This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A172304 #46 Feb 24 2021 02:48:19 %S A172304 0,2,6,14,22,30,46,62,70,86,110,134,166,190,238,278,302,318,342,382, %T A172304 430,470,526,582,646,710,782,838,902,950,1030,1118,1150,1182,1246, %U A172304 1318,1382,1422,1486,1566,1662,1766,1910,2006,2134,2254,2414,2526,2622 %N A172304 L-toothpick sequence starting with two opposite L-toothpicks. %C A172304 The same as A172310 but starting with two L-toothpicks. %C A172304 We start at stage 0 with no L-toothpicks. %C A172304 At stage 1 we place two large L-toothpicks in the horizontal direction, as a "X", anywhere in the plane. %C A172304 At stage 2 we place four small L-toothpicks. %C A172304 At stage 3 we add eight more large L-toothpicks. %C A172304 At stage 4 we add eight more small L-toothpicks. %C A172304 And so on ... %C A172304 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 %H A172304 Yan Sheng Ang, <a href="/A172304/b172304.txt">Table of n, a(n) for n = 0..201</a> %H A172304 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a> %H A172304 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.] %H A172304 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a> %Y A172304 For a similar version see A172310. %Y A172304 Cf. A161330 (snowflake). %Y A172304 Cf. A139250, A160120, A160170, A160172, A161206, A161328, A172305, A172306, A172307, A172308, A172309, A172311, A172312, A172313, A212008, A220500. %K A172304 nonn %O A172304 0,2 %A A172304 _Omar E. Pol_, Feb 06 2010 %E A172304 Terms beyond a(14) from _Yan Sheng Ang_, Dec 10 2012