Why is the set containing a cell $(x, y)$ of sqr grid iff $\exists$ integers $a, b \geq 0$ satisfying $a\;xor\;b=x$ and $a+b=y$ a Sierpinski triangle?

Question

Let G be a square grid. Let S be a set of cells from G. A cell $(u, v)$ from G is in S $\iff$ there exist two non-negative integers a and b satisfying $a \oplus b=u$ and $a+b=v$. Why is S a Sierpinski triangle?