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A070950 Triangle read by rows giving successive states of cellular automaton generated by "Rule 30". 19
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; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 27.

LINKS

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

EXAMPLE

1; 1,1,1; 1,1,0,0,1; 1,1,0,1,1,1,1; ...

MATHEMATICA

ArrayPlot[CellularAutomaton[30, {{1}, 0}, 50]] (N. J. A. Sloane, Aug 11 2009)

PROG

(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

CROSSREFS

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: A175608 A111940 A129572 * A071031 A141679 A152904

Adjacent sequences:  A070947 A070948 A070949 * A070951 A070952 A070953

KEYWORD

nonn,tabf,nice,easy

AUTHOR

N. J. A. Sloane, May 19 2002

EXTENSIONS

More terms from Hans Havermann, May 24 2002

STATUS

approved

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Last modified May 25 16:08 EDT 2017. Contains 287039 sequences.