Artificial Life - Term Project   ·   L-Systems   ·   marc mathis & ivo schindler

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Koch Curves

1. Simple Koch Curve:

The Koch Curves are very good samples of exact self-similarity at all scales after an "infinite" number of scales. After many iterations they already look like a final fractal, because of the finite resolution of your screen.
The Koch Curve is of infinite length. With each further step it increases its length by about 4/3.
It first appeared in a paper from Niels Fabian Helge von Koch in 1906.
Recursions: ∞
Angle     : 60
Axiom     : F
Rule      : F=F+F--F+F

  1. We start with a single straight line. By deviding the line into three equal parts and replacing the center part with two line segments each one-third in length we get...(click on the image below). The figure now contains four equal linesegments. In the next step each of the four segments is replaced again in the same way. This is to be repeated endlessly, so to generate the Koch Curve.
    F
  2. F+F--F+F
  3. F+F--F+F+F+F--F+F--F+F--F+F+F+F--F+F
  4. ...





2. Koch Snowflake:

If we fit three Koch Curves together we get the Koch-Snowflake
Recursions: 1-6
Angle     : 60
Axiom     : +F--F--F
Rule      : F=F+F--F+F


  1. We start with a samesided triangle. Each side is a straight line.
    +F--F--F

  2. We then divide the straight lines into three equal parts and replace the center part with the top of another triangle.

    +F+F--F+F--F+F--F+F--F+F--F+F

    We get a star. Repeating this process on and on,...



  3. ... we get some nice snowflake like figure.






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