OFFSET
0,4
COMMENTS
Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
Y
/
/
0 ---- X
We define the family {A_n, n >= 0} as follows:
- A_0 corresponds to the points (0, 0), (1, 1) and (3, 0), in that order:
. __+__ .
__---- ----__
+ . . +
0
- for any n >= 0, A_{n+1} is obtained by arranging 4 copies of A_n as follows:
+
/B\
+ / \
/B\ /A C\
/ \ --> +-------+
/A C\ /B\C B/A\
+-------+ / \ / \
O /A C\A/B C\
+-------+-------+
O
- the space filling curve A is the limit of A_n as n tends to infinity.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..8192
Zbigniew Fiedorowicz, The Peano Curve Theorem
Rémy Sigrist, PARI program for A341164
EXAMPLE
The curve A starts as follows:
.
. .
. 5 .
4 . . 6
. . 3 . .
. 1 . . 7 .
0 . . 2 . . 8
- so a(0) = a(2) = a(8) = 0,
a(1) = a(7) = 1,
a(3) = 2,
a(4) = a(6) = 3,
a(5) = 4.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Feb 06 2021
STATUS
approved