A172304 L-toothpick sequence starting with two opposite L-toothpicks.

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

Offset

0,2

Comments

The same as A172310 but starting with two L-toothpicks.

We start at stage 0 with no L-toothpicks.

At stage 1 we place two large L-toothpicks in the horizontal direction, as a "X", anywhere in the plane.

At stage 2 we place four small L-toothpicks.

At stage 3 we add eight more large L-toothpicks.

At stage 4 we add eight more small L-toothpicks.

And so on ...

The L-toothpick 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), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-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