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A273702 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 865", based on the 5-celled von Neumann neighborhood. 1
3, 17, 12, 35, 37, 35, 45, 72, 52, 59, 65, 87, 101, 83, 101, 147, 89, 131, 125, 135, 177, 136, 132, 195, 133, 127, 105, 207, 185, 175, 161, 307, 233, 207, 253, 215, 217, 255, 177, 335, 245, 239, 205, 323, 341, 267, 277, 399, 333, 255, 301, 331, 365, 323, 269 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..127

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=865; 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}];

on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)

CROSSREFS

Cf. A273699.

Sequence in context: A033467 A096475 A088122 * A273710 A087964 A174182

Adjacent sequences:  A273699 A273700 A273701 * A273703 A273704 A273705

KEYWORD

nonn,easy

AUTHOR

Robert Price, May 28 2016

STATUS

approved

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Last modified March 5 14:38 EST 2021. Contains 341823 sequences. (Running on oeis4.)