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A271277 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 331", based on the 5-celled von Neumann neighborhood. 4
1, 5, 5, 40, 13, 100, 21, 193, 28, 325, 16, 493, 44, 661, 80, 841, 80, 1157, 44, 1421, 92, 1673, 120, 2021, 148, 2397, 88, 2833, 224, 3177, 232, 3681, 152, 4173, 380, 4521, 448, 5109, 292, 5905, 236, 6425, 480, 6877, 540, 7737, 304, 8473, 316, 9193, 521 (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

Robert Price, Table of n, a(n) for n = 0..128

Robert Price, Diagrams of the first 20 stages.

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

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=331; 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}];

Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

CROSSREFS

Sequence in context: A271091 A271289 A271083 * A269829 A270058 A270156

Adjacent sequences:  A271274 A271275 A271276 * A271278 A271279 A271280

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 03 2016

STATUS

approved

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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)