How to add more squares on the checkerboard inscribed inside of a circle

 width=input('Enter a positive number:  ');

    disp(' ');
while width<0

    width=input('Enter a positive number:  ');
    disp(' ');
end

   dimension=input('Input an integer greater than 1: ');
   disp(' ');

 while (dimension<=1)

   dimension=input('Input an integer greater than 1: ');
end
   reorint=0;
while reorint==0
   if isreal(dimension)&&rem(dimension,1)==0
      reorint=1;
   else
      dimension=input('Input an integer greater than 1: ');
      reorint=0;
   end
end
   fprintf(1,'\n');

    color1=input('Enter 1st color:red(r), yellow(y), green(g), black(k), blue(b), magenta(m), white(w), cyan(c): ','s');

    color2=input('Enter different 2nd color:red(r), yellow(y), green(g), black(k), blue(b), magenta(m), white(w), cyan(c): ','s');

 N=4; %SQUARE
 R=width; %SQUARE SIZE
 Phase=pi/4;

 theta=zeros(1,N);

 for k=1:N+1
    theta(k)=2*pi*(k-1)/N;
 end

 x1=R*cos(theta+Phase)/sqrt(2);
y1=R*sin(theta+Phase)/sqrt(2);
plot(x1,y1);
fill(x1,y1,color1);
hold;

 x2=R*cos(theta+Phase)/sqrt(2)+R;
y2=R*sin(theta+Phase)/sqrt(2);
plot(x2,y2);
fill(x2,y2,color2);

This is my code so far. I was wondering how I could make the checkerboard with more squares instead of just two. The input 'dimension' is how many squares both sides of the checker board are going to be. I know that I have to use a loop but I don't know how I'd do it. Thank you in advance!