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A270685 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 193", based on the 5-celled von Neumann neighborhood. 4
1, 4, 9, 24, 21, 72, 45, 112, 93, 224, 117, 320, 173, 464, 205, 528, 293, 848, 225, 1100, 145, 1488, 361, 1396, 593, 1744, 537, 2036, 681, 2352, 700, 2301, 1072, 2969, 792, 3589, 616, 4093, 1044, 4201, 1260, 4753, 1180, 5205, 1468, 5621, 1608, 5905, 1504 (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=193; 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: A319762 A196034 A196037 * A272252 A067801 A062775

Adjacent sequences:  A270682 A270683 A270684 * A270686 A270687 A270688

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 21 2016

STATUS

approved

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)