A349041 a(n) is the Y-coordinate of the n-th point of the terdragon curve; sequence A349040 gives X-coordinates.

0, 0, 1, 1, 2, 1, 2, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 6, 7, 6, 6, 5, 6, 5, 6, 5, 5, 4, 4, 5, 5, 4, 4, 3, 4, 3, 4, 3, 3, 2, 3, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 6, 7, 6, 6, 5, 6, 5, 6, 6, 7, 7, 8, 7, 8, 8, 9, 9, 10, 9, 10, 9

Offset: 0

Author

Rémy Sigrist, Nov 06 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 terdragon curve can be represented using an L-system.

A265671, when interpreted as a sequence of directions, yields the same curve.

Examples

			The terdragon curve starts (on a hexagonal lattice) as follows:
              +-----+
              8\    9
                \
           +-----+7
           6\   /4\
             \5/   \
              +-----+
              2\   3
                \
           +-----+
           0     1
- so a(0) = a(1) = 0,
     a(2) = a(3) = a(5) = 1,
     a(4) = a(6) = a(7) = 2,
     a(8) = a(9) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6561
• Rémy Sigrist, Colored representation of the first 1 + 3^11 points of the terdragon curve (where the hue is function of the number of steps from the origin)
• Rémy Sigrist, PARI program for A349041
• Wikipedia, Terdragon
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A080846, A265671, A349040.

Programs

PARI

See Links section.