Thus far, almost all fractal antennas comprise fractal geometries with straight segments or rectilinearly-edged blocks, such as Koch curve series [13-15], Minkowski curve , and Sierpinski Carpet series [8, 17-20].
CAKC is similar to Koch curve in the panorama and iterative process, only the initiator and the generator are replaced with circular arcs.
Koch curve is a good example of self-similar, space-filling fractals which have been used to develop wideband, multiband or miniaturized antennas [21-27].
The standard Koch curve can be constructed iteratively replacing the central segment of the unit interval by two segments of length 1/3, both forming the upper part of an equilateral triangle .
the W operator previously defined generating by successive iterations the Koch curve
As a first example of the use of these symbols, we introduce the Koch curve Lsystem:
Some generations of the Koch curve are displayed below.
to the anti-knife crime campaign in memory of Ben Kinsella "The Koch Curve
, the basis of the snowflake design, is a beautiful bit of mathematical recycling; an endless harmonic loop like a bell that never stops ringing"
The website describes the integration of several mathematical systems including "Phi, Pi, L-systems, Penrose tiling, and an all-encompassing Koch curve
The records of the New Zealand census detailed volumes on Religious Professed from 1891 to 1966, ranked by size appear to conform to this Koch curve
(also known as the snowflake curve).
D is very approximate to log4/log3, which is the fractal dimension of Von Koch Curve
, because it is Koch-like.
4 shows the recursive construction of a triadic Koch curve
up to three fractal iterations.