Koch curve source:
Koch curve 1 iteration:
Koch curve 2 iterations:
Koch curve 3 iterations:
Fractal Explorer
The Koch curve
The Koch curve fractal was first introduced in 1904 by Helge von Koch. It was one of the first fractal objects to be described.
To create a Koch curve
- create a line and divide it into three parts
- the second part is now rotated by 60°
- add another part which goes from the end of part 2 to to the beginning of part 3
- repeat with each part
Mathematical aspects:
The perimeter of the Koch curve is increased by 1/4. That implys that the perimeter after an infinite number of iterations is infinite. The formula for the perimeter after k iterations is:
The number of the lines in a Koch curve can be determined with following formula: