/\
       /  \
      /    \
     /      \
    /        \
   /          \
  /            \
 /              \
/________________\
Perimeter = 3

        /\
       /  \
______/    \______
\    /      \    /
 \  /        \  /
  \/          \/
  /            \
 /              \
/________________\
      \    /
       \  /
        \/
Perimeter = (4/3)1 * 3

       _/\_
      |/  \|
__/\__/    \__/\__
\ ¯¯ /      \ ¯¯ /
|\  /        \  /|
 ¯\/          \/¯
 _/            \_
|/              \|
/________________\
¯ \/  \    /  \/ ¯
      |\  /|
       ¯\/¯
Perimeter = (4/3)2 * 3
       .xx.
      |/  \|
..xx..x    x..xx..
x ¯¯ /      \ ¯¯ /
x\  /        \  /x
 ¯x/          \x¯
 x/            \x
|/              \|
x________________x
``xx``\    /``xx`¯
      |\  /|
       `xx`
Perimeter = (4/3)n * 3
Where n is the current iteration.

Since fractals iterate infinitly, the perimeter of a koch snowflake is infinite.