# Sierpinski 3D Arrowhead Curve

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The Sierpinski arrowhead curve is a classic fractal that approximates the Sierpinski triangle. Like many two-dimensional fractal curves, it can be extended to three dimensions; this extension approximates the tetrix (or Sierpinski tetrahedron).

Contributed by: Robert Dickau (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: creation of the figure begins with a simple seed

Snapshot 2: each iteration is created by rotating and translating the previous image in such a way that the endpoints match up, making an unbroken curve; increasing the "stretch" factor between iterations emphasizes how the figure is connected

Snapshot 3: higher iterations approximate the tetrix

## Permanent Citation

"Sierpinski 3D Arrowhead Curve"

http://demonstrations.wolfram.com/Sierpinski3DArrowheadCurve/

Wolfram Demonstrations Project

Published: March 7 2011