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A271888 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 406", based on the 5-celled von Neumann neighborhood. 1
4, 3, 12, 0, 28, -11, 40, -32, 92, -53, 96, -60, 148, -132, 180, -183, 276, -184, 300, -257, 376, -368, 456, -388, 540, -464, 508, -443, 632, -621, 692, -632, 904, -815, 988, -909, 1068, -992, 1112, -1068, 1320, -1196, 1360, -1199, 1444, -1453, 1632, -1571 (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=406; 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. A271885.

Sequence in context: A270987 A204291 A270324 * A271098 A269718 A099377

Adjacent sequences:  A271885 A271886 A271887 * A271889 A271890 A271891

KEYWORD

sign,easy

AUTHOR

Robert Price, Apr 16 2016

STATUS

approved

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Last modified October 3 07:51 EDT 2022. Contains 357231 sequences. (Running on oeis4.)