OFFSET
0,2
COMMENTS
On the infinite square grid we start with no toothpicks.
At stage 1, we place a cross as a "X", formed by 4 D-toothpicks of length sqrt(2) and centered at the origin. At stage 2, we place 8 toothpicks of length 1. At stage 3, we place 16 D-toothpicks of length sqrt(2). And so on.
The sequence gives the number of toothpicks and D-toothpicks in the structure after n-th stage. The first differences (A194435) give the number of toothpicks or D-toothpicks added at n-th stage.
Apparently this cellular automaton has a fractal behavior (or fractal-like behavior) related to power of 2, similar to A194270 and very similar to A194432. The octagonal structure contains a large number of distinct closed polygonal regions. For more information see A194270, A194440 and A194442.
First differs from A220514 at a(13). - Omar E. Pol, Mar 23 2013
Observation: at least for the terms in the Data section the graph also appears to be a companion of the graph of A187210 but that could be different comparing more terms. - Omar E. Pol, Jun 24 2022
LINKS
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Paolo Xausa, Animated version for n = 0..31
Paolo Xausa, Animated version for n = 0..63
Paolo Xausa, Illustration of initial terms for n = 0..63 (multipage PDF)
FORMULA
a(n) = 4*A194444(n).
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Sep 03 2011
EXTENSIONS
More terms from Omar E. Pol, Mar 23 2013
STATUS
approved