OFFSET
0,15
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 alternate terdragon curve can be represented using an L-system.
LINKS
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.
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 A349198
FORMULA
a(9^k) = 0 for any k >= 0.
a(9*n) = 3*a(n).
EXAMPLE
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(1) = a(4) = a(5) = a(8) = a(9) = a(11) = 0,
a(6) = a(7) = -1,
a(2) = a(3) = a(10) = a(12) = a(13) = 1.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign
AUTHOR
Rémy Sigrist, Nov 10 2021
STATUS
approved