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A070887 Triangle read by rows giving successive states of cellular automaton generated by "Rule 110". 7
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

New state of cell is 1 in every case except when the previous states of the cell and its two neighbors were all the same, or when the left neighbor was 1 and the cell and its right neighbor were both 0.

A cellular automaton using Rule 110 with arbitrary inputs is a universal Turing machine.

Row n has length n.

T(n,k) = A075437(n-1,k-1), k=1..n. - Reinhard Zumkeller, Jun 26 2013

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 31ff..

LINKS

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Eric Weisstein's World of Mathematics, Rule 110

Wikipedia, Rule 110

Index entries for sequences related to cellular automata

EXAMPLE

1;

1,1;

1,1,1;

1,1,0,1;

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

MAPLE

A070887 := proc(n, k)

    option remember;

    local lef, mid, rig ;

    if k < 1 or k > n then

        0;

    elif n = 1 then

        1;

    else

        lef := procname(n-1, k-2) ;

        mid := procname(n-1, k-1) ;

        rig := procname(n-1, k) ;

        if lef = mid and mid = rig then

            0 ;

        elif lef = 1 and mid =0 and rig =0 then

            0;

        else

            1 ;

        end if;

    end if;

end proc:

for n from 1 to 12 do

    for k from 1 to n do

        printf("%d ", A070887(n, k)) ;

    end do:

    printf("\n")

end do: # R. J. Mathar, Feb 18 2015

MATHEMATICA

rows = 14; ca = CellularAutomaton[110, {{1}, 0}, rows-1]; Flatten[ Table[ca[[k, rows-k+1 ;; -1]], {k, 1, rows}]] (* Jean-François Alcover, May 24 2012 *)

PROG

(Haskell)

a070887 n k = a070887_tabl !! (n-1) !! (k-1)

a070887_row n = a070887_tabl !! (n-1)

a070887_tabl = zipWith take [1..] a075437_tabf

-- Reinhard Zumkeller, Jun 26 2013

CROSSREFS

Cf. A070950, A070886.

Cf. A047999.

Sequence in context: A077010 A071023 A166280 * A110242 A273592 A054527

Adjacent sequences:  A070884 A070885 A070886 * A070888 A070889 A070890

KEYWORD

nonn,tabl,nice,easy

AUTHOR

N. J. A. Sloane, May 19 2002

EXTENSIONS

More terms from Hans Havermann, May 26 2002

STATUS

approved

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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.