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

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

Author

Rémy Sigrist, Nov 11 2021

Keywords

• sign

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.

Examples

			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.
		

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 A349219
• Jeffrey Ventrella, Brainfilling Curves: The Root 7 Family
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

See A349041 and A349198 for similar sequences.

Cf. A349218.

Programs

PARI

See Links section.