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Article #375

space filling curves (e.g. Hilbert)

#375
From: Wolfgang Burke
Date: Wed, 21 Feb 1996 00:00
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I'm not sure if this is the correct group, but I don't know a better group to
place this request. (If you know one, please tell me.)

I am looking for enumeration schemes of points in a n-dimensional space such 
that proximate points get adjacent numbers. I was looking at space filling
curves and pictures of the Hilbert curve in the plane seemed very promising
so now I am searching for generalized Hilbert curves in n-dimensional spaces.
Is there a generalization of Hilbert curves for an arbitrary n (or other
space filling curves with similar properties)? 

The curve transforms every coordinate of a point in the n-dimensional space to
a point (number) in one-dimensional space (according to its position on the
Hilbert curve). Do you know of any algorithm that given the space coordinates
computes the number of the point on the Hilbert curve?

Please reply by e-mail since I usually don't read this newsgroup.

Excuse me if this is a FAQ, but I don't know much about fractals.

Thanks,
   Wolfgang

-- 
Wolfgang Burke					burke@ira.uka.de
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From: burke@ira.uka.de (Wolfgang Burke)
Subject: space filling curves (e.g. Hilbert)
Date: 1996/02/21
Message-ID: <4gerlk$95e@nz12.rz.uni-karlsruhe.de>
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