Simulating a 1D Random Walk

This is my code:

% Function to simulate 1D random walk

function trajectory = simulateRandomWalk(N)

% Initialize position
position 
= 0;


% Initialize trajectory array
trajectory 
= zeros(1, N+1);

trajectory(1) = position;


% Simulate random walk

for step = 1:N
    
    % Generate a random number to decide left or right movement
    move 
    = randi([0, 1])*2 - 1; % -1 for left, 1 for right
    
    
    % Update position
    position 
    = position + move;
    
    
    % Store the current position in the trajectory array
    
    trajectory(step+1) = position;
    
end

end
% Step 2: Plot the entire trajectory for a single random walk

N 
= 100; % Number of steps
single_trajectory 
= simulateRandomWalk(N);

figure
;

plot(0:N, single_trajectory, '-o');

title('1D Random Walk - Single Trajectory');

xlabel('Steps');

ylabel('Position');

% Step 3: Repeat the process for different values of P and create histograms

P_values 
= [50, 500, 5000, 50000, 500000];


for p_index = 1:length(P_values)
    P 
    = P_values(p_index);
    final_positions 
    = zeros(1, P);
    
    
    for i = 1:P
        single_trajectory 
        = simulateRandomWalk(N);
        
        final_positions(i) = single_trajectory(end);
        
    end
    
    
    % Plot histogram of final positions
    figure
    ;
    
    histogram(final_positions, 'Normalization', 'probability');
    
    title(['Histogram for P = ' num2str(P)]);
    
    xlabel('Final Position');
    
    ylabel('Probability');
    
end

Its giving me an error on N.

[Image Analyst]

This is not valid MATLAB code. You cannot have a script that starts with a function. It will, and does, throw an error. Your function needs to be at the END of your script. Or else don't have it be a function. Also, don't put the right hand side of the = sign be on the line below the line that takes the assignment.

Answer 1

[Torsten]

% Step 2: Plot the entire trajectory for a single random walk
N = 100; % Number of steps
single_trajectory = simulateRandomWalk(N);
figure
plot(0:N, single_trajectory, '-o')
title('1D Random Walk - Single Trajectory')
xlabel('Steps')
ylabel('Position')

% Step 3: Repeat the process for different values of P and create histograms
P_values = [50, 500, 5000, 50000, 500000];
for p_index = 1:length(P_values)
    P = P_values(p_index);
    final_positions = zeros(1, P);
    
    
    for i = 1:P
        single_trajectory = simulateRandomWalk(N);
        
        final_positions(i) = single_trajectory(end);
        
    end
    
    
    % Plot histogram of final positions
    figure
    
    histogram(final_positions, 'Normalization', 'probability')
    
    title(['Histogram for P = ' num2str(P)])
    
    xlabel('Final Position')
    
    ylabel('Probability')
    
end

% Function to simulate 1D random walk
function trajectory = simulateRandomWalk(N)
% Initialize position
position = 0;
% Initialize trajectory array
trajectory = zeros(1, N+1);
trajectory(1) = position;
% Simulate random walk
for step = 1:N
    
    % Generate a random number to decide left or right movement
    move = randi([0, 1])*2 - 1; % -1 for left, 1 for right
    
    
    % Update position
    position = position + move;
    
    
    % Store the current position in the trajectory array
    
    trajectory(step+1) = position;
    
end
end

[William]

Thank you so much!!!

[William]

Can you also help me on this question as well? https://www.mathworks.com/matlabcentral/answers/2057329-simulating-a-2d-random-walk?s_tid=srchtitle