Koch curve is one of the earliest fractal curves of which you are familiar with a description. It appeared for the first time in a document of 1904 entitled Sur une sans courbe continuous tangent, obtenue par une construction géométrique élémentaire from the Swedish mathematician Helge von Koch.
The construction of Koch curve is done by repeating execution of a instruction program or recursive procedure.The algorithm of the curve is the repetition of the cycle below:
1.starting from a segment of given length, divide the segment into three equal segments;
2. clear the central segment, replacing it with two identical segments which are the two sides of an equilateral triangle;
-3. return to step 1 for each of the current segments.
Starting from a segment, you get then four (constituting a broken line) in the first cycle, 4x4 = 16 in the second cycle and so on, generating an elegant fractal. Zooming in any detail the fractal, you still get the same fractal: this is the self similarity of fractals at any level of scale.
Related links:
http://en.wikipedia.org/wiki/Koch_snowflake
http://www.efg2.com/Lab/FractalsAndChaos/vonKochCurve.htm
http://mathworld.wolfram.com/KochSnowflake.html
Gif source:
http://www.functor.co/post/68301590848/line-inside-a-fractal-inside-a-fractal-inside-a
Into the gif: line inside a fractal inside a fractal inside a fractal inside a draw() loop
Žádné komentáře:
Okomentovat