Problem 60576. Perimeter of a Koch snowflake
A Koch snowflake is an iteratively generated (fractal) shape built out of successively smaller equilateral triangles by following these steps:
- Draw an equilateral triangle. (n = 0)
- Divide the line segment into three segments of equal length.
- Draw an equilateral triangle that has the middle segment from step 2 as its base and points outward.
- remove the line segment that is the base of the triangle from step 3. (n = 1)
- Repeat steps 2 - 4. (n = 2,3,...)
In the limit of
this shape has an infinite perimeter and a finite area. For
, this perimeter is calculable. Calculate both of these values for any input value of n and any starting triangle edge length, s.
[A1,P1] = KochSnowflake(n,s)
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1 Comment
Christian Schröder
on 12 Jul 2024 at 18:13
Nice problem!
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