information:extraction
Arrowhead construction of Sierpiński gasket

Another construction for the Sierpinski gasket shows that it can be constructed as a curve in the plane. It is formed by a process of repeated modification of simpler curves, analogous to the construction of the Koch snowflake:

At every iteration, this construction gives a continuous curve. In the limit, these approach a curve that traces out the Sierpinski triangle by a single continuous directed (infinitely wiggly) path, which is called the Sierpinski arrowhead. In fact, the aim of the original article by Sierpinski of 1915, was to show an example of a curve (a Cantorian curve), as the title of the article itself declares.