SierpinskiCurve

SierpinskiCurve[n] gives the line segments representing the nth-step Sierpiński curve.

Examples

First few iterations:

Graphics[SierpinskiCurve[3]]

Higher resolution:

Graphics[SierpinskiCurve[5], AspectRatio -> Automatic]

Animate the curve development:

Table[Graphics[SierpinskiCurve[n]], {n, 1, 6}]

Please visit the official Wolfram Language Reference for more details.