The Swedish mathematicion Niels Fabian Helge von Koch (18701924) constructed the
Koch curve in 1904
as an example of a continuous, nondifferentiable 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
triangle:
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:
notes
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.
