[go: up one dir, main page]

login
A349195
a(n) is the X-coordinate of the n-th point of the R5 dragon curve; A349196 gives Y-coordinates.
3
0, 1, 1, 0, 0, 1, 1, 0, 0, -1, -1, -2, -2, -1, -1, -2, -2, -3, -3, -4, -4, -3, -3, -4, -4, -3, -3, -4, -4, -5, -5, -6, -6, -5, -5, -6, -6, -5, -5, -4, -4, -5, -5, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -7, -7, -8, -8, -7, -7, -6, -6, -5, -5, -6, -6, -5, -5
OFFSET
0,12
COMMENTS
The R5 dragon curve can be represented using an L-system.
LINKS
Joerg Arndt, Matters Computational (The Fxtbook), section 1.31.5 Dragon curves based on radix-R counting.
Kevin Ryde, Iterations of the R5 Dragon Curve, see index "point".
Rémy Sigrist, Colored representation of the first 1 + 5^9 points of the R5 dragon curve (where the hue is function of the number of steps from the origin)
FORMULA
a(5^k) = A006495(k) for any k >= 0.
EXAMPLE
The R5 dragon curve starts as follows:
+-----+
24| 25
|
|
+-----+ +-----+ +-----+
23 22| 11| 10| 7| 6|
| | | | |
21| 12| 9| 8| |
+-----+-----+-----+-----+-----+
20| 17| 16| 13| 4| 5
| | | | |
| | | | |
+-----+ +-----+ +-----+
19 18 15 14 3 2|
|
|
+-----+
0 1
- so a(0) = a(3) = a(4) = a(7) = a(8) = 0,
a(1) = a(2) = a(5) = a(6) = 1,
a(9) = a(10) = a(13) = a(14) = -1.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign
AUTHOR
Rémy Sigrist, Nov 10 2021
STATUS
approved