Is it possible to color all lattice points (\(\mathbb Z\times \mathbb Z\)) in the plane into two colors such that if four distinct points \( (a,b), (a+c,b), (a,b+d), (a+c,b+d)\) have the same color, then \( d/c\notin \{1,2,3,4,6\}\)?

(The next POW problem will be posted on October 20. Happy Chuseok and good luck with your midterm exams.)