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I understand the concept of a Moore curve in 2D:

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However I find it a bit tough to conceptualize and generalize it to 3D or higher dimensions. Can someone kindly help me out by providing some resources and maybe a computer code to do so ?

Regards

Ujjwal

Zev Chonoles
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Ujjwal Aryan
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    http://demonstrations.wolfram.com/HilbertAndMoore3DFractalCurves/

    You can see some iterations here. I think that gives a general idea for conceptualization.

     – grantfgates Jul 09 '13 at 06:59
  • What is the mathematical form of Moore curve and its generation principle in an arbitrary dimension ? – Ujjwal Aryan Jul 09 '13 at 07:17

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You can use a L-System but it's not trivial at all. It's also possible to use the gray-code. The trick is in 2d you have only 1 possible gray code:http://www.tiac.net/~sw/2008/10/Hilbert/ and look this answer:https://stackoverflow.com/questions/14519267/algorithm-for-generating-a-3d-hilbert-space-filling-curve-in-python

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Micromega
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