

A172304


Ltoothpick sequence starting with two opposite Ltoothpicks.


8



0, 2, 6, 14, 22, 30, 46, 62, 70, 86, 110, 134, 166, 190, 238, 278, 302, 318, 342, 382, 430, 470, 526, 582, 646, 710, 782, 838, 902, 950, 1030, 1118, 1150, 1182, 1246, 1318, 1382, 1422, 1486, 1566, 1662, 1766, 1910, 2006, 2134, 2254, 2414, 2526, 2622
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OFFSET

0,2


COMMENTS

The same as A172310 but starting with two Ltoothpicks.
We start at stage 0 with no Ltoothpicks.
At stage 1 we place two large Ltoothpicks in the horizontal direction, as a "X", anywhere in the plane.
At stage 2 we place four small Ltoothpicks.
At stage 3 we add eight more large Ltoothpicks.
At stage 4 we add eight more small Ltoothpicks.
And so on ...
The Ltoothpick cellular automaton has an unusual property: the growths in its four wide wedges [North, East, South and West] have a recurrent behavior related to powers of 2, as we can find in other cellular automata (i.e., A212008). On the other hand, in its four narrow wedges [NE, SE, SW, NW] the behavior seems to be chaotic, without any recurrence, similar to the behavior of the snowflake cellular automaton of A161330. The remarkable fact is that with the same rules, different behaviors are produced. (See Applegate's movie version in the Links section.)  Omar E. Pol, Nov 06 2018


LINKS

Yan Sheng Ang, Table of n, a(n) for n = 0..201
David Applegate, The movie version
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


CROSSREFS

For a similar version see A172310.
Cf. A161330 (snowflake).
Cf. A139250, A160120, A160170, A160172, A161206, A161328, A172305, A172306, A172307, A172308, A172309, A172311, A172312, A172313, A212008, A220500.
Sequence in context: A228649 A268641 A162796 * A160164 A074729 A099901
Adjacent sequences: A172301 A172302 A172303 * A172305 A172306 A172307


KEYWORD

nonn


AUTHOR

Omar E. Pol, Feb 06 2010


EXTENSIONS

Terms beyond a(14) from Yan Sheng Ang, Dec 10 2012


STATUS

approved



