OFFSET
0,8
COMMENTS
We define the family {C_n, n >= 0}, as follows:
- C_0 corresponds to the points (0, 0), (0, 1), (1, 1), (2, 1) and (2, 0), in that order:
+---+---+
| |
+ +
O
- for any n >= 0, C_{n+1} is obtained by arranging 4 copies of C_n as follows:
+ . . . + . . . +
. B . B .
+ . . . + . . .
. B . .A C.A C.
. . --> + . . . + . . . +
.A C. .C . A.
+ . . . + . B.B .
O .A . C.
+ . . . + . . . +
O
- the space filling curve C is the limit of C_{2*n} as n tends to infinity.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..16384
F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no. 1, 1982.
Rémy Sigrist, PARI program for A341121
FORMULA
EXAMPLE
Points n and their locations X=A341120(n), Y=a(n) begin as follows. n=7 and n=9 are both at X=3,Y=2, and n=11,n=31 both at X=3,Y=4.
| |
4 | 16---17 12--11,31
| | | |
3 | 15---14---13 10
| |
2 | 8---7,9
| |
1 | 1----2----3 6
| | | |
Y=0 | 0 4----5
+--------------------
X=0 1 2 3
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin Ryde and Rémy Sigrist, Feb 05 2021
STATUS
approved