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A070950
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Triangle read by rows giving successive states of cellular automaton generated by "Rule 30".
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20
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1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1
(list;
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OFFSET
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0,1
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COMMENTS
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If cell and right-hand neighbor are both 0 then new state of cell = state of left-hand neighbor; otherwise new state is complement of that of left-hand neighbor.
A simple rule which produces apparently random behavior. "... probably the single most surprising discovery I have ever made" - Stephen Wolfram.
Row n has length 2n+1.
A110240(n) = A245549(n) = value of row n, seen as binary number. - Reinhard Zumkeller, Jun 08 2013
A070952 gives number of ON cells. - N. J. A. Sloane, Jul 28 2014
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 27.
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LINKS
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Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
N. J. A. Sloane, Illustration of initial terms
Eric Weisstein's World of Mathematics, Rule 30
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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1; 1,1,1; 1,1,0,0,1; 1,1,0,1,1,1,1; ...
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MATHEMATICA
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ArrayPlot[CellularAutomaton[30, {{1}, 0}, 50]] (N. J. A. Sloane, Aug 11 2009)
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PROG
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(Haskell)
a070950 n k = a070950_tabf !! n !! k
a070950_row n = a070950_tabf !! n
a070950_tabf = iterate rule30 [1] where
rule30 row = f ([0, 0] ++ row ++ [0, 0]) where
f [_, _] = []
f (u:ws@(0:0:_)) = u : f ws
f (u:ws) = (1 - u) : f ws
-- Reinhard Zumkeller, Feb 01 2013
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CROSSREFS
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Cf. A070951, A070952 (row sums), A051023 (central terms).
Cf. A071032 (mirror image, rule 86), A226463 (complemented, rule 135), A226464 (mirrored and complemented, rule 149).
Cf. also A245549, A110240.
Sequence in context: A194679 A111940 A129572 * A071031 A187037 A190230
Adjacent sequences: A070947 A070948 A070949 * A070951 A070952 A070953
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KEYWORD
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nonn,tabf,nice,easy
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AUTHOR
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N. J. A. Sloane, May 19 2002
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EXTENSIONS
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More terms from Hans Havermann, May 24 2002
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STATUS
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approved
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