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A278444 Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 43", based on the 5-celled von Neumann neighborhood. 4
1, 10, 100, 1011, 10100, 101011, 1010000, 10101111, 101010000, 1010101111, 10101000000, 101010111111, 1010101000000, 10101010111111, 101010100000000, 1010101011111111, 10101010100000000, 101010101011111111, 1010101010000000000, 10101010101111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Empirical g.f.: (1 - x^2 + 11*x^3 - 110*x^4) / ((1 - x) * (1 + x) * (1 - 10*x) * (1 - 10*x^2) * (1 + 10*x^2)). - Colin Barker, Nov 23 2016
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=43; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]][[i]], Range[i, 2*i-1]], 10], {i, 1, stages-1}]
CROSSREFS
Sequence in context: A319418 A283171 A283252 * A164832 A144822 A199763
KEYWORD
nonn,easy
AUTHOR
Robert Price, Nov 22 2016
STATUS
approved

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Last modified July 13 18:54 EDT 2024. Contains 374285 sequences. (Running on oeis4.)