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

0,5

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.

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A080846, A265671, A349040.

Sequence in context: A029202 A173894 A353533 * A285870 A224931 A029195

Adjacent sequences: A349038 A349039 A349040 * A349042 A349043 A349044

Keyword

sign

Author

Rémy Sigrist, Nov 06 2021

Status

approved