Koch2

General Koch snowflake fractal curve

The following generalized Koch Snowflake curve is a fractal constructed by a [custom-user-tool] of EucliDraw (see the user-tools script KochFractalN.txt).This tool generalizes the tool illustrated in Koch.html and operates in three stages: Stage-1: selects an arbitrary closed polygon p(0). Stage-2: selects an arbitrary open polygonal line q and Stage-3: selects an integer number object N. The tool replaces, by similarity, each side of p(0) with q, producing a closed polygon p(1) and repeats this procedure N times, constructing a polygon p(N). p(N) depends on the three objects, selected in the three stages. It has S = a*b^N sides, where a is the number of sides of p(0) and b is the number of sides of polygon q.
The tool is practical for small values of a, b and N, since the number S can grow very fast and exhaust the resources of the computer. The example below shows a curve with a = 5, b = 4 and N = 7, resulting to S = 81920 - sided polygon p(7). The magnifying-rectangle shows a 50 times zoomed in region of the curve.

http://users.math.uoc.gr/~pamfilos/