The On-Line Encyclopedia of Integer Sequences (OEIS)

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A267423

Triangle read by rows giving successive states of cellular automaton generated by "Rule 133" initiated with a single ON (black) cell.
(history; published version)

#8 by Bruno Berselli at Fri Jan 15 10:27:16 EST 2016

STATUS

proposed

approved

#7 by Robert Price at Fri Jan 15 09:53:55 EST 2016

STATUS

editing

proposed

#6 by Robert Price at Fri Jan 15 09:53:51 EST 2016

LINKS

Robert Price, <a href="/A267423/b267423.txt">Table of n, a(n) for n = 0..10000</a>

STATUS

approved

editing

#5 by N. J. A. Sloane at Thu Jan 14 22:44:11 EST 2016

STATUS

proposed

approved

#4 by Robert Price at Thu Jan 14 14:54:02 EST 2016

STATUS

editing

proposed

#3 by Robert Price at Thu Jan 14 14:53:57 EST 2016

EXAMPLE

The first ten rows: 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0

The first ten rows:

1

0 1 0

0 0 1 0 0

0 0 0 1 0 0 0

0 0 1 0 1 0 1 0 0

0 0 0 1 0 1 0 1 0 0 0

0 0 1 0 1 0 1 0 1 0 1 0 0

0 0 0 1 0 1 0 1 0 1 0 1 0 0 0

0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0

0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0

#2 by Robert Price at Thu Jan 14 14:52:59 EST 2016

NAME

allocated for Robert PriceTriangle read by rows giving successive states of cellular automaton generated by "Rule 133" initiated with a single ON (black) cell.

DATA

1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0

OFFSET

0

COMMENTS

Row n has length 2n+1.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

<a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

<a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

EXAMPLE

MATHEMATICA

rule=133; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

KEYWORD

allocated

nonn,tabf,easy

AUTHOR

Robert Price, Jan 14 2016

STATUS

approved

editing

#1 by Robert Price at Thu Jan 14 14:52:59 EST 2016

NAME

allocated for Robert Price

KEYWORD

allocated

STATUS

approved