Peano Curve in 3D

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Can a simple curve completely fill space? Giuseppe Peano first solved this question, and now space-filling curves are called Peano curves in his honor. The Hilbert curve, shown in this Demonstration, is the best-known Peano curve.
Contributed by: Ed Pegg Jr. (March 2011)
Based on code by: Gabriel Chenevert
Open content licensed under CC BY-NC-SA
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"Peano Curve in 3D"
http://demonstrations.wolfram.com/PeanoCurveIn3D/
Wolfram Demonstrations Project
Published: March 7 2011