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

0, 1, 0, 1, 1, 2, 1, 2, 1, 1, 0, 1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 2, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, -1, 0, -1, -1, -2, -1, -2, -1, -1, 0, -1, 0, -1, -1, -2, -1

Offset

0,6

Comments

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.

Links

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 A349218

Jeffrey Ventrella, Brainfilling Curves: The Root 7 Family

Index entries for sequences related to coordinates of 2D curves

Example

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(2) = a(10) = a(12) = a(13) = 0,
     a(1) = a(3) = a(4) = a(6) = a(8) = a(9) = a(11) = 1,
     a(5) = a(7) = 2,
     a(14) = -1.

Prog

(PARI) See Links section.

Crossrefs

See A349040 and A349197 for similar sequences.

Cf. A349219.

Sequence in context: A342627 A220115 A039924 * A364205 A275346 A037888

Adjacent sequences: A349215 A349216 A349217 * A349219 A349220 A349221

Keyword

sign

Author

Rémy Sigrist, Nov 11 2021

Status

approved