Koch curve

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English: The Koch curve is the same as the snowflake, except it starts with a line segment instead of an equilateral triangle.
Deutsch: Die Koch-Kurve oder kochsche Kurve ist ein von dem schwedischen Mathematiker Helge von Koch 1904 vorgestelltes Beispiel für eine überall stetige, aber nirgends differenzierbare Kurve.

See also: Koch snowflake

Illustrations

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Iteration

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  • SVG, 1 step
    SVG, 1 step
  • SVG, 2 steps
    SVG, 2 steps
  • SVG, 3 steps
    SVG, 3 steps
  • SVG, 4 steps
    SVG, 4 steps
  • SVG, 5 steps
    SVG, 5 steps
  • SVG, 6 steps
    SVG, 6 steps
  • SVG, 7 steps
    SVG, 7 steps

Animations

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Variants

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  • Koch surface. Extension in higher dimension
    Koch surface. Extension in higher dimension
  • iterations of the Koch surface.
    iterations of the Koch surface.
  • Quadratic Koch curve (type 1).
    Quadratic Koch curve (type 1).
  • Iterations of the quadratic Koch curve (type 1).
    Iterations of the quadratic Koch curve (type 1).
  • Quadratic Koch curve (type 2).
    Quadratic Koch curve (type 2).
  • Iterations of the quadratic Koch curve (type 2).
    Iterations of the quadratic Koch curve (type 2).
  • Quadratic Koch surface(type 1). After 2 iterations.
    Quadratic Koch surface(type 1). After 2 iterations.
  • Quadratic Koch surface(type 2). After 1 iteration.
    Quadratic Koch surface(type 2). After 1 iteration.
  • A Koch curve extended into three dimensions.
    A Koch curve extended into three dimensions.
  • An animation of a 3D Koch curve.
Źródło: „https://commons.wikimedia.org/w/index.php?title=Koch_curve&oldid=409178352”