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A273077 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 587", based on the 5-celled von Neumann neighborhood. 4
1, 5, 13, 29, 57, 73, 121, 141, 209, 241, 297, 329, 469, 501, 613, 633, 781, 837, 905, 1029, 1177, 1257, 1485, 1441, 1673, 1825, 1905, 2109, 2293, 2413, 2593, 2769, 3001, 3021, 3377, 3401, 3813, 3729, 4157, 4325, 4561, 4689, 4881, 5229, 5509, 5561, 6021 (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=587; 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: A162329 A299895 A273026 * A160430 A023617 A023619

Adjacent sequences:  A273074 A273075 A273076 * A273078 A273079 A273080

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 14 2016

STATUS

approved

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Last modified November 19 12:38 EST 2018. Contains 317351 sequences. (Running on oeis4.)