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A271284 First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 334", based on the 5-celled von Neumann neighborhood. 1
4, 3, 13, -1, 12, 12, 25, -9, 44, -32, 32, 17, 39, 21, -4, 55, 17, 39, -40, 61, 59, 32, 76, 24, 0, 144, -92, 116, 165, -57, 188, -72, -28, 209, -257, 164, 0, 152, 16, 48, 137, 59, 16, 36, 240, 201, -165, 380, -264, 544, -607, 395, 109, 0, 39, 433, -45, 260 (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=334; 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. A271281.

Sequence in context: A178756 A271696 A271090 * A272312 A272117 A271159

Adjacent sequences:  A271281 A271282 A271283 * A271285 A271286 A271287

KEYWORD

sign,easy

AUTHOR

Robert Price, Apr 03 2016

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)