Superior Koch Curve

In this paper, the author presents the design of Superior Koch Curve with different scaling factor, which has wide applications in Fractals Graphics. The proposed curve has been designed using the technique of superior iteration. The Koch curve is the limiting curve obtained by applying the self similar divisions to infinite number of times but in Superior Koch Curve scaling factor is based on superior iteration. replace the middle segment by the two sides of an equilateral triangle of the same length as the segment being removed (the two red segments in the middle figure). Now repeat, taking each of the four resulting segments, dividing them into three equal parts and replacing each of the middle segments by two sides of an equilateral triangle (the red segments in the bottom figure). Continue this construction. The Koch curve is the limiting curve obtained by applying this construction an infinite number of times. For a proof that this construction does produce a “limit” that is an actual curve, i.e., the continuous image of the unit interval, see the text by Edgar. The first iteration for the Koch curve (Figure 2) consists of taking four copies of the original line segment, each scaled by r = 1/3. Two segments must be rotated by 60°, one counterclockwise and one clockwise. Along with the required translations, this yields the following Iterated Function System DOI: 10.4018/jalr.2011100103 International Journal of Artificial Life Research, 2(4), 24-31, October-December 2011 25 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. The fixed invariant set of this IFS (Iterated Function System) is same as the Koch curve. Figure 1. Koch curve Figure 2. First iteration of Koch curve Figure 3. Closed Koch Curve 6 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/superior-kochcurve/62070?camid=4v1 This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Medicine, Healthcare, and Life Science. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2