The \hs{Sierpi\'nski Triangle}{Sierpinski Triangle} is
obtained as the residual set remaining when one begins with
a triangle and applies the operation of dividing it  into
four equal triangles and omitting the interior of the center
one, then repeats this operation on each of the surviving 3
triangles, then repeats again on the surviving 9  triangles,
and so on $\cdots$ . See \cite[Example 2.7]{cd1994}.

The \gs{Sierpi\'nski Triangle}{Sierpinski Triangle} is
homeomorphic to the unique nonempty compact set $K$ of the
complex plane that satisfies
$$
 K= w_1(K) \cup  w_2(K) \cup w_3(K) \quad ,
$$
where $w_1$, $w_2$, $w_3$
are maps of the complex plane defined by
$w_1(z)=z/2$, $w_2=(z + 1)/2$ and $w_3=(z+i)/2$.