How can I set the number of iterations to run in a recursive function in Matlab?

Question

How can I set the number of iterations to run in a recursive function in Matlab? I have the following function

function t=m(x1,x2)
if x1<0.5
    if x2<0.5
        t=(0+m(2*x2, 2*x1))/4;
    else
        t=(1+m(2*x1, 2*x2-1))/4;
    end
else
    if x2>=0.5
       t=(2+m(2*x1-1, 2*x2-1))/4;
    else
       t=(3+m(1-2*x2, 2-2*x1))/4;
    end
end

end 

I want it to perform 10^3 iterations.

I tried with

function t=m(x1,x2,iter)
while iter<=10^3
      if x1<0.5
         if x2<0.5
            t=(0+m(2*x2, 2*x1, iter+1))/4;
         else
            t=(1+m(2*x1, 2*x2-1, iter+1))/4;
         end
      else
        if x2>=0.5
           t=(2+m(2*x1-1, 2*x2-1, iter+1))/4;
        else
           t=(3+m(1-2*x2, 2-2*x1, iter+1))/4;
        end
      end
end
end

and in the main

    x1=0.3;
    x2=0.4;
    iter=0;
    t=m(x1,x2,iter);

but it gives me several errors. Any help?

Answer 1

Firstly, you shouldn't put that loop inside your function. Repeating is the role of recursion. So change your function to:

function t=m(x1,x2,iter)
t = 0;
if iter > 0
      if x1<0.5
         if x2<0.5
            t=(0+m(2*x2, 2*x1, iter-1))/4;
         else
            t=(1+m(2*x1, 2*x2-1, iter-1))/4;
         end
      else
        if x2>=0.5
           t=(2+m(2*x1-1, 2*x2-1, iter-1))/4;
        else
           t=(3+m(1-2*x2, 2-2*x1, iter-1))/4;
        end
      end     
end
end

(supposing you want it to return 0 after the last iteration)

Now you can call your function like this:

m(0.3, 0.4, 10^3)

But before that, call:

set(0,'RecursionLimit',10^3+2)

For these inputs, it converges to 0.1808 after only 8 iterations.