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

Author

Omar E. Pol, Feb 06 2010

Keywords

• nonn

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.

Extensions

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