Simulating a 2D Random Walk

How can I turn a 1d random walk into a 2d random walk???

This is my code for 1d 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')
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 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

Answer 1

[Walter Roberson]

Call simulateRandomWalk twice, once to get an x trajectory and once to get a y trajectory. Then put them together,

plot(first_trajectory, second_trajectory)

[William]

How would I go about doing that?

[Walter Roberson]

N = 100; % Number of steps
x_trajectory = simulateRandomWalk(N);
y_trajectory = simulateRandomWalk(N);
figure
plot(x_trajectory, y_trajectory, '-o')
title('1D Random Walk - Single Trajectory')
xlabel('Steps')
ylabel('Position')

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

Answer 2

[Image Analyst]

See attached demos for random walks. I think all of them are 2-D.