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=> Apollonian Gasket
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=> Rep-Tile
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=> San Marco Fractal
=> Sea Horse Valley
=> Siegel Disk Fractal
=> Sierpiński Arrowhead Curve
=> Sierpiński Carpet
=> Sierpiński Curve
=> Sierpiński Sieve
=> Star Fractal
=> Strange Attractor
=> Tetrix
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Ziyaretçi defteri
 

Sierpiński Curve

SierpinskiCurve

There are several fractal curves associated with Sierpiński. The above curve is one example, and the Sierpiński arrowhead curve is another. The limit of the curve illustrated above has area

A=5/(12).
SierpinskiCross

The area for a related curve due to Sierpiński (1912) illustrated above is

A=1/3(7-4sqrt(2)).

(Steinhaus 1999, pp. 102-103; Cundy and Rollett 1989; Wells 1991, p. 229).

 

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