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Hilbert and Moore 3D Fractal Curves

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iterations
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Hilbert curve 3D
Moore curve 3D
tube end shape
truncated ends
round
square
none
tube join shape
beveled ends
round
miter
none
show multiple iterations
The Hilbert curve and the Moore curve are two famous plane-filling curves that can be extended to 3D space-filling curves. They have similar recursive constructions, here using L-systems. The curves shown in this Demonstration map points in three-dimensional space to points on a one-dimensional line, and thus have properties that make them useful for certain types of data manipulation, such as image processing.
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