OFFSET
0
COMMENTS
Row n has length 2n+1.
The fact that only n cells to the left and right of the initially active cell are updated at step n is contradictory to the usual treatment of a "Rule m" automaton, where all cells are updated depending on their neighborhood. See also the illustration of "Rule 201" on the MathWorld page. - M. F. Hasler, Jul 28 2018
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
EXAMPLE
The first ten rows:
1
0 0 0
1 0 1 0 1
1 1 0 0 0 1 1
1 1 1 0 1 0 1 1 1
1 1 1 1 0 0 0 1 1 1 1
1 1 1 1 1 0 1 0 1 1 1 1 1
1 1 1 1 1 1 0 0 0 1 1 1 1 1 1
1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1
MATHEMATICA
rule=201; 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 *)
PROG
(PARI) A267679_row(n)=if(n==1, [0, 0, 0], binary(1<<(n*2+1)-(bittest(n, 0)*2+5)<<(n-1)-1)) \\ M. F. Hasler, Jul 28 2018
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Robert Price, Jan 19 2016
STATUS
approved