[alogo] Koch Snowflake curve

The Koch Snowflake curve is a fractal constructed by a self-repeating procedure as follows. Start with an equilateral triangle and divide each one of its sides (s) in three equal parts. Then set on the middle part an equilateral as shown in picture (s*). Repeat the procedure on the sides of the resulting 12-gon. By applying the procedure n times you get a polygon with 3*4^n sides. Below is the polygon resulting for n=5, having 3072 sides. The fractal was constructed using the [Fractal Socket] tool of EucliDraw. The 10-fold magnification shows some details of the polygon constructed. The next stage would replace each side of the actual polygon with (s*). The construction took a couple of minutes and the file occupies 1.814.528 bytes of disk space. The reason for such a waste of memory is that for its construction uses some thousands of auxiliary equilateral triangles. Because of the huge memory allocation it is not included in the standard examples folder of the program. It can be obtained uppon request from euclidraw.com. For a generalization with arbitrary triangle instead of an equilateral see Koch_Snowflake_gen.html .

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Produced with EucliDraw©