Revision History for A163336
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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| A163336
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Peano curve in an n X n grid, starting downwards from the top left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
(history;
published version)
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#20 by Alois P. Heinz at Mon Mar 08 06:16:04 EST 2021
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#19 by Jon E. Schoenfield at Mon Mar 08 05:38:40 EST 2021
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#18 by Jon E. Schoenfield at Mon Mar 08 05:38:38 EST 2021
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| NAME
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Peano curve in an Nn xX Nn grid, starting downwards from the top left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
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proposed
editing
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#17 by Jean-François Alcover at Sun Mar 07 23:53:50 EST 2021
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#16 by Jean-François Alcover at Sun Mar 07 23:53:38 EST 2021
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| MATHEMATICA
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b[{n_, k_}, {m_}] := (A[n, k] = m - 1);
MapIndexed[b, List @@ PeanoCurve[4][[1]]];
Table[A[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)
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approved
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#15 by Joerg Arndt at Fri Aug 28 02:05:56 EDT 2020
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#14 by Michel Marcus at Fri Aug 28 02:00:51 EDT 2020
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#13 by Kevin Ryde at Fri Aug 28 01:52:31 EDT 2020
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#12 by Kevin Ryde at Fri Aug 28 01:50:08 EDT 2020
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| NAME
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Hilbert IIPeano curve in an N x N grid, starting downwards from the top left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
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| LINKS
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E. H. Moore, <a href="https://doi.org/10.1090/S0002-9947-1900-1500526-4">On Certain Crinkly Curves</a>, Transactions of the American Mathematical Society, volume 1, number 1, 1900, pages 72-90. (And <a href="https://doi.org/10.1090/S0002-9947-1900-1500428-3/">errata</a>.) See section 7 (figure 3 with Y downwards is the table here).
Giuseppe Peano, <a href="https://doi.org/10.1007/BF01199438">Sur une courbe, qui remplit toute une aire plane</a>, Mathematische Annalen, volume 36, number 1, 1890, pages 157-160. Also <a href="https://eudml.org/doc/157489">EUDML</a> (link to GDZ).
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HilbertCurve.html">Hilbert curve</a>> (this curve called "Hilbert II").
Wikipedia, <a href="http://en.wikipedia.org/wiki/Space-filling_curve">Space-filling curve</a> (Wikipedia gives this curve as an example of a Peano curve, although this is not the one Peano himself gave).>
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| CROSSREFS
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Transpose: A163334. Inverse: A163337. a(n) = A163332(A163330(n)) = A163327(A163333(A163328(n))) = A163334(A061579(n)). One-based version: A163340. Row sums: A163342. Row 0: A163481. Column 0: A163480. Central diagonal: A163343. See A163357 and A163359 for other Hilbert curves.
See A163357 and A163359 for the Hilbert curve.
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| EXTENSIONS
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Name corrected by Kevin Ryde, Aug 28 2020
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approved
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Discussion
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| Fri Aug 28
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| Kevin Ryde: Peano and references as per my last in A163334.
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#11 by Susanna Cuyler at Sat Apr 25 14:48:47 EDT 2020
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