Koch's+Snowflake

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Koch's Snowflake Level 0: pen up gotoxy -121 -80 pen on loop 3 forward 243 left 120 loopend

Level 1: pen up gotoxy -121 -71 pen on loop 3 forward 81 right 60 forward 81 left 120 forward 81 right 60 forward 81 left 120 loopend

Level 2: pen up gotoxy -121 22 pen on loop 6 loop 2 forward 27 right 60 loopend loop 3 forward 27 right 60 forward 27 left 120 loopend loopend

math \\ Level 0 \to P=3\cdot 243\\ Level 1 \to P=(\frac{4}{3})\cdot 243\cdot 3\\ Level 2 \to P=(\frac{4}{3})^2\cdot 243\cdot 3\\ ...\\ Level n \to P=(\frac{4}{3})^n\cdot 243\cdot 3\\ math

Thus the perimeter of the "last" level of Koch's snowflake is math \\ P=(\frac{4}{3})^\infty \cdot 243\cdot 3\\ \text{Since} \frac{4}{3} > 1, \text{the limit goes to} \infty\\ \therefore P=\infty math Therefore, the perimeter of Koch's Snowflake is infinite.