The Snowflake Curve

//To draw the Snowflake Curve of order 0 to 5

Right-click here to download this page and the Java Class File.

The Java applet above draws the Snowflake curve of order n = 0 to 5.
orderlength of Snowflake Curve
011
14/31.333
2(4/3)2 = 16/91.778
3(4/3)3 = 64/272.370
4(4/3)4 = 256/813.160
:::
n(4/3)n:

orderarea of Snowflake Curve
011
11 + 3(1/9)1.333
21 + 3(1/9) + 3(4)(1/9)21.481
31 + 3(1/9) + 3(4)(1/9)2 + 3(4)2(1/9)31.547
41 + 3(1/9) + 3(4)(1/9)2 + 3(4)2(1/9)3 + 3(4)3(1/9)41.577
:::
n1 + (1 - (4/9)n)3/5:

The length of the Snowflake curve of order n approaches infinity as n approaches infinity, while the area approaches 8/5 = 1.6 times the area of the original triangle.