On a Generalization of the Koch Curve Built from n-gons
نویسندگان
چکیده
We study a generalization of the von Koch Curve, which has two parameters, an integer n and a real number c on the interval (0, 1). This von Koch type curve is constructed as the limit of a recursive process that starts with a regular n-gon (or line segment) and repeatedly replaces the middle c portion of an interval by the n− 1 other sides of a regular n-gon placed contiguous to the interval. We show that there are values of n such that the set of c for which the (n, c)-von Koch Curve is simple, i.e. does not intersect itself, is not an interval.
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