A163334 Peano curve in an n X n grid, starting rightwards 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), ... .
0, 1, 5, 2, 4, 6, 15, 3, 7, 47, 16, 14, 8, 46, 48, 17, 13, 9, 45, 49, 53, 18, 12, 10, 44, 50, 52, 54, 19, 23, 11, 43, 39, 51, 55, 59, 20, 22, 24, 42, 40, 38, 56, 58, 60, 141, 21, 25, 29, 41, 37, 69, 57, 61, 425, 142, 140, 26, 28, 30, 36, 70, 68, 62, 424, 426, 143, 139
Offset: 0
Examples
The top left 9 X 9 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...): 0 1 2 15 16 17 18 19 20 5 4 3 14 13 12 23 22 21 6 7 8 9 10 11 24 25 26 47 46 45 44 43 42 29 28 27 48 49 50 39 40 41 30 31 32 53 52 51 38 37 36 35 34 33 54 55 56 69 70 71 72 73 74 59 58 57 68 67 66 77 76 75 60 61 62 63 64 65 78 79 80
Links
- Antti Karttunen, Table of n, a(n) for n = 0..13202
- E. H. Moore, On Certain Crinkly Curves, Transactions of the American Mathematical Society, volume 1, number 1, 1900, pages 72-90. (And errata.) See section 7 (and in figure 3 rotate -90 degrees for the table here).
- Giuseppe Peano, Sur une courbe, qui remplit toute une aire plane, Mathematische Annalen, volume 36, number 1, 1890, pages 157-160. Also EUDML (link to GDZ).
- Eric Weisstein's World of Mathematics, Hilbert curve (this curve called "Hilbert II").
- Wikipedia, Self-avoiding walk
- Wikipedia, Space-filling curve
- Index entries for sequences that are permutations of the natural numbers
Crossrefs
Programs
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Mathematica
b[{n_, k_}, {m_}] := (A[k, n] = 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 *)
Extensions
Links to further derived sequences added by Antti Karttunen, Sep 21 2009
Name corrected by Kevin Ryde, Aug 22 2020
Comments