# Koch curve

## Koch curve

[′kōk ‚kərv]
(mathematics)
A fractal which can be constructed by a recursive procedure; at each step of this procedure every straight segment of the curve is divided into three equal parts and the central piece is then replaced by two similar pieces.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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References in periodicals archive ?
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 [16], 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 [14].
As a first example of the use of these symbols, we introduce the Koch curve Lsystem:
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.
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).

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