%Script to do simulation of random walk in 2D
%
%adjust parameters below for probability of left step,
%right step, or no step.

%by Nasser Abbasi, CSUF, spring 2008, Mathematics 504

clear all; close all;

%
% C O N F I G U R A T I O N     change as needed
%  make sure the probabilites add to ONE
%  I am not going to check for this :)
%

p = 1/2;      %probability of RIGHT step
q = 1/2;      %probability of LEFT step
z = 0;      %probability of NO step

nSteps = 300;  %how many steps

seed  = 10101010; %my seed
rand('twister',seed);

%
% G E N E R A T E   R A N D O M   S T E P S
% Generate random numbers from 1,-1,0 with probability p,q,z
%
steps = ones(nSteps,1);
k = round(q*nSteps);
steps(1:k) = -1;
steps(k+1:k+round(z*nSteps)) = 0;
indx  = randperm(nSteps);
steps = steps(indx);

%
%  Start the simulation
%
lastX = 0;
lastY = 0;
figure(1);
hold on;

for i=1:nSteps

    currentY  = lastY + steps(i);
    currentX  = lastX + 1;

    line([lastX currentX currentX],[lastY lastY currentY]);
    line([0 nSteps],[0 0],'Color','r');
    lastX = currentX;
    lastY = currentY;

    ylim([round(-0.15*q*nSteps),round(0.15*p*nSteps)]);
    title(sprintf('R.W. simulation p(+1)=%3.2f, p(-1)=%3.2f, p(0)=%3.2f, current Step=%d'...
        ,p,q,z,i));

    drawnow;
    pause(0.05);

end