The Koch

Curve is a very simple and very

well known fractal. It
is a member of the

L-system of

fractals. Its formual is:

`F - F + + F - F`.

The first 2 steps of the fractal look thus:

0) --------
/\
1) / \
-- --

For each iteration, on each line, a triangle is drawn in the middle.
This causes the length of the line to

explode. The length of the
line is as follows:

iteration length
0 1
1 4/3
2 16/9
3 64/27
4 256/81
5 1024/243
n 4^{n}/3^{n}

As part of a

triangle (called the Koch

Snowflake) inscribed in a

circle, the Koch Curve has the
interesting properties of having

infinite perimeter but

finite surface
area.