# Random Walk in MATLAB®

How to make Random Walk Plots in MATLAB® with Plotly.

A random walk can be thought of as a random process in which a token or a marker is randomly moved around some space, that is, a space with a metric used to compute distance. In the visualizations below, we will be using scatter plots as well as a colorscale to denote the time sequence of the walk.

## Random Walk in 1D

The jitter in the data points along the x and y axes are meant to illuminate where the points are being drawn and what the tendency of the random walk is.

N = 500 ; % number of steps
X = 6 ;  % number of dimensions

% positions, starting at (0,0,...,0)
P = cumsum(full(sparse(1:N, randi(X,1,N), [0 2*randi([0 1],1,N-1)-1], N, X))) ;

figure ;
hold on ;
for k=1:size(P,2),
plot(1:size(P,1),P(:,k),'.-') ;
text(size(P,1),P(end, k), sprintf(' dim %d',k)) ;
end

xlabel('Step') ;
ylabel('Position') ;
hold off ;

fig2plotly(gcf);


## Random Walk in 2D

N = 10; % Length of the x-axis, also known as the length of the random walks.
M = 60; % The amount of random walks.
x_t(1) = 0;
y_t(1) = 0;

for m=1:M
for n = 1:N % Looping all values of N into x_t(n).
A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
x_t(n+1) = x_t(n) + A;
A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
y_t(n+1) = y_t(n) + A;
end
plot(x_t, y_t);
hold on
end

fig2plotly(gcf);