Using MATLAB create a movie that simulates a random walk on a 1000 x 1000 grid.

Question

Using MATLAB create a movie that simulates a random walk on a 1000 x 1000 grid. Start the walk in the center (500 x 500) and increase/decrease x and y by, about, 10 units depending on the value of rand.

*For example, If the value of rand is less than .25, increase both x and y by 10. If the value of rand is less than .5 but greater than .25, decrease x by 10 and increase y by 10, etc.

You can run your walk for a set number of iterations or have it walk until it reaches the border of the plot window. Update the plot title with the current x,y values. Save your movie as an AVI file.

Please show all work. Thanks!

Explanation / Answer

clear;

clc;

x=0:1000;
y=0:1000;

Nj = 10;

Ns = 100;


forj=1:Ns
  
fork=1:Nj

Snx(1) = 500;

Sny(1) = 500;

fori=1:j

s = rand(1,2);
if(s(1,1) < .25)

x=x+10;
y=y+10;

elseif(s(1,1) < .5 && s(1,1)>.25)

X = x-10;
Y = Y+10;


end

end

Snx(i+1) = Snx(i) + X;

Sny(i+1) = Sny(i) + Y;

end


if(k==1 && j == Ns)

figure(1);

plot(Snx,Sny,'-k','LineWidth',4);

holdon;

plot(Snx(Ns+1),Sny(Ns+1),'.k','MarkerSize',40);

elseif(k==2 && j == Ns)

plot(Snx,Sny,'-r','LineWidth',3);

plot(Snx(Ns+1),Sny(Ns+1),'.r','MarkerSize',50);

elseif(k==Nj-1 && j == Ns)

plot(Snx,Sny,'-b','LineWidth',2);

plot(Snx(Ns+1),Sny(Ns+1),'.b','MarkerSize',50);

elseif(k==Nj && j == Ns)

plot(Snx,Sny,'-g','LineWidth',1);

plot(Snx(Ns+1),Sny(Ns+1),'.g','MarkerSize',50);

holdoff;

gridon;

xlabel('x');

ylabel('y');

end

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