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A270680 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 189", based on the 5-celled von Neumann neighborhood. 1
7, -4, 40, -35, 99, -87, 191, -192, 333, -329, 489, -465, 660, -663, 895, -892, 1153, -1137, 1396, -1344, 1688, -1712, 2004, -1908, 2308, -2372, 2809, -2753, 3209, -3201, 3669, -3637, 4108, -4015, 4523, -4511, 5147, -5111, 5619, -5551, 6219, -6123, 6783 (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=189; 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. A270677.

Sequence in context: A271007 A271053 A270629 * A270904 A270937 A270320

Adjacent sequences:  A270677 A270678 A270679 * A270681 A270682 A270683

KEYWORD

sign,easy

AUTHOR

Robert Price, Mar 21 2016

STATUS

approved

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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)