The * Sierpiski 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 . See [36, Example 2.7].

The Sierpiski Triangle is
homeomorphic to the unique nonempty compact set *K* of the
complex plane that satisfies

where