What is the area of this figure?

Question

Each side (of unit length) of an equilateral triangle is divided into thirds. On the middle third of each side another equilateral triangle is constructed, so as to form a 6-pointed star. The exposed (outer) two sides of each of the six equilateral triangles so formed are further divided into thirds. There are now 18 smaller equilateral triangles around the outside of the figure. The process continues indefinitely by further dividing the exposed sides of the equilateral triangles into thirds, and the "snowflake" figure becomes more and more spiky. Although the perimeter tends to infinity as the number of triangles approaches infinity, the area of the figure converges to a finite limit which can be calculated. What is the limit of this area?

Answer 1

That's the Koch Snowflake.  Formulas are on the Wikipedia page.

https://en.wikipedia.org/wiki/Koch_snowflake

Comments

Actually, it's not quite. The Koch snowflake has extra triangles sprouting after the third iteration, because these appear in the concave parts of the polygon. Perhaps my question is ambiguous, because it only requires each protruding (outer) triangle to be trisected and this leads to a simpler solution than the one associated with Koch. But thanks for the pointer, John, it is an interesting subject.