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A071030
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Triangle read by rows giving successive states of cellular automaton generated by "Rule 54".
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8
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1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1
(list;
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listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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Row n has length 2n+1.
Even rows r sum to r/2 + 1, odd rows r sum to 3r to produce the sequence {1, 3, 2, 6, 3, 9, 4, 12, ...} = A064455(n + 1). - Michael De Vlieger, Oct 07 2015
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 0..10000
Michael De Vlieger, Visualization of rows 0 - 31 of Rule 54
S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601--644.
S. Wolfram, A New Kind of Science
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata
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EXAMPLE
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From Michael De Vlieger, Oct 07 2015: (Start)
First 12 rows, replacing "0" with "." for better visibility of ON cells:
1
1 1 1
1 . . . 1
1 1 1 . 1 1 1
1 . . . 1 . . . 1
1 1 1 . 1 1 1 . 1 1 1
1 . . . 1 . . . 1 . . . 1
1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
1 . . . 1 . . . 1 . . . 1 . . . 1
1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1
1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1
1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1
(End)
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MATHEMATICA
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clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; clip /@ CellularAutomaton[54, {{1}, 0}, 8] // Flatten (* Michael De Vlieger, Oct 07 2015 *)
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CROSSREFS
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Cf. A064455. See A118108 and A118109 for two other versions of this sequence.
Sequence in context: A130630 A059318 A071029 * A355938 A268240 A104037
Adjacent sequences: A071027 A071028 A071029 * A071031 A071032 A071033
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KEYWORD
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nonn,tabf
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AUTHOR
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Hans Havermann, May 26 2002
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EXTENSIONS
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Corrected by Hans Havermann, Jan 07 2012
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STATUS
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approved
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