A349198 -id:A349198 - cp's OEIS frontend

A349197 a(n) is the X-coordinate of the n-th point of the alternate terdragon curve; sequence A349198 gives Y-coordinates.

0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 5, 6, 6, 7, 7, 6, 6, 5, 5, 6, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 8, 8, 7, 8, 7, 8, 7, 7, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 8, 8, 7, 8, 7

Offset: 0

Rémy Sigrist, Nov 10 2021

nonn

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows (the Y-axis corresponds to the sixth primitive root of unity):
           Y
          /
         /
        0 ---- X
The alternate terdragon curve can be represented using an L-system.

			The alternate terdragon curve starts as follows:
                  14
                   \
                    \
         2----3,12--10,13
          \   / \   / \
           \ /   \ /   \
      0----1,4--5,8,11--9
                 / \
                /   \
               6-----7
- so a(0) = a(2) = 0,
     a(1) = a(3) = a(4) = a(12) = a(14) = 1.

Rémy Sigrist, Table of n, a(n) for n = 0..6561
Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves -- I and II, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. Reprinted in Donald E. Knuth, Selected Papers on Fun and Games, 2011, pages 571-614. See end of section 5.
Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. [Cached copy, with permission]
Kevin Ryde, Iterations of the Terdragon Curve, see index "AltPoint".
Rémy Sigrist, Colored representation of the first 1 + 9^6 points of the alternate terdragon curve (where the hue is function of the number of steps from the origin)
Rémy Sigrist, PARI program for A349197
Index entries for sequences related to coordinates of 2D curves

See A349040 for a similar sequence.

Cf. A349198.

PARI
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See Links section.
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a(9^k) = 3^k for any k >= 0.

a(9*n) = 3*a(n).

A349219 a(n) is the Y-coordinate of the n-th point of the 7-dragon curve; sequence A349218 gives X-coordinates.

Original entry on oeis.org

0, 0, 1, 1, 0, 0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 2, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 4, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 6, 6, 5, 6, 5, 5, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 7, 6, 6, 7, 7, 8, 7, 8, 8, 9, 8, 9, 8, 8

Offset: 0

Rémy Sigrist, Nov 11 2021

sign

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows (the Y-axis corresponds to the sixth primitive root of unity):
           Y
          /
         /
        0 ---- X
The 7-dragon curve can be represented using an L-system.

			The 7-dragon curve starts as follows:
         14    12
          \   / \
           \ /   \
          10,13--8,11
             \   / \
              \ /   \
         2---3,6,9---7
          \   / \
           \ /   \
      0----1,4----5
- so a(0) = a(1) = a(4) = a(5) = 0,
     a(2) = a(3) = a(6) = a(7) = a(9) = 1,
     a(8) = a(10) = a(11) = a(13) = 2,
     a(12) = a(14) = 3.

Rémy Sigrist, Table of n, a(n) for n = 0..16807
Rémy Sigrist, Colored representation of the first 1 + 7^7 points of the 7-dragon curve (where the hue is function of the number of steps from the origin)
Rémy Sigrist, PARI program for A349219
Jeffrey Ventrella, Brainfilling Curves: The Root 7 Family
Index entries for sequences related to coordinates of 2D curves

See A349041 and A349198 for similar sequences.

Cf. A349218.

PARI
```
See Links section.
```

cp's OEIS Frontend

A349197 a(n) is the X-coordinate of the n-th point of the alternate terdragon curve; sequence A349198 gives Y-coordinates.

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