Sierpiński square snowflake | Sierpiński square snowflake curve | square curve

There are several fractal curves associated with Sierpiński. The area for the first Sierpiński curve illustrated above (Sierpiński 1912) is A = 1/3(7 - 4sqrt(2)). The curve is called the Sierpiński curve by Cundy and Rollett, the Sierpiński's square snowflake by Wells, and is pictured but not named by Steinhaus. The n th iteration of the first Sierpiński curve is implemented in the Wolfram Language as SierpinskiCurve[n]. The limit of the second Sierpiński's curve illustrated above has area A = 5/12.

exterior snowflake | Gosper island | Hilbert curve | Koch antisnowflake | Koch snowflake | Peano curve | Peano-Gosper curve | Sierpiński arrowhead curve