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HL TYPE 1 By Abhishek Chhabria (Math HL) International Baccalaureate B.D.Somani International School INTRODUCTION The Koch curve was named after Helge von Koch in 1904. The generation of this fractal is simple. We begin with a straight line of unit length and divide it into three equally sized parts. The middle section is replaced with and equilateral triangle and its base is removed. After one iterations, the length is increased by four-thirds. As this process is repeated, the length of the figure tends to infinity as the length of the side of each new triangle goes to zero. Assuming this could be iterated an infinite number of times, the result would be a figure which is infinitely wiggly, having no straight lines whatsoever. The construction is very simple but still looks really beautiful. Throughout, let us consider- 1. Using an initial side length equal to 1, we deduce a table which...

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