A349197 a(n) is the X-coordinate of the n-th point of the alternate terdragon curve; sequence A349198 gives Y-coordinates.
0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 3, 3, 2, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 5, 6, 6, 7, 7, 6, 6, 5, 5, 6, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 8, 8, 7, 8, 7, 8, 7, 7, 6, 7, 6, 7, 7, 8, 8, 9, 8, 9, 8, 8, 7, 8, 7
Offset: 0
Keywords
Examples
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(2) = 0,
a(1) = a(3) = a(4) = a(12) = a(14) = 1.
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. See end of section 5.
- Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. [Cached copy, with permission]
- Kevin Ryde, Iterations of the Terdragon Curve, see index "AltPoint".
- 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 A349197
- Index entries for sequences related to coordinates of 2D curves
Programs
-
PARI
See Links section.
Formula
a(9^k) = 3^k for any k >= 0.
a(9*n) = 3*a(n).
Comments