%%% A script to generate simple random walks in 1 and 2 dimensions
clc
format compact
format short g
n=1000 % The length of the walk
A = 2*random('unid',2,6,n)-3; % Generates random steps +1 or -1 for 6 (or 3) walks
%Adds a starting point at 0 or (0,0)
A = [zeros(6,1),A]; 
% Turns this into a walk
A2 = cumsum(A')';
% Matrix to allow for a 2-d Random Walk as well
B = 1/2*[1 -1; 1 1];
figure(1)
subplot(3,1,1)
n1=50
plot([0:n1],A2(1,1:n1+1),'-o',[0 n1],[0 0],'k')
% New Walk - Longer Distance
subplot(3,1,2)
n1=200
plot([0:n1],A2(3,1:n1+1),[0 n1],[0 0],'k') 
% Last Walk - Longest Distance
subplot(3,1,3)
n1=n
plot([0:n1],A2(5,1:n1+1),[0 n1],[0 0],'k') 

%%% 2-d random walks
% Short Walk
figure(2)
subplot(3,1,1)
n1=50
C = A2(1:2,1:n1+1);
C2=B*C;
plot(C2(1,:),C2(2,:),'-o')
% Longer Walk
subplot(3,1,2)
n1=200
C = A2(3:4,1:n1+1);
C2=B*C;
plot(C2(1,:),C2(2,:))
% Longer Walk
subplot(3,1,3)
n1=n
C = A2(5:6,1:n1+1);
C2=B*C;
plot(C2(1,:),C2(2,:))