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A118102 Triangle read by rows giving successive states of cellular automaton generated by "Rule 94" initiated with a single ON (black) cell.

%I A118102 #29 Feb 16 2025 08:33:00
%S A118102 1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,
%T A118102 1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,
%U A118102 0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0
%N A118102 Triangle read by rows giving successive states of cellular automaton generated by "Rule 94" initiated with a single ON (black) cell.
%C A118102 Totals for row k, starting with k = 0, are {1, 3, 4, 6, 6, 8, 8, 10, 10, 12, 12, ...}, i.e., {1, 3} followed by A052928(k + 3). - _Michael De Vlieger_, Oct 08 2015
%D A118102 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A118102 Robert Price, <a href="/A118102/b118102.txt">Table of n, a(n) for n = 0..9999</a>
%H A118102 Michael De Vlieger, <a href="/A118102/a118102.png">Visualization of rows 0 - 31 of Rule 94</a>
%H A118102 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule94.html">Rule 94</a>
%H A118102 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A118102 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A118102 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A118102 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A118102 From _Michael De Vlieger_, Oct 08 2015: (Start)
%e A118102 First 12 rows, replacing "0" with ".", ignoring "0" outside of range of 1's for better visibility of ON cells:
%e A118102                         1
%e A118102                       1 1 1
%e A118102                     1 1 . 1 1
%e A118102                   1 1 1 . 1 1 1
%e A118102                 1 1 . 1 . 1 . 1 1
%e A118102               1 1 1 . 1 . 1 . 1 1 1
%e A118102             1 1 . 1 . 1 . 1 . 1 . 1 1
%e A118102           1 1 1 . 1 . 1 . 1 . 1 . 1 1 1
%e A118102         1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1
%e A118102       1 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 1
%e A118102     1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1
%e A118102   1 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1 1
%e A118102 1 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 1
%e A118102 (End)
%t A118102 clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; FromDigits[#, 2] & /@ Map[clip, CellularAutomaton[94, {{1}, 0}, 24]] ; clip /@ CellularAutomaton[94, {{1}, 0}, 9] // Flatten (* _Michael De Vlieger_, Oct 08 2015 *)
%Y A118102 Cf. A052928.
%Y A118102 This sequence, A118101 and A071033 are equivalent descriptions of the Rule 94 automaton.
%K A118102 nonn,tabf
%O A118102 0,1
%A A118102 _Eric W. Weisstein_, Apr 12 2006