Hilbert Curve

Author

Eric W. Weisstein
January 20, 2017

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Fractals/HilbertCurve.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HilbertCurve.html.

©2017 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

3-D Hilbert curve by
Michael Trott
The Mathematica GuideBook for Programming.
New York: Springer-Verlag, p. 97, 2004

Plots

Hilbert I

CurveArray[Hilbert,{1,5},2000,ImageSize->500]

V11.1

GraphicsRow[Table[Graphics[HilbertCurve[n]],{n,4}]]

Hilbert II

CurveArray[HilbertII,{1,3},10^4,ImageSize->500]

V11.1

GraphicsRow[Table[Graphics[PeanoCurve[n]],{n,4}]]

Both

V6

GraphicsGrid[{Hilbert[#,2000]&/@Range[5],HilbertII[#,10^4]&/@Range[3]}]

3-D

Graphics3D[HilbertCurve[3,3]/.Line[x_]:>Tube[x,.2],Boxed->False]

Graphics3D[HilbertCurve[4,3]/.Line[x_]:>Tube[x,.2],Boxed->False]