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A273538 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 779", based on the 5-celled von Neumann neighborhood. 4
1, 5, 17, 37, 61, 97, 125, 197, 237, 305, 337, 473, 521, 617, 629, 901, 973, 1105, 1137, 1401, 1449, 1609, 1561, 2089, 2169, 2361, 2345, 2785, 2785, 3001, 2789, 3845, 3981, 4241, 4273, 4793, 4841, 5129, 4953, 5993, 6073, 6393, 6249, 7073, 6945, 7289, 6697 (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=779; 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: A119456 A264904 A257582 * A273212 A273274 A273250

Adjacent sequences:  A273535 A273536 A273537 * A273539 A273540 A273541

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 24 2016

STATUS

approved

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)