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].
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 .
As a first example of the use of these symbols, we introduce the Koch curve
the W operator previously defined generating by successive iterations the Koch curve
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 Koch curve
, first described in 1904, is a continuous loop to infinity, never intersecting itself, and the total area remains finite.
A typical fractal example called Koch curve
is shown in Figure 1.
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.
This network is derived from the class of Koch curves
. They are one of the interesting families of fractals.
The antenna design consisted of a microstrip fractal dipole with its 2 arms formed by square Koch curves
in its second iteration (n = 2).