The Sierpinski Triangle is usually described just as a set: Remove from
the initial triangle its "middle", namely the open triangle whose vertices are
the edge midpoints of the initial triangle. (open means: only the interior of
the middle triangle is removed, not its edges.) Of the remaining 3 triangles
remove again their middles. Of the remaining 9 triangles remove again their
middles - and so on. Observe that no point on an edge of a removed triangle
is removed in a later step, all these edges belong to the final set.
The Sierpinski Triangle is more than just a set. It is the image of a continuous
curve! This sequence shows the first few approximations by polygons. These polygons
converge to a continuous limit curve whose image is the Sierpinski Triangle.
