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A268195 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 366", based on the 5-celled von Neumann neighborhood. 4
1, 5, 8, 21, 24, 37, 52, 77, 88, 109, 108, 141, 176, 197, 228, 325, 288, 328, 373, 328, 380, 445, 452, 548, 504, 584, 693, 684, 749, 884, 997, 1224, 1197, 1096, 1257, 1128, 1252, 1304, 1257, 1460, 1497, 1416, 1568, 1657, 1644, 1708, 1973, 1848, 2164, 2133 (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=366; 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: A034737 A271156 A272115 * A169705 A138810 A105634

Adjacent sequences:  A268192 A268193 A268194 * A268196 A268197 A268198

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 07 2016

STATUS

approved

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Last modified March 24 06:56 EDT 2019. Contains 321444 sequences. (Running on oeis4.)