von Koch curve
Instructions:
Draws nth iteration of von Koch curve.
Description:
Neils Fabian Helge von Koch (1870-1924) curve first appear in his paper Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane published in 1906. This curve is constructed by dividing a line segment into three equal parts and replacing the middle segment by the other two sides of an equilateral triangle constructed on the middle segment. Repeat on each of the (now 4) segments. Repeat indefinitely. It gives a continuous curve which is of infinite length and nowhere differentiable.
You can observe process of creation of Koch curve by setting up the first step and incrementing number of steps using "+" button.
If one starts with an equilateral triangle and applies the construction, one gets the von Koch snowflake (sometimes called the von Koch star) as the limit of the construction.
Others von Koch curves:
Von Koch curve for a square
Von Koch curve for triangles
Random von Koch curve
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