'The Koch snowflake is an example of a fractal. It is constructed in the following way: You start with an equilateral triangle. You then remove the inner third of each side, and build another equilateral triangle at the location where the side was removed. You then repeat the process indefinitely."

The question is;

- What is the perimeter of the nth stage of a Koch Snowflake fractal?

A good website for a diagram is

and any help I could get would be deeply appreciated. Thank you.

## Answers (1)

Let the original snow-flake have side lengths s. At each stage the number of sides is multiplied by 4 but the length of each side is 1/3 of the previous stage. Therefore the perimeter P(n) at stage n is given by the formula

P(n) = 3s*[4^(n - 1)]

[(1/3)^(n - 1)] = 3s[(4/3)^(n - 1)]P(1) = 3s*(4/3)^0 = 3s

P(2) = 3s*(4/3)^1 = 4s

P(3) = 3s*(4/3)^2 = 16s/3