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 4n/3n
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.