The Swedish mathematicion Niels Fabian Helge von Koch (1870-1924) constructed the
Koch curve in 1904
as an example of a continuous, non-differentiable curve. Karl Weierstrass
had demonstrated the existence of such a curve in 1872.
Other names for the curve are Koch star and Koch island.
The curve is a base motif
fractal which uses a line segment as base. The motif is to divide the line
segment into three equal parts and replace the middle by the two other sides of an equilateral
The fractal dimension of the Koch curve is equal to
log4/log3, what is about 1.2619 1).
Three copies of the Koch curve placed at the the sides of an equilateral
triangle, form a Koch snowflake:
1) Fractal dimension = log N / log e, where N is the number of line segments
and e the magnification.
For the Koch curve: N=4, e=3.