# Simulating a 1D Random Walk

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William on 6 Dec 2023
Commented: William on 11 Dec 2023
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 on 6 Dec 2023
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.

Torsten on 6 Dec 2023
Edited: Torsten on 6 Dec 2023
% 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 on 6 Dec 2023
Thank you so much!!!
William on 11 Dec 2023