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A269702 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 243", based on the 5-celled von Neumann neighborhood. 4
1, 5, 9, 41, 21, 101, 49, 185, 61, 309, 97, 449, 125, 633, 201, 829, 177, 1117, 205, 1445, 181, 1681, 385, 1925, 437, 2337, 465, 2717, 521, 3141, 765, 3465, 729, 4117, 673, 4697, 761, 5117, 1013, 5613, 933, 6337, 1133, 6797, 1345, 7437, 1549, 8189, 1293 (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=243; 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: A304849 A270622 A270673 * A271016 A176967 A110421

Adjacent sequences:  A269699 A269700 A269701 * A269703 A269704 A269705

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 28 2016

STATUS

approved

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Last modified January 22 07:09 EST 2021. Contains 340360 sequences. (Running on oeis4.)