Question: Random Walks in plane


I'm trying to create a code that allows me to model a random walk for 50 people. I'm using r[i]= {X[i],Y[i]} where i is the number of steps and r[i] the position in the i-th term.

I have created three possibilities:
2r[i]-r[i-1] - go stright forward

{x[i]+y[i]-y[i-1],y[i]-x[i]+x[i-1]} - turn right

{x[i]-y[i]+y[i-1],y[i]+x[i]-x[i-1]} - turn left

The first step I want them to make is to point (1,0) and from there I want them to take 1500 random steps.

M:=50; N:=1500; R3:=rand(1..3):

for i from 1 to M do
for j from 1 to N do
if j=1 then X[i,1]:=1; Y[i,1]:=0;
elif j>1 then
if r=1 then R[i,j]:=2*R[i,j]-[R[i,j-1];
elif r=2 then R[i,j]:=[X[i,j-1]+Y[i,j-1]-Y[i,j-2],Y[i,j-1]-X[i,j-1]+X[i,j-2]];
elif r=3 then R[i,j]:=[X[i,j-1]-Y[i,j-1]+Y[i,j-2],Y[i,j-1]+X[i,j-1]-X[i,j-2]];
end if;
end if;
end do:
end do:


The first and second step works, but from there it seems Maple is having trouble getting the correct digigts, because the formulas coming out are correct.

I have tried putting in different types of X, Y and R reads, but have gotten stuck. If someone could help me spot what this code is missing I would be very gratefull. I think Maple is just missing a way of reading X and Y but i might be wrong.

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