Koch Snowflake Curve
Calculator and formulas for calculating a Koch curve
This function calculates the height and length of the Koch curve. For the calculation enter the number of iterations and a length or height of the curve.
The Koch curve is an example of a curve that is constant everywhere, but nowhere differentiable. It is one of the first formally described fractal objects. The Koch curve is also known as Koch's snowflake, which is created by combining three Koch curves.
Construction
At the beginning the curve consists of a single line. The iteration now consists in dividing this section of the route into thirds. The middle third is removed and instead an equilateral triangle is erected with its side lengths \(\frac {1} {3} \) corresponds to the length of the original line. The angles between these lines are 240 °, 60 ° and 240 °. In the next step, each of the 4 route sections is replaced by a curve as above.
You can find detailed information about this at Wikipedia
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Formulas for the Koch curve (Koch snowflake)
Height
Length after iterations
Original line length
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