Sierpiński fractal | 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 curve 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 nth 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